INlS-m£—13026 DAE SYMPOSIUM
NUCLEAR PHYSICS
CONTRIBUTED PAPERS VOLUME 33B (1990) '
UNIVERSITY OF.MADRAS • AND ANNAUMIVERSITY-
MADRAS. '
December 1 - 4, 1990
Organised by DEPARTMENT OF ATOMIC" ENERGY GOVERNMENT OF INDIA DAE SYMPOSIUM ON NUCLEAR PHYSICS
CONTRIBUTED PAPERS VOLUME 33B (1990)
UNIVERSITY OF MADRAS AND ANNA UNIVERSITY
MADRAS
December 1 -4,1990
Organised by DEPARTMENT OF ATOMIC ENERGY GOVERNMENT OF INDIA ORGANISING COMMITTEE OF THE DAE SYMPOSIUM ON NUCLEAR PHYSICS (1990)
Dr. S. Kailas, BARC (Convener) Prof. T.Nagarajan, Univ. Madras (Convener, Local Orgn. Committee) Dr. P. Singh, BARC (Secretary) Prof. Y.K. Agarwal, TIFR Shri M.R. Balakrishnan, BARC Dr. M.G. Betigeri, BARC Dr. M.A. Eswaran, BARC Prof. Y.K. Gambhir, IIT Bombay Dr. S.K. Gupta, BARC Dr. B.K. Jain, BARC Dr. S.S. Kapoor, BARC Prof. G.K. Mehta, NSC Delhi Dr. D.M. Nadkarni, BARC Prof. K.G. Prasad, TIFR Dr. V.S. Ramamurthy, IP,Bhubaneswar Dr. B.C. Sinha, VECC Representative from SINP PROGRAMME
Saturday, 1 December 1990 0930-1030 Inauguration
1030-1100 Tea/Coffee
1100-1300 Session I: Invited talk II: B.K. Jain Nuclear Physics : Beyond Neutrons and Protons Invited talk 12: G. Rajasekaran Low Energy Nuclear Physics Experiments Contributing to Particle Physics Oral Presentations : 043 - 047
1300-1400 Lunch
1400-1600 Session II: Invited talk 13: B. Banerjee Quark-Gluon Plasma in the Laboratory and in the Early Universe Oral Presentations : 048 - O56
1600-1630 Tea/Coffee
1620-1800 Ph.D. Theses Presentations: Tl - T4, Sunday. 2 December 1990
0900-1100 Session III: Invited talk 14: G. Sharaaugam Exotic Nuclear Decay by Spontaneous Heavy Ion Emission Invited talk 15: A. Saxena Fission as a Probe to Understand Heavy Ion Reaction Mechanism and Dynamics Oral Presentations : 017 - 021
1100-1130 Tea/Coffee
1130-1300 Oral Presentations : 022 - 032
1300-1400 Lunch
1400-1600 Session IV: Seminars on Instrumentation for Accelerators Based Research Seminar A: Recoil Mass Separator 51. P. Singh 52. A.K. Sinha Seminar B: Multi Element BGO Setup 53. R.K. Bhowmik 54. R.K. Choudhury
1600-1630 Tea/Coffee
1630-1800 Poster Presentations: Pi - P55 Monday. 3 December 1990
0900-1100 Session V: Invited talk 16z P. Mukherjee Structure of High Spin States in Nuclei near the Closed Shell Invited talk 17: A.K. Rath Recant Developments in High Spin States Oral Presentations: Ol - O5
1100-1130 Tea/Coffee
1130-1300 Poster Presentations : P56 - P107
1300-1400 Lunch
1400-1600 Session VI: Invited talk 18: U. Garg Super Deformation in A"190 Region Invited talk 19: J.B. Gupta Recent Developments in Dynamic Deformation Theory Oral Presentations : 06 - 010
1600-1630 Tea/Coffee
1630-1800 Session VII: Invited talk 110: S.S. Ramamurthi Accelerator Programme at CAT Oral Presentations : 057 - 062 Tuesday, 4 December 1990
0900-1100 Session VIII: Invited talk 111: S.B.Khadkikar Neutrinoless Double Beta Decay Using a Quark Model with Relativistic Harmonic Confinement Invited talk 112: S. Sana Signatures of Parity Mixing Among the Nuclear States Oral Presentations : Oil - 016
1100-1130 Tea/Coffee
1130-1300 Oral Presentations : 033 - 042
1300-1400 Lunch
1400-1600 Session IX: Seminar C: Scintillation Detector Development 55. P. Ramasamy New Trends in the Growth of Scintillation Detector Crystals 56. R.V.Srikantiah Barium Fluoride - A New Scintillation Detector Material Oral Presentation : 063 - 066
1600-1630 Tea/Coffee
1630-1730 Concluding Session CONTENTS
I : INVITED TALK
T $ THESIS
0 : ORAL
P : POSTER INVITED TALKS/SEMINARS 11. NUCLEAR PHYSICS : BEYOND NEUTRONS AND PROTONS, B..K. Jain, NPD, BARC. 12. LOW ENERGY NUCLEAR PHYSICS EXPERIMENTS CON- TRIBUTING TO PARTICLE PHYSICS, G. Rajasekaran, Matscience, Madras. 13. QUARK GLUON PLASMA IN THE LABORATORY AND IN THE EARLY UNIVERSE, B.Banerjee, T.I.F.R., Bombay. 14. EXOTIC NUCLEAR DECAY BY SPONTANEOUS HEAVY ION EMISSION, G.Shanmugam, Presidency College, Madras. 15. FISSION AS A PROBE TO UNDERSTAND HEAVY ION REACTION MECHANISM AND DYNAMICS, A.Saxena, NPD, BARC, Bombay. 16. STRUCTURE OF HIGH SPIN STATES IN NUCLEI NEAR THE CLOSED SHELL, P. Mukherjee, SINP, Calcutta. 17. RECENT DEVELOPMENTS IN HIGH SPIN STATES, A.K.Rath, Institute of Physics, Bhubaneswar. 18. SUPER DEFORMATION IN A"190 REGION, U.Garg, Notre Dame University, U.S.A. 19. RECENT DEVELOPMENTS IN DYNAMIC DEFORMATION THEORY, J.B. Gupta, Ramjas College, Delhi. 110. ACCELERATOR PROGRAMME AT CAT, S.S.Ramamurthi, CAT, Indore. 111. NEUTRINOLESS DOUBLE BETA DECAY USING A QUARK MODEL WITH RELATIVISTIC HARMONIC CONFINEMENT, S.B.Khadkikar, Physical Research Lab., Ahmedabad. 112. SIGNATURES OF PARITY MIXING AMONG THE NUCLEAR STATES, S.Saha, TIFR, Bombay. SEMINARS INSTRUMENTATION FOR ACCELERATORS BASED RESEARCH A. RECOIL MASS SEPARATOR 51. P. Singh, BARC, Bombay. 52. A.K. Sinha, NSC, Delhi. B. MULTI ELEMENT BGO SETUP 53. R.K. BhowmiJc, NSC, Delhi. 54. R.K. Choudhury, BARC, Bombay.
C. SCINTILLATION DETECTOR DEVELOPMENT 55. NEW TRENDS IN THE GROWTH OF SCINTILLATION DETEC- TOR CRYSTALS, D. Arivuoli, J. Kumar and P.Ramasamy, Anna University, Madras. 56. BARIUM FLUORIDE - A NEW SCINTILLATION DETECTOR MATERIAL, M.P.Chouganonkar, V.H. Gokhale, S.M.D.Rao, R.V. Srikantiah, BARC, Bombay. THESES PRESENTATION Tl. DELTA PRODUCTION IN NUCLEAR REACTIONS, A.B.Santra, Nuclear Physics Division, BARC, Bombay. T2. THEORY OF CLUSTER TRANSFER RESONANCES IN HEAVY ION REACTIONS AND THE RELATED PHENOMENA, Rajeev Kumar Puri, Physics Department, Panjab University, Chandigarh 160 014. T3. INTERNAL CONVERSION STUDIES ON SOME M4, M3 AND E3 TRANSITIONS, K. Radha Krishna, Dept. of Nuclear Physics, Andhra University, Waltair. T4. K-CAPTURE PROBABILITIES BY SUM-PEAK METHOD, Bhaskara Rao Katiki, Dept. of Nuclear Physics, Andhra University, Waltair. a) NUCLEAR STRUCTURE. MODES OF EXCITATION AND Page RADIOACTIVITY 01. FEEDING TIME AND HALF-LIVES OF EXCITED NUCLEAR 1 STATES IN 40K, H.C. Jain, S. Chattopadhyay, Y.K. Agarwal, M. Dasgupta, M.L. Jhingan and A. Roy, T.I.F.R., Bombay 400 005. 02. HIGH SPIN ISOMER IN 151Sm, J.M.Chatterjee, 3 Somapriya Basu, K.Kar, D.Banik, SINP, Calcutta, R.K. Chattopadhyay, Ananda Mohan College and R.P.Sharma, S.K. Pardhasaradhi, VECC, Calcutta„ 03. MEASUREMENT OF K ELECTRON CAPTURE DECAY PROB- 5 ABILITY IN 161Ho, 125I AND 131Ba, G. Sree Krishna Murty, M.V.S.Chandrasekhar Rao, M. Ravi Kumar, G. Satyanarayana, D.L. Sastry, Andhra University and S.N. Chintalapudi, VECC, Calcutta 700 064.
04. r-PRQCESS CONTRIBUTION TO ABUNDANCE OF 180Ta, 7 P.C. Sood', R.K«Sheline+, R.W. Hyff and A.K. Jain#. ^Banaras Hindu Univ. Varanasi, ^Physics Dept.,Univ. of Roorkee, Roorkee 247 667. +Florida State Univ., Tallahassee, USA. Lawrence Livermore National Lab., USA. 05. AN EMPIRICAL MODEL FOR 3qP ROTATIONAL BANDS, 9 Kiran Jain and Ashok K.Jain, Dept. of Physics, Univ. of Roorkee, Roorkee 247 667. 06. HIGH SPIN STATES AND SUPERDEFORMATION, Bijay H Agrawal and C.R. Praharaj, Institute of Physics, Bhubaneswar 751 005. 07. YPAST TRAPS IN 152Er, M. Rajasekaran and D. 13 Caleb Chanthi Raj, University of Madras, Madras. 08. STUDY OF BETA SOFTNESS IN 158DY, J.B. Gupta and 15 H.M. Mittal, Ramjas College, Univ. of Delhi, Delhi. 09. SAMARIUM ISOTOPES IN IBM: WEAK COUPLING CAL- 17 CULATIONS, Y.D. Devi and VrK.B. Kota, Physical Re- search Lab, Ahmedabad 380 009. 010. IBM AND THE DYNAMIC HF FERMION BASIS FOR Zn 19 ISOTOPES, Subrata Sarangi and Jitendra C. Parikh, Physical Research Laboratory, Ahmedabad 380 009.
011. STRUCTURE OF DOUBLY ODD ISOTOPE 82Br, R.Sahu, 21 Berhampur University, Berhampur and S.P.Pandya, Physical Research Laboratory, Ahmedabad 380 009. 012. MAGNETIC MOMENTS IN CRANKED HFB APPROACH, 23 M.Saha and S.Sen S.I.N.P., Calcutta 700 009. 013. EFTECTIVF: SINGLE-PARTICLE ENERGIES IN THE f-p 25 GHELL, V. Potuhare and N. Tressler, Physics Dept., M.S. University, Baroda. 014. FIELD THEORITIC STUDY OF THE PROPERTIES OF 4He 27 - A VARIATIONAL APPROACH, P.K. Panda, S.K. Patra, S.P. Misra, Institute of Physics, Bhubaneswar. 015. ON THE CONTROVERSY OF B DATA OF 6He AND 10Be, 29 Mohammad Shoeb, AMU, Aligarh and Q.N.Ui - r, J.M.I., New Delhi 110 025. 016. VALIDITY OF THE MULTI-PARTICLE SHELL I WITH 31 TWO-BODY EFFECTIVE INTERACTION, Y.K. Gambi .r, IIT, Bombay and F.Monti, G.Bonsignori and M. Savoia, Univ. of Bolognsa, Bolognsa, Italy. PI. SIGNATURE EFFECTS IN ODD-YB ISOTOPES, C.R. 33 Praharaj and A.K. Rath, Institute of Physics, Bhubaneswar-751 005. P2. STUDY OF N=«8 AND N=90 ISOTONES IN THE IBM-1, 35 H.M. Mittal and J.B. Gupta, Ramjas College, Univ. of Delhi, Delhi 110 007. P3. MODIFIED ROTATION VIBRATION MODEL FOR 194?t 37 + ++ NUCLEUS, A.K. Varshney, D.K. Gupta , K.K. Gupta r R. Prasad and R.K. Tyagi, Z.H. Engg. College, Aligarh Muslim University. +S.V. College, Aligarh. ++Govt. College, Sarkaghat (H.P.). P4. HIGH SPIN STATES B(E2) VALUES IN 78Kr NUCLEUS, 39 A.K. Varshney, K.K. Gupta+, V.P. Varshney, D.K.Gupta , R. Prasad and R.K. Tyagi, Z.H.College of Engg., Aligarh Muslim University. +Gcvt. College, SarJcaghat, H.P. S.V. College, Aligarh P5. SPECTROSCOPY OF HIGH SPIN STATES IN 92Mo, Pragya 41 Singh, R.G. Pillay and H.G. Devare, TIFR, Bombay. P6. CORIOLIS COUPLING IN DOUBLY-ODD ROTATIONAL 43 BANDS, Kiran Jain and Ashok K.Jain, Dept. of Phys. University of Roorkee, Roorkee 247 667.
P7. CORIOLIS EFFECTS IN 2qp ROTATIONAL BANDS OF 45 EVEN-EVEN NUCLEI, Alpana Goel and A.K. Jain, Dept. of Physics, Univ. of Rocrkee, Roorkee. P8. MICROSCOPIC STUDY OF HIGH-SPIN YRAST SPECTRA IN 4 7 DOUBLY EVEN CADMIUM ISOTOPES, P.K.Mattu and S.K. Khosa, Dept. of Physics, Janmu University, Jammu. P9. CORIOLIS CORRECTIONS IN QUADRUPOLE MOMENTS OF 49 ODD-ODD NUCLEI, Shakti D. Sharina, Aravind Sharma and Praveen Sharina, Dept.of Physics, Panjabi University, Patiala 147 002. P10. STUDY OF Z=64 SUBSHELL EFFECT ON THE PROTON 51 SPECTROSCOPIC FACTORS IN 152-160GD, J.B.Gupta and Satendra Sharma, Ramjas College, Univ. of Delhi. Pll. STUDY OF SU(3) WAVEFUNCTIONS IN THE SU(5) 53 BASIS, J.B. Gupta and H.M. Mittal, Ramjas College, Univ. of Delhi, Delhi 110 007. P12. A LOW SPIN BAND CROSSING IN 175Os, J.A. Sheikh, 55 Daresbury Lab., Warrington, U.I{. and C.R. Prahara j, Institute of Physics, Bhubaneswar 751 005. P13. MULTICHANNEL STRUCTURE OF 4He, B.K. Chikara and 57 V.K. Sharma, Dept. of Phys., Institute of Advanced Studies, Meerut University, Meerut 250 004. P14. A NEW ANALYTICAL MODEL FOR EXOTIC DECAY 59 STUDIES, G. Shanmugam, Presidency College, Madras and S.I.A. Philomin Raj, Madras Christian College. P15. EFFEO; '•)'• CENTRIFUGAL BARRIER ON EXOTIC DECAY 61 PROBABILIT1ES, G. Shanmugain and B.KamaLaharan, Dept. of Physics, Pi *;-» idoncy College, Madras. P16. NUCLEAR LV/KT,-DENSITY PARAMETER IN HOT ROTATING 63 LIGHT NUCLEI, G."hanrcugara, M. Thiagasundaram and A. Chitra, Preside • -;y College, Madras, "Pa^haiyappa's College, Madras.
?17. SHAPE TRANSJ !'IONS IN EXCITED sd SHELL NUCLEI, 65 G. Shanmugam, X. Xartamurthi and Kalpana Sankar, Presidency Coll or;f_-, Madras, " Bharathidasan Univer- sity, Trichy. ri3. SYMMETRY •\OUP AND COLLECTIVE MODES, P.Rudra, 67 ;japt. of Physic . Univ'. of Kalyani, Kalyani-741235. P19. GENERATOR COORDINATE TECHNIQUE FOR ANTISYM- 69 METRIZATION OF THREE-CLUSTER WAVE FUNCTIONS, B.B. Srivast.ava and Piyush Sinha, Phys. Dept., Meerut University, Meeri.it. 250 005.
P20. INTERPRETATION OF BACKBENDING IN 100Mo IN A 71 CRANKED NILSSON MODEL WITH PAIRING, Tripti Mathur and S.N. Mukherjee, Dept. of Physics, BHU,Varanasi.
P21. STUDY OF Os-185 AND Re-186 DECAYS, J.Goswamy, ^3 B. Chand, D.Mehta, N.Singh and P.N.Trehan, Dept. of Physics, Panjab University, Chandigarh.
P22. LIFETIME MEASUREMENT OF SOME NUCLEAR LEVELS 75 USING A BaF2-BaF2 SET UP, C.C. Dey, B.K. Sinha and R. Bhattacharya, S.I.N.P., Calcutta.
P23. ANGULAR DISTRIBUTION MEASUREMENTS IN 127I, 77 T.S.Cheema, D.Mehta and B.K.Arora, Dept. of Phys., Panjab University, Chandigarh 160 014.
P24. CONVERSION ELECTRON, X X-AND GAMMA-RAY INTEN- 79 3ITY MEASUREMENTS IN Cd-111, J.Goswamy, B.Chand, D.Mehta, N.Singh and P.N.Trehan, Panjab Univ., Chan- digarh. P25. K-CAPTURE PROBABILITIES IN THE DECAY OF 152Eu 81 AND 169Yb USING HPGe DETECTOR, K.Bhaskara Rao, S. Lakshminarayana and V. Seshagiri Rao, Andhra Univer- sity, Visakhapatnam. P26. A STUDY OF INTERNAL CONVERSION COEFFICIENTS, 83 M.V.S. Chandrasekhar Rao, G. Sree Krishna Murty, K. Radha Krishna, S. Bhuloka Reddy, G. Satyanarayana, D.L. Sastry, Andhra University and S.N.Chintalapudi, VECC, Calcutta 700 064. P27. LEVEL DENSITIES AT HIGH SPINS, M.Rajasekaran 85 and D.Caleb Chanthi Raj, Dept. of Nucl. Phys., University of Madras, Madras. P28. VALIDITY OF THE INM MODEL IN THE EXTREME LOW 87 MASS REGION, R.C. Nayak, K.K. College, Berhaxnbur and L. Satpathy, Inst. of Physics, Bhubaneswar 751 005. P29. VARIATIONS OF THE NUCLEAR LEVEL DENSITY 89 PARAMETERS IN DIFFERENT RANGES OF MASS NUMBERS, Asok Sana, Dept. of Physics, Univ. College of Science, 92 APC Road, Calcutta 700 009.
P3 0. THE TOP-MOST NUCLEON SEPARATION ENERGY AND TO- 91 TAL BINDING ENERGY: THEIR CONNECTION, M.K. Basu, Dept.of Physics, Univ. College of Science, Calcutta. P31. IMPROVED SOLUTIONS OF THE SPINOR-TYPE BETHE- 93 SALPETER EQUATION, A. Banerjee and Y.S.T. Rao, Dept. of Physics, North Eastern Hill Univ., Shillong. P32. K-SHELL IONISATION FOLLOWING BETA DECAY, 95 Lakshmi Natarajan, Phys. Dept., Univ. of Bombay. b) LOW AND MEDIUM ENERGY NUCLEAR REACTIONS AND FISSION 017. ANGULAR MOMENTUM AND CROSS SECTION IN NEAR- 97 BARRIER FUSION OF 28Si +68 ZJl, 32S +64 Ni AND 37C1 + 9Co, M.Dasgupta, A. Navin*, Y.K. Agarwal, C.V.K. Baba, S. Chattopadhyay, H.C.Jain, M.L.Jhingan and A.Roy, TIFR, Bombay. NPD, BARC, Bombay. 018. DISPERSIVE CONTRIBUTION TO THE NUCLEUS-NUCLEUS 99 POTENTIAL FOR THE SYSTEM 160 + 209Bi, P.Singh, S. Kailas, A.Chatterjee, A.Navin, S.S.Kerekatte, A. Nijasure and B. John, NPD, BARC, Bombay 400 085.
019. TEMPERATURE DEPENDENCE OF EMISSION BARRIERS FOR 101 PROTON AND ALPHA FROM COMPOUND NUCLEI IN MASS REGION A=110, Aruna N., A.K.Mohanty, A.Chatterjee, A.Saxena, B.John, S.Kailas, S.S.Kapoor, S.K.Kataria, K. Kumar, S.Kumar and P. Singh, NPD, BARC, Bombay.
020. EVIDENCE FOR ALPHA PARTICLS DOORWAY STATE IN 103 28Si AROUND 44MeV EXCITATION THROUGH THE REACTIONS 12C(16O,8Be)20Ne* AND 12C(16O,4He)24Mg , Suresh Kumar, M.A.Eswaran, E.T.Mirgule, D.R.Chakrabarty, V.M.Datar, H.H.Oza, N.L.Ragoowansi and Uttam K.Pal, NPD, Bhabha Atomic Research Centre, Bombay 400 085.
021. SHAPE EVOLUTION AT HIGH SPIN AND EXCITATION 105 ENERGY IN THALLIUM ISOTOPES, Y'. K . Agar wa 1 , C.V.K.Baba, H.C.Jain, A.Roy, M.K.Sheiran, R.Varma, TIFR, Bombay and D.R.Chakrabarty , V.M.Datar, R.K.Choudhury, B.K. Nayak and S.V.S.Sastry, NPD, BARC, Bombay 400 085.
022. HIGH ENERGY T-RAYS IN THE FISSION OF 252Cf, 107 V.M.Datar, D.R.Chakrabarty , NPD, BARC and Y.K.Agarwal and C.V.K.Baba, TIFR, Bombay.
023. FISSION FRAGMENT ANGULAR DISTRIBUTIONS FOR THE 109 SYSTEM 19F^232Th, S.Kailas, A.Navin, A.Chatterjee, P.Singh, R.K.Choudhury, A.Saxena, S.S.Kapoor, D.M. Nadkarni, B.K.Nayak, V.S.Ramamurthy and S.V. Suryanarayana, BARC, Bombay. IP, Bhubaneswar.
024. FISSION OF Au-197, Lu-175 AND Ho-165 WITH 0-16 111 IONS: CROSS SECTIONS AND ANGULAR DISTRIBUTIONS, R.H. Iyer, A.K.Pandey, P.C.Kalsi and R.C.Sharma, Radiochemistry Division, BARC, Bombay 400 085.
025. 10B-INDUCED FISSION CROSS-SECTIONS OF 235U AT 113 DEEP SUB-BARRIER ENERGIES, R.P.Anand, K.N.Iyengar, D.M.Nadkarni and S.S.Kapoor, NPD, BARC, Bombay-85. CZS. :\}SS-RESOLVED FRAGMENT ANGULAR DISTRIBUTION IN 115 1 'c :- 2-JTh SYSTEM AT 72 MeV, S.B.Manohar, Ashok Cosuani, f\.v.R Ready, 3.S.Tomar, P.P.Burte and Satya Pra.kash, Radiochemistry Divn, and Bency John, Aruna I'iiasure, S.K.Kataria and S.S.Kapoor, NPD, BARC.
027. MEASUREMENT Of FISSION FRAGMENT ANGULAR COR- 117 RELATION IN ^32Th(l9F,f) REACTION AT 104.4 MeV, Alok Saxena, D.C.Biswas, P.M.Nadkarni, V,S.Ambekar, R.K. Choudhury and S.S.Kapoor, NPD, BARC and P. Bhat- tacharya, P. Basu, S. Bhattacharya, and M.L. Chat- terjee, SINP, Calcutta.
023. YIELDS OF PROJECTILE-LIKE FRAGMENTS IN 12C + 119 2J2Th REACTIONS AT NEAR BARRIER ENERGIES, D.C.Biswas, B.K.Nayak, V.S.Ambekar, B.V.Dinesh, S.V.S.Sastry, L.M.Pant, D.'l.Nadkarni and R.K. Choud- hury, Nuclear Physics Division, BARC, Bombay. 029. STUDY OF EXCITATION FUNCTION FOR ALPHA INDUCED 121 REACTIONS IN NATURAL IRIDIUM FROM 17-55 MeV, M.K. Bhardwaj, H. Singh, I.A.Rizvi and A.K. Chaubey, Dept. of Physics, AMU, Aligarh 202 002. 030. MEASUREMENT AND ANALYSIS OF EXCITATION FUNC- 123 TIONS FOR a-INDUCED REACTIONS IN 165Ho AND 209Bi, B.P. Singh, M.G.V. Sankaracharyulu, M.A. Ansaii and R. Prasad, Dept. of Physics, AMU, Aligarh 202 002. 031. ALPHA SCATTERING FROM 6Li NEAR THE a-d BREAK-UP 125 THRESHOLD, C.Samanta, S.Ghosh, M. Laiiri, SINP, S. Ray, Univ. of Kalyani and S.R. Banerjfe, VECC. 032. MICROSCOPIC ANALYSIS OF 9Be(a,a•)9Be* AT E=65 127 MeV, Subinit Roy, H.Majumdar, J.Chatterji and S.K. Datta, SINP, Calcutta and S.N.Chintalapudi and S.R. Banerjee, VECC, Calcutta.
033. ANGULAR DISTRIBUTION OF NEUTRONS EMITTED IN 129 THERMAL NEUTRON INDUCED FISSION OF 235U, M.S.Samant, R.P.Anand, R.K.Choudhury, D.M.Nadkarni and S.S. Kapoor, NPD, B.A.R.C., Bombay 400 085. 034. FISSION FRAGMENT TEMPERATURES AND LEVEL DEN- 131 SITIES IN THERMAL NEUTRON INDUCED FISSION OF 235U M.S.Samant, R.P.Anand, R.K.Choudhury, K.Kumar, D.M. Nadkarni and S.S.Kapoor, NPD, BARC, Bombay 400 085.
035. CROSS-SECTIONS FOR THE 46Ti(n,2n)45Ti AND 50Cr 133 (n,2n)49Cr REACTIONS AT 14 MeV NEUTRONS, P.M.Dighe, G.R.Pansare and V.N.Bhoraskar, Univ. of Poona, Pune. 036. ION-ION POTENTIAL FOR VARIOUS FORMS OF NN - IN- 135 TERACTION, R.C.Mishra, Madhup Seth, VSSD College, Kanpur and Ravi Datt Godiyal and Ashok Kumar, DBS College. Dehradun.
037. TEMPERATURE DEPENDENCE OF NUCLEON DRIP-LINE, 137 J.N.De, VECC, D. Bandyopadhyay and S.K- Samaddar, SINP and N. Rudra, Kalyani University, Kalyani.
038. MODEL PARAMETRTSATION OF DISTRIBUTIONS OF FU- 139 SION BARRIER, A.K.Mohanty, S.K.Kataria, BARC, Bombay and V.S.Ramamurthy, Inst. of Physics, Bhubaneswar.
039. PENETRATION THROUGH TIME DEPENDENT BARRIERS, 141 S.K. Kataria, S.V.S.Sastry, A.K.Mohanty, NPD and K.V.Bhagwat, SSPD, BARC, Bombay. 040. A VARIABLE-HEIGHT PARABOLIC BARRIER FOR HEAVY 143 ION FUSION, Zafar Ahmed, NPD, BARC, Bombay 400 085. 041. DIRECT CLUSTER-TRANSFER REACTIONS USING THE 145 QUANTUM MECHANICAL FRAGMENTATION THEORY, Hemant Kumar and Raj K. Gupta, Panjab Univ., Chandigarh.
042. CONSERVATION OF CHANNEL SPIN IN TRANSFER REAC- 147 TION, V.S.Mathur, Dept. of Physics, Banaras Hindu University, Varanasi 221 005. P33. EQUIVALENT LOCAL POTENTIAL FOR NUCLEON + 16O 149 SCATTERING, O.D.Sharma and H.M.Singh, Meerut College and B.B.Srivastava, Meerut University, Meerut. P34. MEASUREMENT OF 14 MeV (n,n'r) REACTION CROSS 151 SECTIONS USING CYCLIC ACTIVATION, H.M.Agrawal, Dept. of Physics, G.B.Pant University, Pantnagar 263 145. P35. (n,2n) CROSS SECTIONS AT 14.0 MeV, N.L. Singh, 153 M.S.University, Baroda and S.Mukherjee, A.V. Mohan Rao, L. Chaturvedi and J. Rama Rao, BHU, Varanasi 221 005. P36. PARAMETRIC STUDY OF NEUTRON EMISSION SPECTRA 155 235 FROM FISSION FRAGMENTS IN U(ntn,f) USING ALICE CODE, K.Kumar, M.Samant, R.P.Anand, R.K.Choudhury and S.S.Kapoor, NPD, B.A.R.C., Bombay 400 085. P37. EVALUATION OF MAGNETIC SUBSTATE POPULATIONS IN 157 THE (p,p'r) REACTIONS, C. Singh and D.C. Tayal, Physics Dept., NREC College, Khurja 203 131.
P38. STUDY OF THE SPECTRUM OF 75Se FROM THE 159 75As(p,n)75Se REACTION, G.P.S.Sahota, V.K.Mittal, S.D.Sharma, H.S.Sahota, Punjabi University, Patiala and G.Singh, S.S.Datta and i.M.Govil, Panjab Univer- sity, Chandigarh. P39. PHASE SHIFTS IN ALPHA PROTON INTERACTION AT 40 161 MeV, S.Karmakar and S.S.Dasgupta, Dept. of Physics, Burdwan University, Burdwan 713 104. P40. ALPHA^INDUCED EXCITATION FUNCTIONS FOR SILVER, 163 R.P.Gautam , M.K.Bhardwaj , H.Singh and A.K.Chaubey,. Dept. of Physics, AMU, Aligarh 202 002. *Dept. of Physics, Janta College, Bakewar (Etawah) 206124. P41. EQUILIBRIUM AND PRE-EQUILIBRIUM EMISSION OF 165 NEUTRONS AND PROTONS IN ALPHA-INDUCED REACTIONS ON ANTIMONY, B.P.Singh, H.D.Bhardwaj an£ R. Prasad, Aligarh Muslim University, Aligarh. DSN College, Unnao.
P4 2. EXCHANGE EFFECTS IN ALPHA SCATTERING FROM 6Li, 167 Subinit Ray and C. Samanta, SINP, Calcutta 700 064. P43. DWIA 3-BODY COUPLING MODEL CALCULATIONS FOR 169 140MeV 2H(a,ap)n KNOCKOUT REACTION, Arun K. Jain, Nuclear Physics Division, BARC, Bombay 400 085. P44. a-n RELATIVE ENERGY IN ad BREAK-UP, S. Mandal 171 and S.S.Dasgupta,Burdwan University, Burdwan. P45. COULOMB INTERFERENCE EFFECTS IN THE PRIOR FORM 173 DWBA ANALYSIS OF LIGHT ION ELASTIC BREAK UP REAC- TIONS, D.N. Basil, VECC, Calcutta 700 064.
P4 6. DETERMINATION OF ROOT-MEAN-SQUARE RADIUS OF 175 NEUTRON ORBITS FROM EXACT FINITE RANGE ANALYSIS OF SUB-COULOMB (t,d) REACTIONS, H.S.Sudheendra, M.P. Sathyavathiamma and N.G. Puttaswamy, Bangalore Univ. P47. COULOMB CORRECTION TO ELASTIC a-a-SCATTERING, 177 U.Das and P.K. Bera, Visva Bharati, Santiniketan. P48. PHASE-FUNCTION METHOD FOR HULTHEN-MODIFIED 179 SEPARABLE POTENTIALS, A.K. Jana, Visva Bharati and U. Laha, Physics Dept., RIT, Jamshedpur 831 014.
P49. ON INTEGRAL REPRESENTATIONS OF THE COULOMB 181 FUNCTIONS, A.K. Jana and B. Talukdar, Physics Dept., Visva-Bharati, Santiniketan 731 235.
P50. CALCULATIONS OF TENSOR ANALYZING POWER IN BACK- 183 WARD (p,d) ELASTIC SCATTERING USING ANALYTICAL WAVE FUNCTION FOR DEUTERON D-STATE- V.N.Pai, Parle Col- lege and R.J. Kulkarni, Univ. of Bombay, Bombay. P51. A STUDY OF ELASTIC a-40Ca SCATTERING WITH ALAS, 185 Ashok Kumar, S.R. Verma and V.K. Bhatnagar, D.B.S. College, Dehra Dun and O.D. Sharma, Meerut College. P52. ELASTIC SCATTERING OF 32S PROJECTILE FROM 28Si 137 TARGET AT Elab = 135 MeV, Ashok Kumar, Ravi Datt Godiyal, K. Eswaraiah, Madhup Seth, D.B.S, College, Dehra Dun and R.C. Mishra, VSSD College, Kanpur. P53. FOLDING MODEL ANALYSIS OF 32S + 32S AT 160MeV, 1" Ashok Kumar, K. Eswaraiah, Ravi Datt Godiyal, D.B.S. College, Dehra Dun, P.K. Bhatnagar, Hindu College, Sonepat and B.B.Srivastava, Meerut University.
P54. CHARACTERISTIC. FEATURES OF ELASTIC SCATTERING 191 OF IDENTICAL NUCLEI, Ashok Kumar, Ravi Datt Godiyal, K. Eswaraiah, D.B.S. College, Dehra Dun, P.K. Bhat- nagar, Hindu College, Sonepat. "'35. EVIDENCE OF THRESHOLD ANOMALY IN 32S + 40Ca 193 ELASTIC SCATTERING ABOVE THE COULOMB BARRIER, Ashok Kumar, K. Eswaraiah, Ravi DatL Godiyal and Madhup Seth, D.B.S. College, Dehra Dun, R.C. Mishra, VSSD College, Kanpur and B.B.Srivastava, Meerut Univer- sity, Mearut.
P56. SOME ASPECTS OF BARRIER RESONANCES, B.M.Jyrwa, 195 B. Sahu, C.S. Shastry, Phys. Dept., NEHU, Shillong. P57. ION-ION POTENTIAL IN PSEUDONUCLUEON SIMULATION 197 MODEL, R.C. Mishra, Madhup Seth, VSSD College, Kan- pur and Ravi Datt Godiyal and Ashck Kumar, DBS Col- lege, Dehra Dun. P53. FUSION SPIN DISTRIBUTIONS IN THE MACROSCOPIC 199 MODEL OF NUCLEAR SHAPE EVOLUTIONS, S.V.S. Sastry, A.K.Mohanty, S.K.Kataria, BARC, Bombay and V.S. Ramamurthy, Inst. of Physics, Bhubaneswar.
P59. PROXIMITY EFFECTS IN MOLECULAR CONFIGURATIONS 201 IN LIGHT NUCLEI, G.Shanmugam, Presidency College and M.D.Padmini, Quaid-e-Millet Govt. Collage for Women, Madras. P60. ANALYSIS OF 12C+16O AND 160+160 RESONANCES, 203 S.Datta, U. Abondannp*, N. Cindro+, Univ. College of Science, Calcutta. *Univ. of Trieste. +Rudjer Bos- kovic Institute, Zagreb, Yugoslavia. P61. QUASI-MOLECULAR STATES IN C12 + O16 SYSTEM, 205 Pradip K. Sahu, P. Sarangi and L. Satpathy, In- stitute of Physics, Bhubaneswar 751 005. P62. NUCLEUS-NUCLEUS COLLISIONS AND THE VIBRATIONAL 207 MODEL, Z.A. Khan, Dept. of Physics, AMU, Aligarh.
P63. SUPERDEFORMATION AND NUCLEON EMISSION SPECTRA 209 OF 28Si, M.Rajasekaran and T.R.Rajasekaran, Dept. of Nucl. Physics, Univ. of Madras, Madras 600 025.
P64. IMPORTANT ASPECTS OF FRAGMENT ANGULAR MOMENTUM 2H IN MEDIUM ENERGY FISSION, H. Naik, T. Datta, S.P. Dange, C.N. Patra and Satya Prakash, Radiochemistry Division, BARC, Bombay 400 085. P65. SIMPLE FORMULA OF HEAVY-ION POTENTIALS WITH 213 SPIN-DENSITY TERM IN ENERGY DENSITY FORMALISM: s-d AND £7t2 SHELL NUCLEI, Rajeev K. Puri and Raj K. Gupta, Dept. of Phys., Panjab Univ., Chandigarh. P66. ALPHA-CLUSTERING TRANSFER EFFECTS IN COLLIDING 215 s-d SHELL NUCLEI, Rajeev K. Puri and Raj K. Gupta, Dept. of Phys. Panjab University, Chandigarh. P67. FUSION LIMITED BY TEMPERATURE, D.Bandyopadhyay 217 and S.K. Samaddar, SINP and J.N. De, VECC, Calcutta. P68. A SIMPLE TWO-CHANNEL BARRIER PENETRATION MODEL 219 OF HEAVY ION FUSION, Zafar Ahmed, NPD, BARC, Bombay.
P69. DATA ANALYSIS OF 54Zn (20.1 MeV/u) + 9Be REAC- 221 TION, VECC-RIKEN COLLABORATION.
P70. DISINTEGRATION OF HEAVY HYPERNUCLEI, K.Goswami, 223 Phys. Dept., Goalpara College, and T.D. Goswami, Phys. Dept., Gauhati University, Gauhati. P71. BINARY FISSION OF HIGHLY EXCITED NUCLEI, K. 225 Goswami, Phys. Dept., Goalpara College, and T.D. Goswami, Phys. Dept., Gauhati University, Gauhati.
P72. ANALYSIS OF PARTICLE PRODUCTION IN THE SPALLA- 227 TION REACTION, Amar Sinha and M. Srinivasan, Neutron Physics Division, BARC, Bombay.
C) NUCLEAR MATTER AND NUCLEAR COSMOPHYSICS 043. APPLICATION OF THOMAS-FERMI THEORY FOR FINITE 229 SYSTEMS, V.S.Uma Maheswari, V.S.Ramamurthy and L. Satpathy, Inst. of Physics, Bhubaneswar. 044. NON-EXISTENCE OF SUPERLUMINOSITY OF SPEED OF 231 SOUND IN NUCLEAR MATTER, B.K.Das and R.K.Satpathy, Sambalpur University, Burla-768 019. P7 3. QUARK-ANTIQUARK BOUND STATES, A.K.Gautam and 233 A.K. Shiromani, Phys.Dept., R.B.S. College, Agra. P74. HOT NUCLEAR MATTER IN A CHIRALLY INVARIANT FER- 235 MIONIC FIELD THEORY, Safayet Karim Chowdhury and Sasabindu Sarkar, Indian Association for the Cul- tivation of Science, Calcutta 700 032. d) INTERMEDIATE ENERGY NUCLEAR REACTIONS AND NON-NUCLEONIC DEGREES OF FREEDOM 045. N-N SCATTERING WITH COGEP, K.B. Vijayakumar and 237 S.B. Khadkikar, Physical Research Lab, Ahmedabad. 046. FERMI-BREIT INTERACTION AMONG CONFINED QUARKS 239 AND GLUONS, P.C.Vinodkumar, K.B. Vijayakumar and S.B.Khadkikar, Physical Research Lab, Ahmedabad. 047. E2/M1 RATIO FOR /\ >N+T IN A CHIRAL QUARK 241 MODEL, B.Ghosh and S.C.Phatak, I.P., Bhubaneswar.
P 048. A LOWER LIMIT OF g 1 FROM NRQM, R.Nag, S. 243 Sanyal and S.N. Mukherjee, Dept. of Physics, Banaras Hindu University, Varanasi 221 005.
049. DISTORTION EFFECTS IN (p,/\++) REACTION, 245 Neelima G. Kelkar and B.K.Jain, NPD, BARC, Bombay 400 085. 050. MULTIFRAGMENTATION VERSUS LIQUID-GAS PHASE 247 TRANSITION IN NUCLEAR SYSTEMS, A. Das, M. Mishra and L. Satpathy, Inst. of Physics, Bhubaneswar and M. Satpathy, Phys. Dept., Utkal University, Bhubanes- war. 051. STUDY OF SECONDARY PARTICLES PRODUCED IN HIGH 249 ENERGY HADRONIC INTERACTIONS, H.Khushnood and Ansari A.R., Dept. of Phys., Jamia Millia Islamia, N.Delhi. P75. N-N INTERACTION IN CONFINEMENT MODEL FOR QCD, 251 K.B. Vijayakumar, Physical Research Lab, Ahmedabad. P7 6. CHESHIRE CAT SYNDROME IN N-N SCATTERING, S.B. 253 Khadkikar and K.B. Vijayakumar, PRL, Ahmedabad.
P77. BARYON SPECTRCSCOPY IN CHIRAL COLOR DIELECTRIC 255/ MODEL, S.C.Phatak and S.Sahu, I.P., Bhubaneswar. P78. MASS SPECTRA OF BARYONS, Harikesh Singh, Inst. 257 of Basic Sciences, Khandari and A.K.Gautam, RBS Col- lege, Agra. P79. COULOMB ENERGY AND MASS YIELDS IN NUCLEAR MUL- 259 TIFRAGMENTATION PROCESS, M.Mishra and L.Satpathy, Institute of Physics, Bhubaneswar 751 005. P80. INSTANTON CONTRIBUTION TO ELECTROMAGNETIC MASS 261 DIFFERENCES OF BARYONS, C.P.Singh, S.Singh, VSSD College, Kanpur and R.L. Singh, APS Univ., Rewa(MP). P81. PION CLOUD CONTRIBUTION TO HADRON MASSES IN 263 VARIABLE BAG PRESSURE MODEL, C.P.Singh, S.Singh, VSSD College, Kanpur and R.L.Singh, APS University. P82. ROLE OF RHO IN CHARGE EXCHANGE REACTIONS, A.B. 265 Santra and B.K. Jain, NPD, B.A.R.C., Bombay 400085. e) RELATIVISTIC HEAVY-ION COLLISIONS AND OUARK-GLUON PHASE 052. A STUDY OF COLLECTIVE FLOW OF NUCLEAR MATTER IN 267 La + Ag(Br) REACTION, H.S.Palsania, Bhagwan Singh, A. Gill, V. Kumar, K.B.Bhalla and S.Lokanathan, Dept. of Physics, Univ. of Rajasthan, Jaipur. 053. A STOCHASTIC MODEL FOR MULTIPARTICLE PRODUC- 269 TION, A.K.Chaudhuri, VEC Centre, Bidhan Nagar, Cal- cutta , 054 . FORWARD-TRANSVERSE ENERGY CORRELATIONS IN 271 ULTRA-RELATIVISTIC HEAVY ION COLLISIONS, S.K.Gupta, and Swapan Das, NPD, BARC, Bombay 400 085. 055. ENERGY DISTRIBUTION OF MUON PAIRS AND PHOTON 273 PAIRS IN RELATIVISTIC HEAVY ION COLLISIONS, G.Janhavi and P.R. Subramanian, Dept. of Nuclear Physics, University of Madras, Madras 600 025.
056. PHASE TRANSITION FROM A QGP TO HADRONS IN THE 275 EARLY UNIVERSE, K. Sakthi Murugesan and P.R. Sub- ramanian, Dept. of Nucl. Physics, Univ. of Madras. P83. QUARK MATTER IN COLOUR-DIELECTRIC MODEL, S.K. 277 Ghosh and S.C.Phatak, Inst. of Physics, Bhubaneswar. P84. ON THE RELATIVISTIC NUCLEAR REACTIONS AND 279 QUARK-ANTIQUARK RECOMBINATION MODEL, A.P.Sharma, Dept. c-f Physics, J.MU, Aligarh 202 002.
P85. EQUATIONS OF STATE AND ENTROPY PER BARYON IN A 281 QCD PHASE TRANSITION, K. Sakthi Murugesan and P.R. Subramanian, Dept. of Nucl. Phys., Univ. of Madras. P86. RELATIVISTIC QCD-MOTIVATED POTENTIAL MODEL OF 283 HEAVY-LIGHT QUARKS CONFINED NUCLEONS, R.Swarup, R.N. Singh, Dept. of Physics, D.S.College, Aligarh. P87. Si + NUCLEUS COLLISIONS AT 4.5 A GeV: A 284 PRELIMINARY RESULTS, I.D.Ojha, B.K.Singh, S.N. Tripathi and S.K. Tuli, Physics Dept., Banaras Hindu University, Varanasi 221 005.
P88. EXOTIC BOSON MAPPINGS, Y.K. Gambhir, Dept. of 285 Physics, I.I.T., Bombay 400 076.
P89. FORWARD ENERGY FLOW-SECTION IN ULTRA- 287 RELATIVISTIC HEAVY-ION COLLISIONS, Swapan Das and S.K. Gupta, NPD, BARC, Bombay 400 085.
P90. FISSION IN q-NUCLEUS, Arun Kumar Pati, Th.P.D., 289 BARC, Bombay 400 085. f) NUCLEAR INSTRUMENTATION, EXPERIMENTAL TECHNIQUES ACCELERATORS 057. FIRST EXPERIMENTAL RESULTS FROM THE HIGH CUR- 291 RENT ION SOURCE, N.M.Thakur and R.C. Sethi, NPD, BARC, Bombay 400 085. 058. DEVELOPMENT AND PROGRESS IN THE DEUTERON RFQ, 293 R.C.Sethi, V.T.Nimje, N.M. Thakur and S.S.Kapoor, NPD, BARC, Bombay 400 085. 059. STATUS OF ISOL FACILITY AT VECC, A.Chakrabarti, 295 A. Bandyopadhyay, Arup Bandyopadhyay, S.K.Basu, N.C. Bhattacharya, S.Chattopadhyay, M.D. Mazumdar, T. Mukhopacihyay, A. Poley and A.K.Mazumdar , VECC, Cal- cutta. Phys. Dept., Phillips Univ., Germany. 060. BEAM CURRENT MONITOR AND SCANNING SYSTEM FOR 297 THE RACE-TRACK MICROTRON, S.D.Dhole and V.N.Bhoraskar, Dept. of Physics, Univ. of Poona, Pune-7. 061. STUDIES ON NARROWING OF TIME PROFILE OF A 299 CYCLOTRON BEAM BY SHAPING THE SLIT OF THE ION SOURCE, P.R.Sarma, VECC, Calcutta 700 064. 062. K-SHELL VACANCIES AT OXYGEN IONS MOVING INSIDE 301 THIN FERROMAGNETIC FOILS, L.C. Tribedi, R.G.Piliay, K.G.Prasad and P.N. Tandon, TIFS, Bombay 400 005. 063. HEAVY ION CHANNELING IN THIN SILICON SINGLE 303 CRYSTAL, V.S.Nanal, P.R.Apte, M.B.Kurup and K.G. Prasad, Tata Inst. of Fund. Research, Bombay. 064. PC-HORIZON BASED DATA ACQUISITION SYSTEM WITH 305 ETHERNET LINK, A.Chatterjee, Vineet Kumar, A.K. Mohanty, B.K. Nayak and Surendra Kumar, NPD, Bhabha Atomic Research Centre, Bombay 400 085.
065. PDP-11/23 AND STARBURST BASED MULTIPARAMETER 307 DATA ACQUISITION SYSTEM, Alok Saxena, Surendra Kumar, A.K.Mohanty, S.K. Kataria, NPD, BARC, Bombay. 066. A ND-100 BASED DATA ACQUISITION FACILITY AT 309 VECC, A.Roy, P.K.Dasgupta, A.Bandyopadhyay, S.K.De, VECC, Calcutta. P91. LOCATION OF MAGNETIC CENTRE IN MULTIPOLE FIELDS 311 BY OPTICAL METHOD, M.H.Rashid, G.Rodrigues*, J.Mallik and N.K.Mukhopadhyay, VECC, Calcutta. Nuclear Science Centre, Delhi.
P92. COMBINED OPERATION OF THE LIGHT AND HEAVY ION 313 BUNCHERS OF THE NSC PELLETRON FOR INCREASING THE EF- FICIENCY, P.N. Prakash and A.P. Patro, NSC, N.Delhi. P93. SPACE CHARGE EFFECTS IN RECIRCULATION INJEC- 315 TION, Arvind Jain, Nuclear Physics Divn, BARC, Bom- bay. P94. QUARTER WAVE RESONATOR DESIGN, B. Srinivasan, 317 NPD, BARC, Bombay and R.G. Pillay, TIFR, Bombay. P95. A POST-ACCELERATOR FOIL STRIPPER FOR THE BARC- 319 TIFR PELLETRON FACILITY, S.D.Narvekar, R.R.Hosangadi L.C.Tribedi, R.G.Pillay, K.G.Prasad and P.N.Tandon, Tata Inst. of Fund. Research, Bombay 4 00 085. P96. TRIPLE AXES MULTIPLE TARGET HOLDER ASSEMBLY, 321 L.C Tribedi, S.D. Narvekar, R.G. Pillay and P.N.Tandon, Tata Inst. of Fund. Research, Bombay. P97. AUTOMATION OF DOUBLE AXIS GONIOMETER FOR 323 CHANNELING/BLOCKING MEASUREMENTS, V.S.Nanal, W.A. Fernandes, M.B. Kurup and K.G. Prasad, TIFR, Bombay. P98. USE OF MULTIDETECTOR TELESCOPE SYSTEM FOR IM- 325 PROVING P,\RT1-LE IDENTIFICATION IN HEAVY ION REAC- TIONS, S.Mythili, B.J.Roy, S.K.Charagi, N.G.Badiger , R.V.Srikantiah, M.G.Betigeri and S.K.Gupta, NPD, BARC, Bombay. Dept. of Phys., Univ. of Bangalore.
P99. AN EXPERIMENTAL TECHNIQUE FOR THE STUDY OF 327 HEAVY IONS IN THE COSMOS, A.P.Sharma, AMU, Aligarh 202002.
P100. SIMPLIFIED RELATIONS FOR THE CALCULATIONS OF 329 ENERGY LOSS RATE & RANGE OF HEAVY IONS IN PHOSPHATE AND QUARTZ GLASS DETECTORS, Shyain Kumar, S.K.Sharma, Dept. of Physics, Kurukshetra University and A.P. Sharma, Dept. of Physics, A.M.U., Aligarh 202 001. P101. EMPIRICAL RANGE ENERGY RELATION FOR ELECTRONS 331 OF ENERGY LESS THAN 10 KEV, Sarita M. Agrawal. P.B. Pal , V.P. Varshney, S.V. College, Aligarh, Dept. of Physics, Ganjdundwara College, Etah 207 242.
P102. TOTAL STOPPING POWER IN# LOW ENERGY ELECTRONS, 333 Manoranjan Agrawal, P.B. Pal , D.K. Gupta aid V.P. yarshney, Dept.of Phys., S.V.College, Aligarh, Dept. of Physics, Ganjdundwara College, Etah. P103. STOPPING POWER RELATION FOR ±LOW ENERGY 335 POSITRONS, Manoranjan Agrawal, P.B.Pal , p.K.Gupta and V.P.Varshney, S.V.College, Aligargh, Dept. of Physics, Ganjdundwara College, Etah. P104. CONTRIBUTION OF PAIR PRODUCTION PROCESS TO THE 337 EFFICIENCY OF Ge DETECTORS, M.Sudarshan and R.Singh, Phys. Dept., NEHU, Shillong 793 003.
P105. DATA-ACQUISITION SYSTEM WITH SERIAL LINK TO 339 PC(XT), A.L.Khandwe and V.M.Misra, Computer Divn, B.A.R.C, Bombay 400 085.
P106. DEVELOPMENT OF INDIGENOUS WILKINSON TYPE ADCs 341 (50/lOOMHz) , V.M.Misra, A.A.Nadai.e, V.Geetha, M.D. Mahajan and L.S.Rajput, Computer Divn, BARC, Bombay. P107. ANALYSIS OF Fe AND Ti BASED ALLOYS FOR ZIR- 343 CONIUM CONTENT BY 14 MeV NAA, G.R. Pansare, P.M. Dighe and V.N. Bhoraskar, Dept. of Physics, Univ. of Poona. INVITED TALKS
AND
S E M I N A R'S NUCLEAR PHYSICS. BEYOND NEUTRONS AND PROTONS B.K. Jain Nuclear Physics Division Bhabha Atomic Research Centre, Bombay 400 085. In the contemporary picture the constituents of the nucleus, neutrons and protons. are composed of quarks and gluons. Their dynamics is described by the QCD, in which the chiral symmetry is a basic ingredient. Around the centre of the nucleons this symmetry is very much obeyed, which near the surface it is violated, giving rise to the non-conservation of the axial vector current. It is believed that on the surface of the nucleons this symmetry is restored by the birth of pions. Thus, looking from the inside of the nucleons the pions provide an additional axial vector current to restore the chiral symmetry and for nuclear physics they provide the basic starting point for its dynamics. The nucleons themselves, in this picture, are surrounded by a cloud of pions and their resonances. Physically this picture leads to the differences in the measured radii of the nucleons using different probes and a simple description of the charge- exchange spin-isospin flip reactions. It also puts the propagation of pions and rho-mesons (a resonant state of two pions probably) in nuclear medium in a category of basic importance. The first excited state of the nucleor the A. -isobar, to which the pions couple vei, strongly, acquire, in a natural way, a very significant place m the nuclear dynamics. The talk will give a general over view of the above.
II ENERGY NUCLEAR PHYSICS EXPERIMENTS CONTRIBUTING TO
PARTICLE PHYSICS
G. Rajasekaran Institute of Mathematical Sciences Madras 600 113
ABSTRACT
We discuss the following three Classes of experiments which have the potential of contributing to the understanding of certain fundamental questions in particle physics, (1) High-precision experiments in beta decay as well as internal bremsstrahlung in electron cepture can throw light on the question of neutrino masses and neutrino wixing. (2) Axions, light Higgs bosons and other particles of low mass which may possibly exist must be looked for in nuclear decays, Discovery of these particles or establishment of their absence have profound consequences for our understanding of QCD, CP, and electroweek symmetry breaking. (3) Search for long-range forces (QCD Van der Waals forces) among nucleons or nuclei will throw light on QCD and colour confinement which are very poorly understood at present. We may also discuss other possible low-energy experiments which may help indirectly in overcoming the energy-barrier which seems to be preventing fundamental advances in particle physics at present. 12 Quark-gluon Plasma in the Laboratory and in the Early Universe B.Banerjee Tata Institute of Fundamental Research,Homi Bhabha Road Bombay 400005
Abstract
Quantum Chromodynamics predicts a first order phase transition from confined hadronic matter to unconfined quark-gluon plasma(QGP)at a temperature in the range 100-200 MeV.lt is probable that such a tempearture can be reached in collisions between two heavy ions moving at relativistic energies.Such experiments have been performed in CERN and BNL in the last two years,although so far it has been possible to use only light nuclei as projectiles.The main problem thrown up by these experiments is the determination of the signal for the formation of the QGP.We shall discuss the suggestions made so far and their status. In the standard big-bang (SSB) model of the universe,for explaining the primordial nucleosynthesis it is assumed that the universe started with a uniform distribution of hadrons and leptons. When the temper- ature of the universe fell below 2 MeV the nucleons fused together to form the light nuclei 2H,iHe and rL*.Recently it has been pointed out that when the temperature of the universe was about 100 MeV it would have undergone the same phase transition mentioned above,albeit from the QGP to the hadronic phase. As a result there would have been an inhomogeneous distribution of nncleons and not a homogeneous one as assumed in SSB.Because of the inhomogeneity the primordial nu- cleosynthesis processes would have been altered/The consequences and implications of this changed picture of the nucleosynthesis in the early universe will be discussed.
13 EXOTIC NUCLEAR DECAY BY SPONTANEOUS HEAVY ION EMISSION
C.Shanmugam Department of Physics Presidency College, Madras 600 005
Nuclei with Z > 40 are metastable with respect to spontaneous decay into two fragments with masses M, and M^ and Q value given by
Q = M(A.Z)-M, (A, ,Z, )-M2(Ai.,Z2)> 0. When A%-= 1, we get alpha decay and the case in which Aj m A2 corresponds to cold fission. The intermediate case between these two in which 4
14 FISSION AS A PR03E TO UNDERSTAND HEAVY ION REACTION MEOiANJSM AND DYNAMICS Alok Saxena, Nuc lr»ar Physics Division, B-A. R. C-, Bombay
The study of nucleus-nurleus co.1.1 JBJDIIS provides a way to learn about, the? nurlsar equilibration process in Rpvpra) ro.13pr.tive degrees of freeiioiri of much physical significance and their character ist. ic re3a>:3tion times. The reactions resulting from nmtlaus-nuclsus collisions at intermediate enegies can be broadly classified in four typesiRla&tir (and quasi elastic) reaction, dinucleus reactions involv- ing deep inelastic collisions , non--compound nucleus first on reaction-.;; like fast-fission, quasi-fission and pr e -equi 1 i br i urn fission and true compound nuiileus reactions. Experimentally, it is not always passible to identify uniquely the reaction products 33 belonging to the prR or post compound nucleus phsBe. This often leads to apparent anomaly in the intarprstatian of some of the experimental results in heavy ion reaction studies. Measurements of various ob«=ervables in f issinn-l. iks reactions provider. information shout the reaction mechanism and dynamics. Fission fragment angular distributions, which depend on the spin distribu- tions and the shape parameters of the fissioninq nucleus, give informal ion about the fusion dynamics. Pre* and post scission neutron multiplicities in fusion-fis&ion reactions; are. used to determine pre- scis-sion life times. Fraqmen t-fragment angular cor- relation acts as a probe for .linear momentum tranfer characterising the reaction mechanism. The present talk will summarise the experimental reults on the different aspects of the heavy ion fission studies and the information obtained on the dynamical fea- tures of the heavy ion collisions.
15 Structure of High Spin States in nuclei naar the closed shell,
P. Mukherjae Saha Institute of Nuclear Physics, Calcutta 700 064.
Microscopic structure of high spin steles in deformed
nuclei is yet to be understood both experimentally and
theoretically. Houever, for nuclei near the closed shell the
structure of the high spin states is kno>jn to be pure shell model states involving a fau valence nucleons. A critical survey of the transitions from high spin states in region starting from Po to Ra indicate complete absence of any £2 collective transitions, so characteristic of the deformed nuclei. A challenging experimental problem is to identify the onset for such E2 collectivity in these region.
16 RECENT DEVELOPMENTS IN HIGH SPIN STATES
A.K.Rath and O.R.Praharaj Institute of Physics,Bhubaneswar-751005
High Spin States have been an area of active research in the last ten years. Availability of high quality heavy ion beams and precision mul- tielement detector arrays has resulted in the identification of very high spin states with,super-collective E2 transition rates. Hosts of new bands have been identified and electromagnetic transition rates are now known with great accuracy. Some of these findings are difficult to understand in the traditional models. In the present talk we review these developments and the possi- ble theoretical models which can enhance our understanding of these new experimental findings. Microscopic models dealing with signature effects, violation of K selection rules and superdeformed bands will be discussed.
17 SUPERDEFORMATION IN THE A=19O REGION* Umesh Garg Physics Department, University of Notre Dame, Notre Dame, IN 46556, USA.
Following the initial discovery, with the Argonne-Notre Dame y-ray facility, of a superdeformed band (SD) in the nucleus 19IHg |Ref. 1], an enormous amount of experimental and theoretical work has been performed in this region in a relatively short period. SD bands have since been established in at least ten nuclei viz. 189~ i94Hg> i93,l94Tlt ^d i94,i96Pb [RefS- 2-4] and the present understanding can be summarized as follows: !. AH data currently available support the interpretation that 192Hg is a "doubly magic" SD nucleus, i.e. large shell gaps exist for Z=80 and N=112 at a deformation of p*2 ~ 0.55. 2. For the lighter Hg isotopes, the SD well becomes increasingly shallower and 189Hg is most likely the last SD nucleus in this region. 3. The dynamic moment of inertia 3(2) as a function of rotational frequency shows a gradual increase (by almost 40%) in most bands. This increase can be attributed to the alignment of pairs of nucleons in high-j intruder orbitals. 4. Recent data on 193Hg [Ref.5] provide indications that octupole degrees of freedom play an important role in the SD minimum. 5. As in the A=150 region, SD bands with energies very similar (within 1-2 keV) have been found in the neighboring nuclei: the excited bands of 191Hg have "twins" in 193Hg[Refs.5,6]. This has been explained in terms of intrinsic spin alignment and pseudo-spin symmetry. Details of some of these results will be presented.
*Supported in part by the US National Science Foundation and the US Department of Energy. !E.F. Moore et al., Phys. Rev. Leu. 63 (1989) 360. 2R.V.F. Jansscn et al., in Proc. Int. Conf. on Nuclear Structure in the Nineties, Oak Ridge 1990. 3K. Theine et al., Z. Phys. A336 (1990) 336. 4M.J. Brinkman et al., Z. Physik A336 (1990) 115. 5M.A. Riley et al., Nucl. Phys. A 512 (1990) 178; D.M. Cullen et al., Phys. Rev. Lett. 65 (1990) 1547. 6M.P. Carpenter et al., Phys. Lett. 240B (1990) 44. RECENT DEVELOPMENTS IN DYNAMIC DEFORMATION THEORY J.B. Gupta Ramjas college, University of Delhi, Delhi-110 007
The version-I of the Dynamic deformation theory (DDT-1) of Kumar-Baranger (1968) for the collective nuclear structure of atomic nuclei combines the Pairing-Plus-Quadrupole (PPQ) approx- mation of nuclear force, the time-dependent Hartree-Bogoliubov (TDHB) method and the deformed quasi-particle (DQP) basis. A configuration space of two complete oscillator shells each for protons and neutrons, & the active nucleon space of (Z-40) ,(N-70) is employed in the deformed shell model approach. The later version DDT-2 employes all harmonic osciiitor shells and treats all nucleons as active. The method is based on the Bohr- Mottelson unified collective model, but the restri -ction to axial symmetry and the adiabatic treat- ment of uncoupled rotation-vibration degrees of freedom is not employed. Instead, complete freedom in p~Y space for each nuclear state is allowed. The 7 parameter of the collective Hamiltonian are derived microscopically along with the EM operators. The calculation for one nucleus is completed in a few hours on a fast computer ( > 10 MHz). The fitting parameters for Hc are restri- cted to two, one of which varies through 10 % and the other within a factor of 2. The DDT-1 also called DPPQ proved very successful in predicting the spherical to deformed shape phase transition, prolate to oblate shape transition and the superfluid to normal phase transition, as illustrated by KB for the W -Os -Pt region. In the last two decades, Kumar and Gupta have demcnstxated extensively the usefulness of DDT-1 for the Nd-Sm-Gd-Dy nuclei for predicting shape phase transitions, static and transition moments and interband transitions upto 10 collec- tive bands in a individual nucleus where ample experimental data are available.
19 ACCELERATOR PROGRAMME AT CAT
S.S. Ramamurthi Centre for Advanced Tecnnoiogy Indore-452012
ALS1KACT
The Accelerator Programme at CAT has very broad oased concept under wnicn all types of ac- celerators ara to be taken up for design and faorication. This Centre will be boosing a wide variety of accelerators to serve as a common facility for tine universities, national laboratcies in addition to laboratories under the Department of Atomic Energy.
In tne first phase of tne programme, a series of electron accelerators are designed and faori- catea. They are Synchrotron Radiation Sources of 45y Mei/ (1NOUS-I) and of 2 Ge\/ (1NDUS-II), Microtron up to energy of 20 MeV, linear ac- celerator upto 20 MeV, and DC Accelerator for in- dustrial irradiation upto 750 KeV and 20 KW. A proton accelerator of 3fe)0 MeV with 20 MeV linac injector is also designed. CAT is also to developing a strong oase for support tecnnologias like ultra high vacuum, Radio Frequency and Microwaves, DC pulsed and superconducting magnets, power supplies and controls etc. These tecn- nologias are very useful for other industrial ap- plications also.
To develop user groups to utilise IMDUS-1I synchrotron radiation source, a batch production of Rotating Anode X-ray Generators with power sup- plies nas been initiated. So also, the Sputter Ion Pumps, Electron Guns, Turbo Molecular Pumps are brought into batch production.
110 NEUTRINO!.ESS pP-DECAY USING A QUARK MODEL WITH RELATIVISTIC HARMONIC CONFINEMENT
S.B. Khadkikar Physical Research Laboratory Navrangpura, Ahmedabad 380 009
The nuclear double beta decay without neutrino emission would provide evidence for lepton-non-conservation and the Majorana nature of neutrinos or the right handed nature of the weak current or the see-saw mechanism for generating neutrino mass in conjunction with a Grand Unification Theoretical (GUT) scenario. The impediments in the large number of investigations in the past decade has been the closure approximation to the nuclear part of the amplitude and uncertainty about recoil effects in addition to the effective coupling constants due to non-elementerity of the nucleon. We have been able to avoid these pitfalls. For this purpose,a relativistic quark confinement model is employed to obtain form factors due to hadronic currents in double beta decay. The nuclear pan of the form factor is evaluated in quasi-particle neutron-proton random phase approximation. The double beta decay amplitude formula is developed so as to avoid closure approximation. We also do not have to use effective vector -and axial ' vector coupling constants in the hadronic currents. The recoil matrix elements arise naturally from quark recoil in decaying neutrons. The formalism is applied" to the neutrinoless double beta decay of Ge to the ground state of Se without and with inclusion of p-wave in addition to the dominant s-wave nuclear matrix elements in the decay amplitude. From the experimental lower bound for the decay half-life an upper limit for the effective Majorana mass of the neutrino is deduced and the right banded contribution to the charged week current estimated.
Ill Signatures of Parity Mixing Among the Nuclear States
Satyajit Saha Nuclear Reactions Group, TIFR Bombay 400 005.
Space-time invariance properties of the strong, electiomagnetic and weak interactions have been questioned and put to rigorous tests for the last 30 years since the breakdown of parity symmetry was ob- served in the leptonic weak decays. Although the symmetry violations in the leptonic and the semileptonic processes are well understood and good agreement between theory and experiments are found, it is still an open problem in the nonleptonic sector where evidences of par- ity mixing of the nuclear states are found in the heavier systems but considerable challenge exists in the theoretical interpi- "tations of these data. On the other hand, significant progresses have been made in the theoretical estimates of the observables of parity mixing in lighter systems, but the experimental results are still not conclusive enough to verify these predictions. In this presentation, an overview of the theories of parity mixing for the systems ranging from the lightest to the heavier nuclei will be discussed followed by a review of the relevant experiments to extract the extent of parity mixing in these systems. A side by side comparison of the experimental results and the theoretical estimates will be made next and finally, the recent progresses and future directions in this field will be discussed.
112 SHRI: SPECTROMETER FCC HEAVY RECOIL IONS P. Singh Nuclear Physics Division Bhabha Atomic Research Centre, Bombay 400 065. The recoil mass spectrometer, SHRI, designed for use with the 14UD BARC-TIFR Pelletron is now under fabrication. The spectrometer consists of a combination of electric and magnetic fields in QQEBE configuration. The mirror symmetric 3-dipole system allows energy dispersionless focussing on the detector. Maximum attainable electric and magnetic rigidities have been chosen considering the various target-projectile combinations planned for the Pelletron accelerator. The design studies indicate that a mass dispersion of 1J mm/% and mass resolving power of "300 are feasible e.c a maximum solid angle of 8 msr. In this talk the present status of the spectrometer and planned experiments will be reviewed.
SI HEAVY ION REACTION ANALYZER (HIRA) FACILITY AT NSC A K Sinha Nuclear Science Centre (An Iriter_University Research Facility) JNU New Campus, Post Box 10502, New Delhi-67 A recoil mass separator facility HIRA is being set up by the scientists from NSC and the universities in order to exploit the full potential of the research with the heavy ion beams from the Pelletron at NSC. It is in an advanced stage of installation. The electromagnetic configuration selected for HIRA is QQEMEQQ. The combination EME of electrostatic (E) and Magnetic (M) deflectors is chosen so as to ensure reasonable mass dispersion alongwith achieving a X- (Horizontal displacement) & 0- (Horizontal divergence) focus in energy. In addition to the enhancement in the solid angle of acceptance , the two quadrupole - doublets provide for a lower Y-magnification, a variable mass dispersion and possibility of incorporating suitable higher order fields for correction of some aberrations etc. A multipole magnet is also included before the magnetic dipole to provide for a fine tuning of the HIRA. In some of the experiments planned, it is required to set HIHA at angles different from the normally used zero degree direction. To take care of this, HIRA will be mounted on a rotatable platform and coupled to the beam line with a sliding seal vacuum chamber.
In the proposed talk, the ion optical design considerations involved for recoil mass separator HIRA with its special features in the context of the other similar facilities will be discussed. Details of the hardware planned will be presented. Status of the various electromagnetic elements and summary of the measurements performed so far on them will be given. Status and plans for the vacuum chambers , detector system and the auxilliary equipments will be described.
52 Gamma Ray Multiplicity set up at the BARC/TIFR 14UD Pelletron Accelerator R.K. Choudhury, Nuclear Physics Division, Hhabha Atomic Research Centre, Bombay - 400 085.
Angular momentum plays an important role in the characterisation of heavy ion reaction processes. Gamma ray multiplicity measurements provide a unique method for the determination of the angular momentum of nuclei produced in he&vy ion reactions, and have been used to study the angular momentum distributions in different reaction channels such as transfer, deep inelastic and fusion processes, which have helped in a better understanding of the various aspects of the reaction mechanism in heavy ion collisions. We have set up a gamma ray multiplicity array at the BARC/TIFR 14UD pelletron, consisting of a number of hexagonal DGO detector elements. The present talk will touch upon the salient features of the multiplicity set up, the theory of thn measurements and the results obtained from the first experiments using this set up.
S4 NEW TRENDS IN THE GROWTH OF SCINTILLATION DETECTOR CRYSTALS D.Arivuoli, J.Kumar and P.Ramasamy Crystal Growth Centre, Anna University, Madras-25. A review has been given regarding the growth of different scintiallators comprising organic, inorganic and plastic materials. For the scintillator crystal to have high efficiency, it should possess high density, high physical efficiency (fraction of absorbed energy transformed to light should be large), low opacity to its own emission, short decay time and extremely small afterglow. All these factors depend upon the perfection (purity, dislocation) of the crystal and in certain cases, activator concentration. The different crystal growth techniques (like melt, vapour, and solution) adopted will be discussed in terms of their impurity content (activator), detection efficiency and spectral resolution. Results on currently used ocintillators like BGO and BSO grown both by Czochralski and Travelling solvent zone apparatus will be presented. The role played by stoichiometry and convective flow during growth will also be presented. The advantages of these crystals over other scintillation detectors are discussed.
S5 BARIUM FLUORIDE-A NEW SCINTILLATION DETECTOR MATERIAL M.P. Chougaonkar, V.H. Gokhale, S.M.D. Rao, and R.V.Srikantiah TP&PED BARC BOMBAY 400 085 Abstract
Barium fluoride has emerged as a new scintillator material during past five years. Non hygroscopic nature, chemical as well as mechanical stability, good absorption for gamma rays and high resistance to radiation damage make it an attractive material for specific applications. Barium fluoride exhibits at least two light output components. A fast component appears with low intensity at 2 20nm with a decay constant of 0.6 ns, while the slow one appears with comparatively more intensity at 310 nm with a decay constant of 600 ns. This property of the material can be exploited for the measurement of both energy as well as timing spectroscopy. BARC has been actively involved in the growth and characterisation of Barium fluoride crytals during past few years. Crystals measuring 40 mm dia and 30 mm long have been grown in the High temperature high vacuum furnace using Bridgmann technique. The crystals grown have been characterised for impurity analyses, UV transmission and gamma ray spectra measurements. Improvement in the transmission in the UV region, scintillation characteristics, are the areas in which the work is being carried out. It is also being planned to shift the scintillation •wavelength to the near visible range so that more conventional PMTs can be used. A lot of efforts are needed to improve the quality of the detector. A status and the state of art technology of Barium fluoride detectors are discussed. Further, a general picture of recent trends in the scintillator detectors is highlighted.
S6 Ph.D. THESIS DELTA PRODUCTION IN NUCLEAR REACTIONS A.B.Santra Nuclear Physics Division BARC Bombay 400 085
A free nucleon when excited by energetic pion beams goes over to various resonance states. Delta(A) is the lightest resonance and most strongly excited compared with others in pion nucleon scattering. This resonance has a mass of 1232 MeV, i.e. 300 MeV more than a nucleon, with a spread of about 120 MeV. It has a spin of 3/2 and isospin of 3/2 corresponding to fcs'T charge states. As the nucleus is considered to be an interacting meson nucleon system instead of nucleons alone, the intermediate states in pion nucleon scattering processes inside the nucleus, sometimes go over to the resonant states. It has been found that those processes where intermediate states are resonant states contributes significantly in a variety of nuclear processes. Dynamics of the A in the nucleus must also be considered to describe correctly the physics of the pion nucleus scattering at intermediate energies. It is now well established that deltas, along with pions and nucleons, fora the basic degree of freedom in microscopic description of nuclear physics. Experiments, therefore, have been done to excite them in nuclear reactions so that one can learn directly about A-nucleus dynamics and the A-nucleon interaction. Most common and useful among those reactions are the charge exchange reactions. The delta excitation in these reactions is identified in missing mass spectra by detecting the recoil nucleus, as..in the (p,A ) reaction, or the ejectile nucleus, as in the ( He,t) like reactions. The most elementary of the above mentioned charge exchange reactions are p( He,t)A and p(p,A )n. A large amount of experimental data are available for both of these reactions for a wide range of incident energies. In this work these two reactions are analyzed in detail.
The p( He,t)A reaction is studied in distorted wave Born approximation(DWBA) framework. The production of A in this reaction is considered to be an one step process. The target proton, interacts with one of the protons in He and then either itself gets converted into A or converts the projectile proton into A . The former process is called the target excitation or direct term and the latter process is
Tl known as exchange term. TWs transition from two interacting protons to a neutron and a & is taken to be due to one pion and one rho exchange. The transition potential includes form factors at the interaction vertices to take into account the off shell nature of the exchanged particles. The cut off length parameter, A, in the conventional monopole form factor is taken to be 1.2 GeV/c for pion and 2.0 GeV/c for rho. Though a large energy and momentum transfer occurs at the transition, the continuum particles move along the path of much less momentum transfer. These motions, therefore, can be described by the mean fields. Since the available experimental data are at high incident energies (2.0 GeV to 8.0 GeV), it is expected that eikonal approximation for the description of distorted waves in initial and final channel, would work reasonably well. The angular distribution, triton energy spectra and delta mass distribution are calculated. They are found to agree well with the experimental data. The distortion mainly reduces the magnitude of the cross-section keeping the shape unchanged. It is found that the contribution due to excitation of the projectile nucleon to A depends upon the value of A in the vertex form factor. This contribution is large at all the energies for hard form factors. The contribution of rho exchange is found to be large at higher energies. However, at lower energies this contribution is not significant. p(p,A )n reaction has been studied from threshold to 5.5 GeV/c beam momentum. Considering the fact that a significant part of the total pp cross-section is due to A excitation, a coupled channel formalism has been developed to analyze this reaction. It turns out, in this formalism, that the transition amplitude is similar to that obtained from DWBA framework. The transition potential in this case has been taken to be due to one pion exchange. The cut off length parameter, A , in the vertex form factor is taken to be 1.0 GeV/c. The distorted scattering wave functions are written in eikonal approximation directly in terms of the scattering amplitudes. The distorted waves written in this way, are seen to be modified mostly in the interior region with respect to the plane waves. Calculations have been done for various differential and total cross-sections. The results agree remarkably well with all the experimental data in the corsidered energy region. It is found that the dominant contribution <:omes from the non-central part of the interaction. The distortion as expected, is found to essentially weaken the transition potential in the large momentum domain. It is also found that, with the addition of rho exchange to the one pion exchange potential, the results are not in accord with the measured cross-sections. THEORY OP CLUSTER TRANSFER RESONANCES IN HEAVY-ION REACTIONS AND THE RELATED PHENOMENA Rajeev Kumar Puri Physics Department, Panjab University, Chandigarh-160014.
This thesis is devoted to a theoretical study of some recent experimental data on heavy-ion cluster-transfer resonances and the fusion cross-sections. We have used the energy density formalism (EDF), first derived by Vautherin and Brink (VB) /I/ in its satisfactory version, using Skyrme forces. We have also used the quantum mechanical fragmentation theory (QMFT)/2/ for comparisons of some of our calculations . The Hamiltonian density of VB can be divided into two parts: (i) the nucleon and kinetic energy density dependent part and (ii)the spin density dependent part. In the past, attempts have been made to calculate the heavy-ion potential for the first part only, since the spin density could be calculated only for closed j-shell nuclei. However, if one wishes to study the transfer reactions, the spin density term must be generalized to cases of valence particles ( or holes) outside the closed core. This is done in this thesis. The first part of potential is calculated in proximity approximation of Chattopadhyay and Gupta /3/, for various Skyrme forces .The kinetic energy density is taken in Thomas-Fermi approximation with surface correction. Shell model and Fermi densities are used, which are found to match very well, atleast , in the surface region. The effect of varying the density parameters is also studied. The spin density part of potential is calculated more consistently by using the same shell model wave- functions as for nucleon density . Analyzing a large number of reactions involving s-d and fy,shell nuclei, we are able to give a simple analytical formula for both the proximity and spin density potentials. The spin density potential is obtained within a shell. This depends upon the new concept of what we call" Particle- Strength " and also on masses of the colliding nuclei. The spin-density contribution to ion-ion potential is found to reduce the attraction of nuclear proximity potential by 5-7 MeV. We have applied this formalism to study the phenomenon of «*-transfer resonances, observed in colliding o<-nuclei, which gets suppressed on adding neutrons to target, projectile or both /4/. Analyzing the spin density term first, we find that <*- clustering effects exist in spin density part for the colliding «<-nuclei ( N =Z, A =4n), only if due to an *-particle transfer, atleast, one of the product nucleus becomes a closed j-shell nucleus for both protons and neutrons (here it is the same j- T2 shell that gets completely filled for both protons and neutrons ) . This is manifested as a discontinuity ( a definite step ) in the potential at the new pair of ^-nuclei (transfer products).For non- alpha- colliding nuclei, however, the discontinuities in potential are found to occur also at the transfer of 2-nucleons, irrespective of the above mentioned closed shell effect. The ©{-clustering effects are then investigated in the total potential by adding all terms of the Hamiltonian density,Coulomb potential and the binding energies of two colliding nuclei.The mass frag- mentation yields are calculated by solving Stationary Schrodinger equation in mass asymmetry coordinate /2/. Our results compare more accurately with experimental data than that of Malik et.al. /5/jusing the proximity potential of Blocki et.al.Spin density is found to play an important role in deciding the relative formation yields. The suppresion of alpha-transfer effect on adding neutrons to alpha-nuclei reaction partners is also shown in our calculations. As we go away from N=Z line «*- clustering picture starts breaking down and new clusters, like Be-10, C-14, Ne-24, etc., rather than ot-nuclei, are shown to transfer preferencially, which might have relevance to the observed cluster -radioactivity or to the predicted cluster-decay of " stable" rare-earth nuclei, /6/. The cluster-decay of some light and "stable" rare-earth nuclei, like Zr-80,Gd-154,156,158 , Dy-160,and Er-164. is also studied in order to establish the nature of decay in these nuclei. Decay of "stable " nuclei predict interesting possibilities of being stable against *-decay but meta-stable with respect to many heavy-clusters. Another application of our method is made to fusion- cross sections. Spin density is found to increase the barrier height and decrease its position , which decreases the fusion cross- sections calculated in sharp cut off model, A detailed comparison shows that our results are in better agreement with the empirical estimates,as compared to other available theoretical calculations . A simple analytical formula is also presented for calcuiat"in-r- the interaction barrier heights and positions. Concluding, we have extended the energy density formalism to transfer reactions by generalizing spin density contribution to nuclei with valence particles (holes). Applications of our method to HI cluster transfer resonances and fusion cross-sections are shown to compare nicely v/itn experimental data. Analytical formulation of the problems is made as far as possible. References : 1. D. Vautherin and D.M. Brink, Phys. Rev. C5 (1972) 626. 2. R.K. Gupta et.al., J. Phys. Coll. (Paris),C6,45 (1986) 477. 3. P. Chattopadhyay and R.K. Gupta, Phys. Rev.C3C(1084)1191. 4. R.R. Betts, Bad - Honnef Conf., 1981. 5. S.S. Malik and R.K. Gupta, J. Phys. G: 12(1986) •.. 161. 6. S.S. Malik et.al. Pramana J. Phys. 32(1989) 419. INTERNAL CONVERSION STUDIES ON SOME H4, M3 AND E3 TRANSITIONS K.Radha Krishna Dept. of Nuclear Physics, Andhra University, Waltair
The conversion electron spectroscopy has been offering a powerful tool to assign spin-parity character of a nuclear level and for the classifica- tion of electromagnetic transitions. In the earlier measurements the conversion coefficients were measured using scintillation detectors and magnetic spectrometers. The former are limited by poor energy resolution while the later poor transmission. During the recent times highly sophisticated solid state detectors like Si(Li) and HpGe characterised by high energy resolution and good efficiency have made a good impact in nuclear spectroscopic research. It ^Lg also observed that the disagreement between theory ' and experiment goes to the extent of 20-30% in the previous measurements. In this thesis the radioisotopes for the measurement of conversion coefficients were chosen basing on the following considerations, i) Existence of wide discrepancies in the earlier measurements ii) large uncertainties in the previous values iii) occurance of anamolies in the experimental values iv) to look for possible multipole admixture in a transition and v) a different technique (XPG, NPG or IB) using Si(Li) and HpGe detectors in combination with a computer controlled multichannel analyser is used which is superior to several of the earlier methods employed for these measurements. The present thesis work concerns the measurement of conversion coefficients governing three M4 < Sr, Zn and Hg) , one M3 112m loSm,...... r- • ( In) and one E3 ( Dy) transitions in five isotopes. The K-conversion coefficient is measured in four isotopes ( Sr, Zn, In and Dy) using an X-ray Peak to Gamma and Normalized Peak to T3 Gamma methods. The total conversion coefficient ( " Hg) is measured using the Intensity Balance method. The experiments were carriedout at BARC, Bombay and VECC, Calcutta. The results thus obtained are compared with the theory in table and the same are discussed.
Isotope Transition Energy Tf a. /a PL (keV) K T
388 .4 2.8h 0 .175+0. 006 0 .185 438 .9 14 h 0 .04010 .001 0 .049 In 4 155.0 21m 4 .820+0. 290 5. 120 108..2 1 . 3m 2 .920±0. 080 3.200 Hg 374..0 4 3m 6 .340±0. 290 6.290
References: 1. F.Rosel, H.M.Fries, F.Alder and H.C .Pauli (PL) Atomic Data and Nucl. Data Tables 21(1978)91 2. R.S.Hager and E.G.Seltzer (HS) Nuclear Data 4(1968)1 3. K.Radha Krishna, M.V.S.Chandrasekhar Rao, G.Sree Krishna Murty, S.Bhuloka Reddy, G.Satyanarayana, D.L.Sastry, M.R.Iyer, S.G.Sahasrabhude and D.A.R.Babu Indian Journal of Physics 63A(8)839 (1989) 4. K.Radha Krishna, M.V.S.Chandrasekhar Rao, G.Sree Krishna Murty, N.Venkateswara Ra o, S.Bhuloka Reddy, G.Satyanarayana, D.L.Sastry, M.R.Iyer and S.G.Sahasrabhude Indian Journal of Physics 64A(4)294 (1990) K-CAPTURE PROBABILITIES BY SUM-PEAK METHOD Bhaskara Rao Katiki, Dept. of Nucl. Physics, Andhra Univ.
Employing a large volume HPGe detector, all possible sum-peaks for each electron-captu-e decay are accurately measured for 18 transitions in six radioactive isotope-, namely; Sn~113, Se-75, Yb-169, Eu-152, Ba-133 and Gd-15J. The HPGe detector employed is 48.2mm in crystal length and 44.7mm in crystal diameter and is fitted with a 20mm Beryllium window. Its FWHM at 1.33MeV is 1.75KeV. This detector has been coupled to an ND600 4K channel analyser for recording the data. Several auxiliary experiments have oeen performed before taking up the measurements in order to evaluate the optimum performance of the experimental system. • The experimental setup has been standardised by measuring P^. values to 437 KeV and 383 KeV levels in the decay of Ba-133 as 0.730(12) and 0.809(27) respectively. Necessary outline of the theory is presented in Chapter II. Chapter III contains the experimental details including various experimental methods as well as details of the detector and the electronics employed. The preliminary experiments are given in Chapter IV while the results on the six experimental isotopes are furnished in Chapter V throuph X as summarised below:
Sn-113: Measured PK values for the 646 KeV and 391 KeV levels in In-113 for the first time. Different sum-peaks are analysed and the weighted mean values obtained as 0.867(13) and 0.870(15) respectively. Experimental P. values are derived basing on the theoretical P/P ratios and are 0.116(1) and 0.110(1). The beta disintegration energy is uniquely assigned as 1021 ± 10 KeV. Ths interfering activii . of Sn-119 is carefully avoided in determining the K X-ray intensities. The results are in good agreement with theory. Se-75: Measure P.. values for the three levels at 400 KeV, 279 KeV and 264 KeV in As-75 as 0.888(21), 0.894(17) and 0.902(24) respectively. P value for the 264 KeV level is experimentally determined Tor the first time. There is a marked improvement in the errors associated over those available in literature. P values are derived using P /P ratios and are 0.095(2), OfO93(l) and 0.094(2) respectively. Yb-169: Applying corrections for the cinite life-time of the levels at 379 KeV and 316 KeV in Tm-169, P values arc experimentally determined for the 472 KeV, 379 KeV and 316
T4 KeV levels in the decay of Yb-169. These values are 0.822(16), 0.829(23) and 0.832(16) respectively. Attenuation factors obtained for the finite life-time to the above two cases are respectively 0.91(3) and 0.46(5). The P, values derived for these three levels are 0.151(2), 0.145(4) a. i 0.146(2) and are in agreement with theory. Eu-152: Measuring P value for the 1085 KeV level in Sm- 152 for the first time, the P^ values for two other levels at 1529 KeV and 1233 KeV are also measured. They are 0.861(79), 0.829(21) and 0.840(20) respectively. The uncer- tainities associated with the P., values are greatly reduced compared to the previous measurements. P. values are also derived basing on the theoretical P /V ratios and are 0.141(3), 0.127(3) and 0.127(11) respectively. The results agree well with theory. Ba-133: Altogether four capture transitions are investigated in this isotope. While results for the two levels at 437 KeV and 383 KeV in Cs-133 are used to standardise the experi- mental setup, the P values for the other two levels at 160 KeV and 81 KeV are measured as 0.912(57) and 0.938(62) respectivel. The P. values are also derived for the above four levels as 0.2^3(4), 0.171(5), 0.136(8) and 0.136(8). While the P^ values for the former two levels are in exi llent agreement with the weighted mean of the earlier measurements, the results of the latter two levels are in general agreement with the theory within the experimental uncertainities. Gd-153: Throe P values are measured in the decay of GrJ- 153 feeding the levels at 172 KeV, 103 KeV and 97 KeV in Eu-153. They are 0.431(13), 0.745(11) and U.7471,18) resf • tively. The beta-decay energy is obtained basing on the above three P values as 240 ± 4 KeV. l\ values are al:\j derived using' theoretical P /P^ ratios dnti are 0.429(12), 0.207(3) and 0.200(4) respectively. The results are in excellent agreement with theory. For almost thirteen of the above eighteen capture transitions, atleast three different sum-peak:; are analysed :'i each case and their weighted average values are taken. For the 1085 KeV level in the decay of Ku-152 to Sm-152 and the 103 KeV level in the decay of lJd-153 to f\u-153, however, the usual surn-peaks with the K X-rays are not considered because of severe interferences and the only sum-peaks formed with tho K X-rays are analysed fn determine the PK values. The dependence of P value on the Q-value is tested in each isotope and presented graphically. It is clear from thic stutij that IJ value depends very sensitively on the Q-value when the latter is small. CONTRIBUTED PAPERS a) NUCiEAR STRUCTURE* MODES OP EXCITATION AND RADIOACTIVITY FEEDING TIME AND HALF-LIVES OF EXCITED NUCLEAR STATES IN 40K H.C Jain, S. Chattopadhyay, Y.K. Agarwal, M. Dasgupta, M.L. Jhingan and A. Roy T.I.F.R., Colaba, Bombay - 400 005
The high spin states in K have been studied through heavy ion reactions by P. Herges et al /!/ and H.H. Eggenhuisen et al /2/. These studies established levels with spin upto 10" in 40 40 K. While the low lying levels in K arise due to coupling
of a f7»7 neutron to a d 3/2 proton hole, the higher excited states are understood within the framework of the weak-coupling model /3/ as the coupling of two particle-two holes or three
particle-three holes in f7#~ and d,/9 neutron or proton shells. The structure of these states can be sensitively probed through a measurement of their electromagnetic transition probabilities. 40 27 16 The levels in K were populated through the Al( O, 2pn) reaction at E16O = 60-63 MeV. The lifetimes of the low excited states were measured through the plunger technique /4/. These measurements gave a value of T.i^ = 2.3(10) ps for the 891 + keV (5") state and T./9 = 1103(70) ps for the 2543 keV (7 ) state in 40K. The hali-lives of the higher excited states were measured through the Doppler-shift attenuation method (DSAM). In this measurement, the target was obtained by evaporating about 2 2 300 ug/cm thick Al on to a 10 mg/cm thick Ta backing. The y-ray spectra taken with an HPGe detector at 0° w.r. to beam direction were cleaned up by gating them with neutrons detected in two neutron detector using liquid scintiliator. The experimen- tally observed line shapes for 1245, 1351, 1823 and 2333 keV Y-rays in 40K were fitted using standard energy Joss and the exponential decay equations. The fits also took into account the life-time of the ievel feeding the level of interest. The feeding-time was considered when side feeding was predomi- nant. The experimental lineshape for 2333 keV (9+ •* 7+) transi- tion is shown along with the theoretical fits in fig.l. These measurements gave a value of T^ = 0.56(6) ps for the 4.37
MeV level, T./2 = 0.11(4) ps for the 4.88 MeV level, Ty2 = 0.38(7) ps for the 6.23 MeV level and Ty2 = 0.25(7) ps for the 7.48 MeV level in *°K. The side feeding time ~25 fs was also inferred from the present measurements. The Y - transition probabilities have been calculated from the measured half-lives and the known multipolarities and compared with Weiskopf estimates. References: /I/ P. Herges et al., Nucl. Phys. A372 (1981) 253. Ill H.H. Eggenhuisen et al., Nucl, Phys. 285 (1977) 167 131 R.K. Bansal and 3.B. French, Phys. Lett. 11 (1964) 145 /4/ H.C. Jain et al., DAE Symposium on Nuclear Physics (Dec. 28-31, 1989). 1E4 40 K , 9 -> 7 2333 KeV y Ray 0. l5±.05ps 1000- m
O • 1 O 100-
10 2320 2340 2360 2380 2400 2420 CHANNEL No. 40, Figl: Half-life of the 4.88 MeV(9+) state in K HIGH SPIN LSOMER IN 151Sm
JM.Chatterjcc. Somapriya Basit, K.Kar, D.Banik Saha Institute of Nuclear Physics. Calcutta; R.K.Chaitopadhyay, Ananda Mohan College, Calcutta and R.P.Sharma, S.K.Pardhasaradlii, VECC. BARC. Calcutta.
High spin isomcric states arc always of interest because of their occurence in a region of high angular momentum where shell structure disturbs the collective excitation. High spin isomers in several rare earth nuclei were studied previously (1). Later on, an + isomeric state of positive parity band at energy Ex = 3181.5 keV with /*= 29/2 in 149Sm having 4ns half-life was reported (2). We aimed to study the possible existence of such isomer in other Sm isotopes. The experiment was carried out at the VECC, Calcutta, via the reaction I5oNd(cc,3ny) I51Sm at E„ = 35 MeV using an enriched 150Nd target (96.6% abundant) of thickness iOmg/pcr sq. c ••. The target was made of Nd-oxidc powder centrifuged on kapton backing. A larpc volume vertical HPGe Gamma-X detector was placed below the target at 90" to the beam direction at a distance of 12cm from the target. The study of ZTy-timc distribution was performed by using the time structure of the beam. The data was recorded in the list-mode on the Norsk Data 560 computer using conventional electronics and sub- ;ucnlly analysed off- line on the same computer. The high spin isomcrs with half-lives in the nanosec region was searched by measuring time distribution of y-rays with respect to 4He beam pulses within every observed cascade. Time spectra were projected for all prominent lines observed in the spectrum. The delayed components in all the lines were checked for consistency within every cascade observed in the level scheme. The intensity ratio of the delayed and prompt components of a level, when going up in a cascade which may be populated by a high- lying isomcr should increase. This is shown in fig.l along with the observed cascade. The prompt component should be absent for the actual isomcric transition. The 235.4 - 374.5 - 478.7 - 561.8 kcV cascade did not show any significant delayed component; in agreement with the previously reported result (3). The members of the cascade feeding 261.1 keV (/n=ll/2~) level i.e 184,203,221,238,253,268,282 kcV showed pronounced delayed component with T ul - 23± Ins in the time spectra. The 294 keV y-ray could not be used as gate due to the presence of the prominent 296 kcV neighbouring y-ray. The time distribution of 303 kcV y-ray coincident with the remaining y-ray docs not have any delayed component. The time distribution of 282 kcV y-ray dc-exciting from the 1912.2 kcV(7 "=25/2") level has a ratio of the delayed to prompt component 0.45. No other y-ray of energy upto 300 kcV show any delayed component reveal: )g ciic fact *'iat the 1912.2 kcV level is fed by a high-lying isomcr having half-life,'/' 1/2 = 23± las. ^22057
CA l/l "I [912-2 £
vo '., /361-36
T II07-55
w« 869-45 J I
A45-Z
21 26/-J C'AJ
CHANNEL
Fig 1. shows the prompt :uid delayed component of time distribution of several y-rays observed in cascade in '''Sm.
References:
(1) D.CJ.M.Hagcinan u ;il, 1'hy:,. Letts 84D (1979) 301 (2) E.Haimnarcn el al., Nucl. Pays. A321 (19"9) 71 (3) W.Gclletly cl al., Joiir/i. I'hy.v G2 (1976) IA MEASUREMENT OF K ELECTRON CAPTURE DECAY PROBABILITY IN 161Ho, 125I AND 131Ba G.Sree Krishna Murty, M. V.S.C'handrasekhar Rao, H.Kavi Ku»ar, G.Satyanarayana, D.L.Sastry and t S.N.Chintalapudi Svarra Jnanananda Laboratories for Nuclear Research, Andhra University. VISHAKHAPATNAM. T Variable Energy Cyclotron Centre, CALCUTTA.
The K- electron capture decay probability (P..) measurements were made for the first time in the decay of Ho and I produced via cc- induced reactions at the VECC, Calcutta, India. The KX - r sum coincidence method was employed in these measurements. A high resolution(FWHM=180 eV at 5.9 keV) detector coupled to an ADCAM 100 data acquisition system was used for the detection and the measurement of X and y- intensities. 131Ba isotope was obtained from BARC, Bombay and studied with the same system. The results of these studies are compared with the theoretical values and reported in this paper. 161 159 161 Ho : Produced via Tb(«,2n) Ho (Ti/2= 2.48h) at a beam energy of 30 MeV and a current of 500 nA. The X- and y- spectrum of present interest is shown in figure 1. The final peak areas were obtained after applying the usual corrections. The P experimental and theoretical values were determined using the standard relationships 1-2 . The P values to the concerned daughter levels are given in table 1 together with the theory. Produced via 1/i0Sb(a, 2n)iZO I (60. 2d ) at a beam energy of 28 MeV and a beam current of 200 nA. The P value(experimental and theoretical) to the concerned daughter 125Te level was deduced as in the previous case and is given in table 1. 131 Ba: The P values to the concerned levels in the K 131 daughter nucleus Cs were also obtained experi- mentally and theoretically and are given in table 1 CONCLUSIONS : 1. The experimental and theoretical values are in agreement with the theory except in the case of 7/2~ * 7/2 EC transition in the 1 fi 1 decay of Ho. 2. An attempt to obtain theoretical P values by assuming different mass
relationships to get Q has shown that the PfC is insensitive to (3 above 200 keV. The results in 131 3 Ba are in agreement with those of Sahota et al REFERENCES : l.G.Sree Krishna Murty et al J. of Phys. G 16(1990)1095. 2.M.V.S.Chandrasekhar Rao et al Z. Physik A 335 (1990)25 3.H.S.Sahota and T.Iwashita Phys. Rev C37 (1988) 2143 TABLE 1 LEVEL PK VALUE ISOTOPE ENERGY E.C. (keV) IN TRANSITION EXPERI- THEORY DAUGHTER MENTAL 161 25.65 HU o 7/2~—•5/2~ 0.823±0.019 0.833 103.07 7/2 —•7/2 0.74810.032 0.831 125j 35.46 5/2+-»3/2+ 0.82510.038 0.862 131 620.11 + + Bn a l/2 —>l/2 0.87610.031 0.861 373.23 l/2+->3/2+ 0.88110.046 0.864 X. GAMMA AND SUM SPECTRUM FRO** Ho-161
xio'
E- :=> o 1 -
ENERGY (keV) ^-PROCESS CONTRIBUTION TO ABUNDANCE OF 180 Ta P.C.Sood*, R.K.Sheline+, R.W. H©ff@ and A.K.Jain^ * Physics Dept., Banaras Hindu Univ., Varanasi 221005 + Florida State Univ. Tallahassee FL 32306 USA @ Lawrence Livermore National Lab. Livermore CA 94550 USA $ Physics Dept. Univ. of Roorkee, Roorkee 247667
Nature's rarest stable nuclear species is a high-spin excited isomer of 180 Ta whose abundance cannot be explained by conventional processes of nucleosynthesis. While examining this puzzle, Beer and Ward /!/ postulated its production through off-the-main line s- and r-processes via a small P branch from 5.5 h 8" isomer of 180 Hf, The s-process contribution via production of the latter isomer from neutron capture in 179 Hf has been established 111 accounting for 22% of the 180 Ta abundance. Additional contribution to this channel may come from the post r-process A decays in the A = 180 mass chain through a fractional(f^j) feeding of the 180 Hf isomer from 180 Lu decays. Two different experiments /3,4/ yielded conflicting values for fm which could be reconciled by assuming the existence of a high spin isomer (HSI) in 180 Lu with half-life t less than 3005. Whereas (n,p) reaction studies 15/ revealed no evidence of HSI with l0
• - 'c.'.-.p'o. "• ' .• t :' : ijj Si.e i- •• - The two-i.ii: :-sf ' irlor ' .:..; 1, "••:;!•;. • ••r^r:.'.1S in ho odd-odd •• ;••; ••;•".. ir:
7 evaluated using the observed excitation energies for the single particle orbitals from the spectra of (A-l) isotone/ isotope with the addition of the zero-point rotational energy correction and the residual n-p interaction energy contribution. The single particle excitation spectra takes into account the effect of hexa-decapole deformation which is found to be particularly significant in the location of 9/2[5i4] proton orbital in these neutron-rich nuclei. Revised location of the 9/2[624] neutron orbital based on recent particle transfer reaction studies is included. Further guidance on 2<^ configuration assignments is sought from the beta transition rates /9/. Taking all these considerations into account v/e firmly establish GSB to have K71" = 5+with the 2qp configuration {p9/2[514] + nl/2[510]>. The HST has K77" = 9 with the 2qp configuration{p9/2[514]4n9/2[624]}predicted to lie above the 7*5 rotational level of GSB, to which it can decay by M2 transition in competition with the P branch to the 180Hf isomer leading into the sequential p decay to the 180Ta isomer. A systematic investigation of the AK = 4 M2 transition rate over the region reveals a hindrance factor of ^1(T permitting . a weak p-branch to the 180Lu-180Ta chain as the r-process contribution to the 180Ta abundance within the limits set by the already established s-process contribution to the 180Hf-180Ta chain /2/, consistent with all the available experimental conclusions /3-6/. 1. H.Beer and R.A. Ward, Nature 291, 308 (1981). 2. F.Kappeler et al. Reports Prog. Phys. 52, 245 (1989). 3. W. Eschner et al. Z. Phys. A317, 281 (1984). 4. S.E. Kellogg and E.B.Norman, Phys. Rev. C34, 2248 (1986). 5. K.T. Lesko et al. Phys. Rev. C34, 2256(1986). 6. E.Runte et al. Z. Phys. A328, 119 (1987). 7. K. Rykaczewski et al. Nucl. Phys. A499, 529 (1989). 8. P.C. Sood et al. Proc. Conf. on 'Nuclear Structure in the Nineties', ed. N.R.Johnson (Oak Ridge, 1990) Vol. I, p. 236. 9. P.C. Sood and R.K. Sheline, Atomic Data & Nucl. Data Tables 43, 259 (1989).
8 AN EMPIRICAL MODEL FOR 3QP ROTATIONAL BANDS Kiran Jain and Ashok K. Jain Deptt. of Physics, Univ. of Roorkee, Roorkee-247 667
When a pair in an odd-A nucleus breaks, three- quasi-particIe (3qp) states of four kinds (nnn, PPP. pnn and ppn) become possible each having four resultant K -- |Ki±K2±K3|. A residual interaction splits these four intrinsic states. An empirical model to describe the 3qp multiplets is proposed. We assume that i) the excitation energy of a given configuration is a sum of each of the odd nucleon excitations and is taken from the experimental data for neighboring odd-A nuclei i.e. 2 2
_ rt3Eo I |[<5., rt(l)EN n 3 £<2,3>,0 2,3 1 I K
800
600
CM
i tu
200-
- 7/2
AW Fig.l : Energies of 3qp states for Lu : arrows show spins for unlike(thick) & like(thin) particles.
10 VIQH SPIN STATES AND SUI'KHDKrOJtMATJON
Uijny Agr.wal mid C It. i'r.id.ir.ij Inslilulc Of i'liysirs, Hliubancswar 7f>l(tO.r>
We report deformed 11F and anqular mimionlum jirojrrtii'ii rril for tho superdefoniK'd Ijnml in ""I'd sliid/nl rv|>"nmi'itfa!!v !/)' Stephens nt nl|l| . Our inoclrl riiiisislt of Uio 'w« nisjor shells for die protons anil itciiUon.i. Tlio Rii|nvnlrf 0.98-128_ 1121 -0.0732-1 1/2- 0.7C185. -(J..ri776-I 5/2+ 0.64412 JJ21 -0.68496 7/2+ 0.33605_ -I 17288 1/2+ 0.19277_ -2.97C33 3/2 + -0.70007 5/2+ -3.29902 5/2+ ni -0.82287 3/2 -5.R57G5 1/2^ -3.57004 3/2+ -G.18900 3/2+ -3.62656 1/2+ -7.HC090 1/2+ -5.178G9 1/2+ -9.49040 9/2+ -7.51515 9/2+ -11.42270 7/2+ -8.96040 __7/2^ -12.65443 1/2- -10.61142 1/2- -13.13076 5/2- -11.00768 5/2+ -13.729(55 • M fil'^a 2.5- 2/2- -13 7025! r>/2v -11.60613 3/2- -12.18855 3/2v -15.11232 3/2 * -15.41205 1/2 ^ 1/2* -12.47501 -17.09232 3/2~ -11.2815) ..3/?- -14.53901 1/2- -20.922CJ l/2_- -17.71795 1/2- 11 The superdeformed structure is simultaneously a more deformed and more rotation aligned configuration.The deformation parameter 0 for the ground band is .18 and that of the siiperdeformcd band is .3 in our calcu)ations.The superde3formed band splits up into two brandies with the even angular momentum branch lower in energy and having considerably more rotation alignment. Reference 1. A. O. Macchiavelli et al, Phys. llev. C38, 1088 (1988). YRAST TRAPS IN 152Er M.Pajaaekaran and D.Caleb Chanthi Raj Department of Nuclear Physics, University of Madras, Guindy campus, MADRAS One of the main interests in studying very high spins is to find Yrast traps. The phenomena of yrast traps is related to axially symetric nuclear shapes rotating around its symetry axis. The study of shell effects for a rotating nuclei becomes all the more important because Isomers are expected to appear as a result of interplay between the shell effects and a smooth trend charecteristic of a liquid drop .nodel contribution to the total energy of the rotating nucleus. For this reason we arc. interested in calculation of total energy and shell correction as a function of angular momenta. We prescribed a single particle density of states in our earlier work N] and showed how shell correction can be obtained for different angular momenta by the lagrangian multiplier method. We use the same method to got the shell correction, and the form given by Myers and Swiatecki [2] to get the macroscopic liquid drop energy of a rotating nuclei. The sum of shell correction and macroscopic energy would give the total energy. The single particle levels for protons and neutrons with spin projections are generated using Nilsson Hamilton for biaxially deformed 13 nuclei. The angular momentum is generated by u.v-.!.(.j Jagrangian multipliers We have chosen a3/Er for our study because experiments have shown that ^^Er is non- collective for a fairly wide range of angular momenta. In our calculation we sfie *"pr j_s oblate at ground state with a shell correction of -1.87 MeV. The nucleus remains oblate rotating with its syraetry axis along the rotation axis till 40 h. The yrast sequence is generated using particle-hole excitation across the tilted fermi surface till I = 40 h. We follow Andersson's[3] condition that all states I that are lower in energy than the generated lowest 1-1 and 1-2 states are considered 'traps'. Consequently we observe yrast traps for l-*2£r occuring at I = 11, 16, 28, 37 h. Traps have been observed at I = 16, 28 h experimentally. We observe that traps occur at a given I, if its configuration differs from the neighbouring states. This would possibly slow down the corresponding electromagnetic transition, thus leaving a chance for the existence of an isomer. References : 1) M. Rajasekaran and D. Caleb Chanthi Raj, Nucl . Phys. Symp. (India) 32B, 98 (1989). 2) W. D. Myers and W. J. Swiatecki, Nucl. Phys. A81, 1 (1966). 3) G. Andersson, Hollstron, G. Leander, I. Rangnarsson, S. Aberg, J. Krumlinde, S. G. Nilsson, Z ,S?.ymanski , Nucl. Phys. A309, 141 (1978). 14 STUDY OF BETA SOFTNESS IN 158BY J.B. Gupta and H.H. Mittal Ramjas College, University of Delhi, Delhi-110 007 The nuclear shape phase transition from spherical to axially deformed has been of interest to collective nuclear structure theory/1/. However, the changes in nuclear pattern due to a transition from /3-soft to /3-rigid has received less attention. Recently, Gupta et al./2/, in their application of the dynamic pairing-plus-quadrupole model of Kumar and Baranger/1/ to study upto 7 bands in Dy ("here the 2j3 level 1bgs crossed over 2v in contrast to a lower 2*0 in Dy) there is ambiguity in the input quadrupoie strength and core re-normalizing factor affecting the kinetic coefficients. So that the distinguishing features of /*-, Y~vibrational bands decay to g-band, were not reproduced. For example, t!ie usual greater E2 decay strength of 2y to 0g compared to 2^-&j transition was not obtained and this also affected the ^-g BE(2) ratios which deviated from experiment/2/. To study this problem further , we have studied, the spectral features of Dy in the Interacting Boson Model (IBM-l)/3/. As a calculational tool, the phenomenological IBM provides compelete freedom in the various interaction terms of Hjg^, by a least square fit to the input spectrum. Ir. Dy, we input a total of 16 levels of g, Z9 and /-bands and obtained a fit with an average rms deviation of 34 keV for the lowest 12 levels. However, the deviations are large for 10g» 8*s and 7y, 8yand higher levels. In the T boson operator E2 + + (2) + (2) T = eB[(d s + s d) + X(d cf) ] we took eg=0.13 e.b. and X--0.69, then IBM reproduced B(E2,2g-0g). The 2y -0 value is half of experimenc and 2.a -0 value is 10 times weaker, but 15 •the large decay strength of y-g is obtained, as opposed to the DPPQ model results for Dy where in ft-g, strength is twice of the V~S> in opposition to experiment. This also worsened the /S-g B(E2) ratios prediction in DPPQ model calculation. The IBM values of B(E2) ratios are in fair agreement with experiment (Table 1). Thus the cause of failure in DPPQ model needs further investigation. Table 1. B(E2) values (in and their branching ratios in looDy. Transition Expt. DPPQ/2/ IBM-1 0.93(1) 0.79 0.92 0.030 0.014 0.016 0.011 0.024 0.001 2y-072 0.30(7) 0.17 0.58 2'-2/4 8. 9,( 3 6) 18 16.8 2«-0/2 0.62tll) 19 1.0 2rt-2/4 0.29 0.014 0.25 3y~2/4 1.42(18) 1.33 1.78 4y-2/4 0.12(2) 0.05 0. 21 Work supported in part by U.G.C., Govt. of India. References-" /I/ B.R. Mottelson and S.G. Nilsson, Phys. Rev. 99 (1955) 1614 K. Kumar, Nucl. Phys. A231 (1974) 189 /2/ J.B. Gupta, Nucl. Phys. (India) 31B (1988) 24 and J.B. Gupta, J.H. Hamilton, A.V. Ramayya (to be published) /3/ F. Iachello and A. Arima, The interacting boson model (Cambridge University Press, 1987) 16 The package ::iX' •'•:•'.: developed" for pe-;brm ing large scJe numerical ca;r.ii.i:.,-.•.•> n. space is used to investigate '.he structure of •':; ! 111- two neutron separation energies S (iv) quadrupole moments Q(:T) and the transition moments Q(o*—» 2*) = K167C/5) where we use T (v) magnetic g-factors; the general one-body Ml operator is used, (vi) B(E4'r) values, the E4 operator is taken to be proportional io r i (e,0) (vii) Isomer shift S(O (viii) Isotope-shift A(r") and (ix) Two nucleon rrnasferfTNT) cross-sections for (t,p) and (p,t) reactions. Explicit forms of the various operators, numerical values of the corresponding free parameters that enter in defining them and references to data are available upon request. Here are some comments on the results: 1) thit agreements shown in figs a-{ demonstrate that a truncated weak-coupling calculations is capable of describing the structure of Sm isotopes 2,i the matrix . dimensions' encountered are < 500; the calculations are performed on VAX881O at IPR, Ahmedabad 3) Otsuka and Sugita(OS)'' recently studied Sm isotopes, using Hanree:Bose(HB) approximation, with single set of (F,K) values while we had to use two sets;OS studied only energies and quadrupole properties. It should be clear that one should investigate (i) whether by enlarging the weak coupling basis one set of (F,K) values suffice, (ii) whether the HB gives equally good results for other observables or is the agreement shown by OS ac.i-'enta! (especially for vibrational nuclei) 4) The package SDGIBM1 aiiows one to easily calculate not only energies and B(E2)'s but also B(E4)'s, g-factors, occupancies, TNT etc which may not be the case with FIB 5) Scholten et al."' calculated in sd space, with neutron number dependent d-boson energies, all the observables given in figs a-L The gIBM results which are obtained with far less free parameters are seen to be better 6) EIBM predicts the energies of the \' level in '""'^Sm to be ~ 2.5 -*3 MeV with KMl*)'* 0.1 £. Experimental confirmation of this prediction and confrontation with scissor T state is clearly called for 7) The ratio of the sum of the TNT cross-sections to excited o* states to that of g.s o* shows a peak in the shape phase rmsition domain as seen in data .8) E4 distributions below 3 MeV excitation for ' ~ '5m are predicted. REFERENCES: 1. Y.D.Devi and V.K.B.kota : PRL Technical Note (1990) PRL-TN-90-68; Y.D.Devi .V.K.B.Kota and J.A.Sheikh: Phys. Rev. C39 (1989) 2057. 2.0-Scolten. F.Iachello and A.Arima : Ann. Phys. 115 f I97S.» 325. 3.T.Oisuka and M.Sugita : Phys. LettB 215 (1988) 205. 4. P.E.Garrett. D.G.Burke. Y.D.Devi and V.K.B^Kota: Arima Conf - Abstracts book (Santa Fe, New Mexico Mav 1990) p.57 17 G2n(MeV) R Ex {MeV) A(r2)(fm2) 3(r2)X!Cf3(fm2) B(E4)(-2b4) g + 2t cr(25°) (mb/sr) (mb/sr) -max o - .. o O tn en :\. I \ O * -- en — CO 18 IBM AMD THE DYNAMIC HF FERMI ON BASIS FOR Zn ISOTOPES Subrata Sarangi and Jitendra C.Parikh Physica . Research Laboratory,Navrangpura,Ahmedabad-380009. We propose a prescription to construct the s and d boson wave functions in the dynamical microscopic (fermion) basis from the Hartree-Fock(HF) solutions. The HF calculations are done for even Zn isotopes in ( P3/2- f5/2- P1/2* %^2^ four orbit model spc-ce with SDI as the residual interact ion. The boson wave functions (BWFs) and the SDI are in turn used to calculate the boson s.p. and 2 body matrix elements (MEs). These MEs define the IBM Hamiltonian /I/ for the isotopes considered. a. Construction of BWFs: The quadrupole-deformed parity-conserved HF orbits j m n> for the Zn isotopes are obtained using the HF code. From the occupancies of the orbits in the model space the BWFs are constructed in the following manner. 1. In terms of the occupancy occp(i) of the i model orbit we define c(i)=+ v occp(i)/N where N is the no. of valence v1 z particles. Note that ) c (i)=l. 2. We next define effective jk=±l/2> orbits as follows /2/: 4 ik=l/2> = Y ph(i)*c(i)*[j 1/2 > where ph(i) is the phase of the i orbit in the lowest k=l/2 HF s.p. state. 4 j - |k=-l/2>= 2 (-) *ph(i)*c(i)*| j. '.-1 3. From the determinant of these 2 orbits we project out the coupled normalized states of angular momenta L=0 and 2 and call them the s and d BWFs respectively. The general expression for BWF is : " ' kl k . I = i r,j 1 /2,j, -l/2iL,M^0>Kl/2 t 1/2 t |1 t . 19 where {X} = (L,M=Q,t=l,t3=±l), set of all boson quantum numbers. We have t, --1 for neutron(n) and proton(p) bosons respectively. Note that for a K~Z nucleus the n and p BWFs are identical. We have obtained the BWFs for all even Zn isotopes. As an illustration we give below the ones for Zn (N=Z). 2 2 2 | s>= i bT _n >=. 741 i ( 3/2 ) : 0>+ . 4851 ( 5/2 ) : 0>+ . 465 j (1/2) : 0> 3~~ 2 [d^ib^ _±1>=-.441j (3/2):2>+.298j(3/2,5/2):2> 2 B. Calculation of boson MEs: The s.p. boson energies are the expection values of 1+2 body fermion Hamiltonism with 3DI in the boson space defined above. The boson 2 body reduced non-antisymmetrised MEs are written as L i J , ZJ L3JL4J By varying the (x }s through the allowed values of L and t all boson MEs can be calculated. These matrix elements are computed using standard shell model methods /3/. For Zn^ssjjVJIss^.Q T=C|---0.054 We would like to thank Professors 3.B.Khadkikar,V.K.B.Kota and S.P.Pandya for valuable discussions and suggestions and Professor CR.Prah3.raj, Institute of Physics, Bhubaneshwar for supply ing the KF o.jd-3. /I/. A.Arima ,id F. Iachello, Afin.Phys.^Q (1976) 255 'Zs. J.C.Parikh and K.H.Bhatt,Nucl.Phys.Al O3 (1967) 499 /3s. J.B.French et al. sec. 2. 1.3, Complex Spectroscopy Advances in Nuclear Physics, Vol.3. 20 STRUCTURE OF DOUBLY ODD ISOTOPE 82Br R.Sahu Physics Department, Berhampur University, Berhampur-760007, and S.P.Pandya Physical Research Laboratory, Ahmedabad-380009 The doubly odd nuclei have a very rich structure and give a valuable insight into both the proton and the neutron configurations at different excitation energies and the nature of the mean field which results in various bands of states. These nuclei, therefore, present a greater challenge to "theorists. Funke et al [1] have recently summarized many useful systematics for odd-odd bromine isotopes. We use our deformed configuration mixing shell rnpdel based on HF states to study the odd-odd nucleus Br. This model has successfully been applied to study many nuclei in this region [2]. We consider a closed inert core of Ni with Z-28 and N-28 protons and neutrons occupying the active orbits lpj<2, 0f^2> lPi/2 anc* ^9/2' ^e sm§'e particle energies for these spherical orbits are taken as 0.0, 0.78, 1.08 and 3.50 MeV, respectively. We choose the effective interaction in this configuration space derived by Kuo and modified by Bhatt [3]. With the above input data, we cagey out a straight forward Hartree-Fock calculation for Br. The prolate solution thus obtained is shown in Fig. 1. An analysis of the HF single particle spectrum shows that the odd neutron occupies the k=7/2 state, whereas the odd prcton occupies the 3/2" state, so that the ground state configuration has K = 5 . By performing tagged .HF calculation, we obtain three more intrinsic states with K = 2 , 6 and 1 . Good angular momentum states are projected from each of these intrinsic states and then a band mixing calculation is performed to orthonormalize them [4]. The calculated K=5 and K=2" bands are shown in Fig.2. The agreement is quite satisfactory. Similarly we obtain K=l and 6 intrinsic states by performing lplh excitations As has been done above for the negative parity bands, we have also projected good angular momentum states from the 21 positive parity intrinsic states and performed band mixing calculation. The relative spacing of the levels in K=6 and 1 bands agree quite well with experiment. However the band head energies are higher than the observed states by about 1.6-1.8 MeV. This could be due to assumed energy (3.5 MeV) of the spherical g-orbit being too high. It is also possible that the limitation of the configuration space affects the seperation of the negative and positive parity bands. References L.Funke et al. Z. Phys. A324(1986)127 2. R.Sahu and S.P.Pandya, J.Phys. G 16(1990)429 and references cited therein. 3. D.P.Ahalpara et al. J.Phys.Gl 1(1985)735 4. A.K.Dhar et al. Nucl.Phys. A238( 1975)340 5.0 t (M»V) p b •> •• 0.0 II "I «• *i 2 > -5.0 b '•-. •• •. -10.0 E=-4I.43 MeV 0*21.81 bZ Fifl. I K* 5~ 22 -TAGNETIC MOMENTS IN CRANKED HFB APPROACH Saha Ii'Stir.ute of Nuclear Physics, Calcutta - 700 009 The Cranked Hartree-Fock-Bogoliubov (CHFB) formalism has been used by several workers [1-31 to study variation of g-factors along yrast line in a number of well-deformed rare-earth nuclei for which experimental data are available. Although, all of them are unanimous in attributing the spin variations of the g~factors io rotational alignment effects, r.heir calculaiional details differ in the choice of single ,-artlcle energies, form of residual interaction and their strengths etc. based on their predictions, certain inferences about different aspects of the CHFB formalism have been drawn, which, in our opinion need closer scrutiny. The g-factor variation along the yrast line sensitively depends upon the rotational alignment effect which in turn depends upon the position of the high spin intruder orbitals vis a vis the Fermi level in any nucleus. Therefore, we think that one should clearly delineate the effect of the choice of single particle energies on the predictions of g-factors in the CHFB formalism before making any study on the effect of inclusion of higher order terms in the residual interaction, adjustment of its strength or projection of good particle number and of good angular momentum .With this in view, we 154 have calculated the g-factors for yrast states in Sm, 156,158,160Gd 158,160,164^ 166,168^ an(J 170,172,174Yb nuclei using the pairing-plus-quadrupole hamiltonian of Baranger and Kumar [4] with the strength parameters prescribed by them. The calculation is performed with two sets of spherical single particle energies. One set [BKJ is taken from Baranger and Kumar [4J, other |NILJ from Nilsson et al.'s [5] prescription. The results for Sm, Gd, Er are shown in table 1. The sensitivity of the calculated g-factors on the input values of single particle energies is clearly revealed. Implication of these results will be discussed in detail. 23 TABLE 1.Calculated and experimental g-factor ratios, gr/gr gI '' g2+ Isotope In - exp.a [NILI [BK1 154 + Sm 4 + 0.99(10) 0.96 0.91 6 + 0.96(11) 0.90 0.77 8 + 0.92(13) 0.82 0.62 10 0.87(18) 0.73 0.47 158 Gd 4+ 0.98(1) 0.98 0.97 6 + 0.95(4) 0.94 0.39 s+. 0.90(7) 0.90 0.61 10+ 0.84(11) 0.86 0.36 166 Er 4* 0.97(5) 0.94 0.90 6, 0.83(9) 0.83 0.76 0.74(13) 0.70 0.62 10+ 0.62(25) 0.58 0.53 a Ref.[6] References: [1] A.\T. Mantri et al., Phys.Rev.Lett. 47(1981)308. [2] A. Ansari et al., Nucl.Phys. A415(1984)215. [3] K. Sugawara - Tanabe and K. Tanabe, Phys.Lett. B207(1988)243. [4] M. Baranger and K. Kumar, Nucl.Phys. Al 10(1968)490,529. (51 S.G. Mlsson et al., Nucl.Phys. A131(1969)l. 16] P. Raghavan, At.Data & Nucl.Data Tables, 42(1989)189. 24 --Ji .; ..ngle-particle energies in the f-p shell V.Potbhare and N.Tressler PI; Department, M.S.Univarsity, Baroda. The effective single-particle energy of an orbit in the ground-state region is a convenient concept to understand the structure of nuclei. This can be obtained experimentally, using the following relation/1/ between the centroid energy for orbit s of a particle removal reaction £g, the centroid energy for orbit s of a particle addition reaction £g and the occupancies of orbits in the target nucleus. All of these are measurable via single nucleon transfer reactions. The relation in proton-neutron space is r ( g ~(E)-E)ns(E) = 63 + Int(E) {1- Sst/(2jt+l)} t where § s(^) ^s tne effective single particle energy(S.P.E) of orbit s with angular momentum js, E is the ground-state energy of_the target nucleus, ns is the occupancy of orbit s, Ws^ is the average two- body matrix element between orbits s and t and 6S is fhe external single particle energy of orbit s. Proton and neutron orbits are labelled separately. Recently, Boboshin et.al./2/ have published values of proton effective single-particle energies for four nuclei in the f-p shell using the first part of the equation 1, the input for which comes totally from th^ experimental data. The second part of the equation is the interaction dependent and can be calculated completely using the techniques in Spectral Distribution Methods/3/. We have used two standard Kuo-Brown interactions: (1) KB interaction renormalised with respect to 3p-lh excitations and (2) KB10 interaction which is the f-p shell part of ten-orbit interaction due to Kuo. Table 1 gives the ~£s values for these two interactions and Table 2 gives the coulomb corrected values for proton orbits alongwith the experimental values from reference 2. 25 Tabl' ,: frective 5.P.E. in AeV> - - «|s(g.s. ) orbits Heutron orbits Nucl ..•- i/2 p3/2 pl/2 f5/2 f'7/2 p3/2 pl/2 f5/2 46 F..'3-j •<.'..9 10.] 8.9 8.9 11.7 9.3 8.0 7.3 TI XB i.4 8.7 7.3 6.0 10.2 7.8 6.3 4.6 48 KB 10 15.1 12.4 11.5 11.7 12.6 10.4 9.1 8.2 Ti KB 12.7 9.9 8.6 7.6 10.4 8.1 6.7 4.9 50 KB10 15.9 13.3 12,3 12.6 14.7 1.2.2 11.0 10.9 Cr KB 12.9 10.3 9.2 7.9 11.8 9.3 8.1 6.5 56 KB10 21.1 18.4 17.3 18.1 18.6 15.9 14.4 18.6 Fe KB 15.8 13.7 12.9 10.8 13.6 11.3 10.5 8.4 Table 2: Coloumb corrected -fs(g.s) for proton orbits Nucl. Int. f7/2 p3/2 pl/2 f5/2 46 KB10 5.1 2.2 1.0 1.0 Ti KB 3.6 0.8 -0.6 -1.9 EXPT 5.4 2.5 2.0 0.7 48 KB10 7.3 4.6 3.7 3.9 Ti KB 4.9 2.2 1.0 -0.2 EXPT 7.0 4.0 2.0 1.9 50 KB 10 7.6 4.9 3.9 4.3 Cr KB 4.6 2.0 0.9 -0.4 EXPT 6.5 2.1 1.9 2.7 56 KB10 12.3 9.6 8.6 9.3 Fe KB 7.6 4.9 4.2 2.0 EXPT 8.9 4.6 3.2 4.5 One can see that KB10 interaction gives results much closer to the experimental values in the lower f-p shell. However, as more and more nuclei are added, the renormalized KB interaction improves very rapidly. More experimental results are needed for further meaningful comparison. A detailed study is under progress. References: /I/ J.B.French, Proc.Int.Sch.Phys.Enrico Fermi Course 36 ed. C.Bloch (Academic Press N.Y. 1966)385. /2/ I.N.Boboshin et.al. Nucl.Phys.A496(1989)93-107. /3/ V.K.B.Kota and K.Kar,Pramana 32(1989)647. 26 FIELD THEORETIC STUDY OF THE PROPERTIES OF *He - A VARIATIONAL APPROACH P.K. Panda, S.K. Patra, S.P.Misra Institute of Physics, Bhubaneswar-751005, India. Recently attempts were made to study nut lear matter using non- perturbative varitional techniques in quantum field theory [1]. Here cr-mesons which is not observed is not used. Those effects instead are simulated through isosinglet scalar cloud of pair of pions with a coher- ent state construction along with the nucleons. The coherent states correspond to the quantum picture of classical fields of Waiecka model [2]. The difference however is that the nucleus contains with a small probability of a finite expectation value for off mass shell scalar isosin- glet pion pairs. The method is here applied to 4He. TheA He state is constructed with four nucleons and a cloud of off mass shell quantum pion pairs as stated above. Thus we construct a state of momentum p with transla- tional invaiiance [3] as | 4/fe(p) >= JVfl(27r)-3/2 f JV(x)* exp(C(x)y exp(ip.x)dx \ vac > In the above, wavefunctions of nucleons are included in Af(x). exp(C(x)t) | vac > is a coherent state with pion pairs given by = / dz2. The normalization constant NR is defined through <*He(p)\4He(j?)>=6(p-j?). The energy expectation value is given as 4 4 E = (2TT)3 < ife(0) | W(0) | #e(0) where H(x) is the hamiltonian density of the system including nuclcons, pions and interactions.. Thus E is a functional of nucleon wave function as well as pion dressing- The nucleon wavefunction and the function f(x, 2*1,2*2) for pion dressing are determined by minimising the energy E. The parameters of the present calculation with a simple ansatz are 27 adjusted to get the correct binding energy. Pion number density of the off mass shell pions per nucleon seems to be about 2 /.. It is next examined to see if the off shell pions in the definition of the state can be observed. The pion pair is charge neutral, since they are isosinglet. However, through their coupling to two photon vertex, it is seen that 7r+7r~ annhillation can lead to reactions with the emission of two photons when AHe is excited during a collision. This is suppressed by a2, but, is not suppressed in energy through kinematics. With the above picture of 4ife, the reaction where H is a heavy nucleus is examined. We wished to consider whether this can explain the anomaly present for unusual excess of large energy photons emitted in the experiment of Baba et al [4]. The present calcu- lation indicates the following scenario for high energy photon emission from the above process. (i)The high energy photon must be produced in pairs i.e. with another photon of reasonably high energy. The calculations indicate that with a photon of higher energy ranging from TO MeV to 20 MeV, there shall be a second photon with the average energy of around 4 to 5 MeV. (ii)The two photons are more often perpendicular to each other than otherwise. The calculations are at present incomplete regarding absolute mag- nitudes of the cross-section. REFERENCES [1]. A. Mishra, H.Mishra and S.P.Misra Int. J. Mod. Phys. A5 17 (1990) 3J91; S.P. Misra, Phys. Rev. D35 (1987) 2607. [2]. J.D. Walecka, Ann. Phys. S3 (1974) 491; B.D. Serot and J D. Walecka, Adv. Nucl. Phys. 16 (1986); C.J. Horowitz and B.D. Serot NP A368 (1981) 503; P.-G. Reinhard et al. Z. Phy. A323 13 (1986). [31. M. Bolsterli, Phy. Rev. D13, 1727 (1976). |41. C.V.K. Baba et al. Private communication. 28 ON THK CONTROVERSY OF BAA DATA OF A?He AND \°.He A A A A A A Mohammad Shoeb and Q. N. Utanan i * Dept. Of Physics , A. M. U. , Aligarh 202 002 ** Dept. Of Physics , J. M. I. , New Delhi - 110 025 All the analyses [1] so far have failed to explain simultaneously the BA . data of AAHe and A .Be. Since the AA i »A AA event leading to B,. data of . »Be has been confirmed by independent workers this led to doubt the "germinness" of the event leading ho . <, He. This has created a lot of controversy and evoked muc:; interest in these system in the last two decade. In this note we have investigated the possible cause which might have lead to this controversy. In our earligr variational Monte Carlo analyses[2] of few body systems ( "^He & .Be ) the effect of space-exchange AN potential was found to be quite significant and core polarization energy also turned out to be important. Therefore , the effect of space exchange AN potential is investigated to resolve the incompatibility in the B,. data of A*He and ^Be . The . .He is treated as six-body system and , .Be is considered as partial Ly ten-body problem in A-A-ot—a model. The variational wavefunctions is written as t:he pruduct of two- and three- body correlation functions. The two-body correlation functions are obtained from Schrodinger type two-body equation with appropriate effective potential while three-body correlation functions have analytical form. The Malfliet-Tjon potential is employed for NN system and that of Chien and Brown for CA-O. . Urbana type AN and A A potentials are used and the former is consistent with the Ap scattering data and has space exchange parameter f. =0.25 . The multidimensional integrals involved in the variational 29 calculation of energy -B.. of each system are computed using Monte-Carlo technique alongwith Metropolis random walk method (for details see ref. 2 and 3). The result of our preliminary analysis indicates that depth of AA potential VJJA=-7.0 Mev fits the BAA data of AAHe and A^Be for space exchange AN potential parameter^ =0.25, However .setting space exchange parameter e equal to zero leads to inconsistency in BAA data of the same nature as reported earlier. The ir .ease in depth V?. compared to older value -6.4 due to Bodmer and Usmani [3] seems to be consequence of inclusion of space exchange AN potential. The depth V?A=-7.0 Mev gives a bound state for AA system (called H particle) which signals the importance of quark structure for such systems. This result is consistent with the prediction of bag model [4] and quark cluster model [5]. References [1] R. H. Dalitz et al Proc. R. Soc. London A426 (1989)1 and refrences therein [2] M. Shoeb and Q. N. Usaani Symp. on "Nuclear Physics " Vol. 32B(1989) ; M . Shoeb ; Q. N. Usmani and and A. R. Bodmer submitted to Phys. Lett. B [3] A. R. Bodmer and Q. N. Usmani Nucl. Phys. A468 (1987)653 and references therein [4] See refernces in [1J [5] U. Straub et al Nucl. Phys. A483 (1988) 683 30 VALIDITY OF THE MULTI-PARTICLE SHELL-MODEL WITH TWO-BODY EFFECTIVE INTERACTION Y.K. Gambhir Deparn sent of Physics, I.I.T., Powai, Bombay 400 076 and F. Monti, G. Bonsignori and M. Savoia Department of Physics, University of Bolognsa, Bolognsa, Italy The multi-particle shell-model calculations can only be carried out in practice in highly truncated spaces employing normally two-body effective interactions. On the other hanG Quantum Mechanics tells us that the truncation of the Hilbert space does introduce three-,four-,.... body correlations, even though the starting Hamiltonian contains one- and two- body parts. The question then is that "are these three-,four-,.... body correlations negligible or how to construct the optimal two-body effective interaction appropriate to the desired truncated space". This complex question, though investigated by several authors in the past, still awaits a conclusive answer even formally. Numerically, explicit calculations for three- body correlations have been performed only and that too in the 2s- 1d region and for a single 1f7yp shell. Neverthless, the usage of effective two-body interactions and operators has now become a useful standard accepted practice in nuclear structure calculations. 1 We have analysed this problem using projection method and have calculated three-body and four-body parts of the correlations for Z = 50 isotopes and for N = 50 and N=82 iso- tones employing G-matrix, as well as phenomenological and empirical sets of two-body matrix elements. We find similar ccnclusions in all the cases considered viz: -The three-body and four-body parts are rather small and generally have opposite signs, and therefore cancel each other. Only rarely they add and their sum total become significant. As a sample case we show the results for ^Je (N=82 isotones) obtained with Sussex interaction. Two-,three- and four- body parts in the truncated space (2d and 1g ) for J=0 states are listed in the Table, while the calculated spectrum for low-lying J=0 and 2 states is displayed in the Figure. 31 Our analysis, therefore, lends support to the usage of the two-body effective interaction in the multi-particle shell-model calculations in relatively small model spaces. 1 F. Monti, G. Bonsignori, M. Savoia and Y.K. Gambhir; Phys.Rev.C*n (1990) 1311 and the references cited therein. ^ (J -7, .• The states are defined as: |1 >«=> Uff Wfi ^ |2>"H(?I)n(T I ° ' LL M> |2> |3> |4> |5> J6> 3.18 - 1.18 0.39 •;.3i 0.00 0.00 I1> [0.64 [0.25 [-0.33 [- 0.23 [-0.11 [0.00 - 0.26] -0.12] » 0.28] * 0.08] • 007] - 0.04) - 1.38 • 1.69 -0.60 -0.11 0.020 - 1 25 |2> [0 18 [-0.06 [009 (-0.18 [0.07 [0.28 tOOOJ - 0.03) - 0.051 -0.351 -0.12] - 0.31] 0 63 -0.60 3.15 0.16 -0.35 0.27 |3> [-0.06 [-0.04 [0.01 [0.08 [0.05 [- 0.76 * 0.14] - 0.05] + 0.06] - 0.43] • 0.01) • 0 66] 0 59 -0.11 0.16 3.88 -0.06 0.22 |4> [- 0.05 [- 0.02 [0.14 [- 0.02 (0.23 [0.17 - 0.35) * 0.02) -0.14| • o.i«; -0.201 -0.18) 0.00 0.01 -0.42 -0.11 2 15 002 |5> [- 0.27 [- 0.02 (0 09 (0.06 [0.01 )- 0.05 • 0 29| -0.13) * 0.11) • 0.011 - 0 06| • 0.04] ii • *": 0.00 - 1.47 0.45 0.42 0.02 0.19 JO. 00 |- 0.01 1-0.19 I- 0.01 [- 0.10 [- 0.07 • 0 55] -0.12] - 0.20] - 0.98] • 0.02] • 0.061 EXPT H.t'4> H.,12) 300 -(74%) " (S7%) 200 - (96%) 0D0 '• - (100%) SIGNATURE EFFECTS IN ODD-YB ISOTOPES C.R-Praharaj and A.K.Rath Institute of Physics, Bhubaneswar-751005 Study of the signature effects in odd-A rare-earth nuclei has been a topic of interest for the last several years1. Using a projected HF 2 method we explain the signature effects in the t13/2 rotational bands of odd mass Yb nuclei without assuming gamma asymmetry. For our axially deformed HF calculation we take one major shell each for protons and neutrons outside the l32Sn core. Nilsson single particle energies and surface delta residual interaction are used in our calculation. The lowest 1*13/2 rotational bands in 159~169y& obtained by angular momentum projection from deformed HF configurations are compared3 with experimental spectra. We get signature splitting of the right kind as seen in the experiment: the a = ^ branch being energetically low- ered than the a — -3 branch. In general large contribution to angular momentum from a few nucleons means a lowering of collective rotation and a consequent lowering in energy. As shown in Fig la and lb the rotation-alignment (/iJ3/3) in the a = £ branch is large compared to the a = -\ branch and hence it is energetically lowered. E2 and Ml transition rates are calculated using effective charges of 1.5e for pro- tons , .5e for the neutrons and free nucleon g factors for protons and neutrons. Effect of rotation alignment on the signature dependence of electromagnetic transitions are studied. We find signature inversion in B(E2;I-+ I-l) values for the odd-A Yb isotopes with N>95. We have shown-in Fig 2 the signature dependence in the B(E2;I-* I-l) values for the K=£+ and §+ bands of l63Yb and l65Yb nuclei respectively. Since Fig.l: Ab'gned and collective angular momenta for the A+, %* bands in 163'165K6 nuclei respectively. 33 I [ft] Fig.2: A/ = 1 B(E2) values for the l/2+ and3/2+ bands in respectively, b is barn. E2 transition is dominated by the collective motion of the particles, I —tf-1 E2 transitions in 163V6 show a charecterstic signature dependence (upper curve in Fig.2) which is in phase with the signature dependence 165 of Icore in Fig la. The / -+I-1 E2 transitions in Yb are very collective at low spins (till y ft) and show no signature dependence, a trend that is also apparent in lcore and /;13/3. Beyond Qh where the signature depen- dence in Icore and /tl3/2 becomes pronounced, the I->-1-1 E2 transition matrix elements suddenly drops by an order of magnitude and shows considerable signature effects. To conclude, angular momentum projection from deformed con- figuations is able to account for the signature effects in odd-A Yb nu- clei. Although signature effects in rare earth nuclei have often been parametrised in terms of gamma asymmetry1 by maay authors we find that it is rotation alignment and not gamma deformation which is re- sponssible for the signature dependence. 1. Ikuku Hamamoto Invited talk, conference on "Nuclear Strucure in the Ninties", Oak Ridge, April 23-27, 1990 2. C.R.Praharaj Jou.Phys.G14(1988)843,Phys. Lett 119B(1982)17 3. A.K.Rath and C.R.Praharaj Contributed paper to the International conference on "High Spin Physics and Gamma-Soft Nuclei" .Uni- versity of Pittsburgh, Pittsburgh ; Preprint IP/BBSR/90-26,27 34 STUDY OF N=88 AND N=90 ISOTONES IN THE IBM-1 H.M. Mittal and J.B. Gupta Ramjas College, University of Delhi, Delhi-110007 The phenomenological interacting boson model (IBM-1) /I/ describes the collective properties of atomic nuclei in terms of the s and d boson excitations. The parameters of the IBM-1 Hamiltonian are determined by a fit to the energy spectrum of the given nucleus, and using effective charges, the transition rates can be calculated. Attempts have been made to find a common set of parameters for a group of nuclei (isotopes or isotones) so that the varying nuclear structure with N, Z may be obtained by varying the total boson number (Ng). Chuu et al /2/ used this method for the N=88, 90 (Ba-Yb) isotones and claimed a good fit with a single set of eight parameters of Hjg^. Since the g-band spectra of the isotonic multiplets in the first quadrant of the Z=50-82, N=82~126 major shells vary slowly with Z /3/, a common set of parameters should be easier to obtain. However, we note that the main characteristics of the spectral variation with Z are not reproduced, e.g. in Ref./2/ the variation of E(02) with Z is not given at all (see Fig.l). Same is true for E(2y) state. Hence for a detailed study of a given nucluas? a fit to its nuclear spectrum is required. We have used a 4-parameter IBM-1 Hamiltonian H( €.ao, aj, a2) to study these N=88, 90 isotones. Our results are as follows: (1) The 4-parameters were determined by a fit to all known levels (I71"^ 10 ) for each nucleus, then ^IBM was diagonal!zed. (2) The rms deviations of our calculated energy spectra are much smaller than obtained by using effective HIBM /2/, without using the subshell effects (for N=88). (3) The variation of g-, P~, Y~bands and two higher bands with Z is reproduced fairly well. The fall and rise of E(02) with Z for N=88, 90 is 35 reproduced here in contrast to the linear rise obtained by Chuu et al.(see Fig. 1) Same is true for other band heads. (4) The relative boson energy £ =( G^ - €.g) is large here and varies with Z upto a factor of three. The other 3-parameters are small and vary much less for N=90 isotones, as expected/3/ for isotonic series in this region. (5) The calculated B(E2) values and B(E2) ratios for interband transitions also show a fair agreement with experimental data, and calculated Q(2^) agree with experiment. The detailed results and our calculation will be presented. Work supported in part by Univ. Grants Commission. REFERENCES /I/ F.Iachello and A.Arima, The interacting boson model (Cambridge University Press, 1987) /2/ D.S. Chuu et al., Phys. Rev. C30 (1984) 1300 /3/ J.B. Gupta, J.H. Hamilton and A.V. Ramayya, Int. J. of Modern Phys. A5 (1990) 1155 1200 o Ex 400 A Present x Chuu et al 70 Fig.l 36 194 MODIFIED ROTATION VIBRATION MODSL FOR Pt MUCL2US A.K* Varshney, D.K. Gupta*, K.K.Gupta^R.Prasad and R.K. Tyagi . Applied Physics Deptt., 2.H. 2ngg. Collage, A.M.U., Aligarh - 202002. (U.P.) +S.V. College, Aligarh-202001. ++ Govt. College Sarkaghat (H.P.). The platinum group of isotopes which lies on the boundary of the strongly deformed rare earth nuclei has become a subject of great interest both experi- mentally and theoretically. Platinum nuclei are neither good rotors nor good vibrators but lie in between rotational and vibrational cases. The nucleus 194 Pt is an anharmonic vibrator and one of the most interesting structures in the heavy mass transition region. It has become a focus of much theoretical and experimental work /l,2/« We performed the Rotation Vibration Model (RVM) calculations with three band mixing (RVM-3). These calculations failed badly in reproducing the observed energy spectrum, B(S2) values and branching ratios. We modified the three band mixing rotation vibration model (RVM-4) by introducing two"more parameter under the? assumption of different mass parameters for roT. M-on, bet a-vibration and gamms -vibration. The em .^y levels, B(32)'s and branching ratios have been calculated for 194 Pt using the relations given in references/3,4/. The -Boson. Expansion Technique (33T) results are given for comparison only. It is observed that the RVM-4 predictions are close to the experimental ones in almost all the cases. For 22—*0 /2. ratio the BST's value is hindered by a factor of 190 which in the present calculations deviates by a small enhancing factor of 1.6« 2 2 rat Similarly, for 23~* o/ i io, the BST value which is 8 times faster, has now been reproduced almost exactly. •Present Address* Physics Deptt. G.G.D.S.D. Degrae College, BAUNATH - 176125 (H.P.). 37 194 Table: B(E2)'s and Branching ratios in Pt (in units of e b ) TRANSITION RVM-4 R7M- 3 0.324(3) 0.341 0.343 0.324 °14- 22^ °1 0.0016(7} 0.0046 0,010 0.0051 2 —*• 21 0.423 (15) 0.324 0.491 0.358 4^ 21 0.449(22) 0.426 0.515 0.515 22 0.69 (39) 0.13 0.121 0.307 v* 5 °/h 0.0038 0.006 0.024 2xlO" 2.87 0.597 1.25 2/4i 0.S7 2 3~+ 4/2, 1.05 2.02 4.51 4.931 0.66 0.64 2/2l C«'7l 5.0 23- 2/°l 5.0 1.70 0.885 - 2 23- /°l 3.33 1.10 0.721 - 4 23- /°l 5.33 3.466 4.080 - -f Reference /2/. References: /I/. Nucl. Phys. A270, 317 (197 6) /2/. Phys. Rev. G 22, 888 (i960). /3/. Phys. Rev. C27, 872 (1983). /4/. Muovo Cimento A99# 1 (1988) and references cited therein. 38 • lio.. Oir'j-A .•H.'U.iO U\ Jd£ ) 'Ic-LiV T ' ' * ' .!.:-;- Vcrshnuy , K.X. Guo-o'*", /.P. 7irshne"y", J.K.GuntA*" ... Prar.-.-1 end .1.1'. Tyagi Apol.i^o physics .Deptt., Z.H. College of 2ngg. L i'ech., A..'".I;., Aiigarh - 202002. (L'.P.). + Go'-rc 'JcJ.l^^/ Sarkeghst. (i-i.?-). ->--}- s.v. Tollsge, Alicarh- 232001. 7Q .he nucleus w Kr has b^en the subject of several oxpsrimontal enc? theoretical investigations /I/. As the largo number of know?, yrast and non yract states and 22 transition probabilities provider z sensitive ;ns 'i'he non-axiality paremeter (y)x was corrputcd using the exocrimencel energy ratio i£2+ /^'4+ of Meyertervehn method /5/. Using this V£?lue of non-sxiality parameter (y)/ the energy levels* 3 (32) values and 3(i£2) branching ratios were calculated by relations given in reference /2/. i'he calculated values are given in table. It appears froni the table that the ARM 3 (22) values show a slow increase with increasing spin. However, the A;iM values are in satisfactory agreement with in the experimental uncertainties. The IBM values /!/ ar2 given for comparison only. It is observed that the A?>M ic cs successful as IBM for such a light nucleus. 70 2 4 T-.-.ble; 3{£2) values in ".Cr nucleus (ir- a' fm units). £XP ARM IBM (1) (2) (3) (4) 2r —, 0* 1309 (82) 1317 1309 4+ -+ 2V 1750 (160) 1856 2025 5*" -^ 4+ 1950^on 2046 2281 2141 228 o *Pra.sjnt Addrc:ss: Physics '.Depct., G.G .n.s.D.Degree Cell ^7 2, :3aijn-!th - 175125 (H.P.). (1) (2) (3) (4) lO+-*3+ >1599 2199 2103 12*-r>10 + 2190 2238 - + 14*-*12 ll6Ol3l0 2265 1294 16+~>.14> £620 2286 - 2+i-*0+ 24(4) 49.8 24 2+' -»2+ «675 739.7 319 3+ -*2+ 62(6) 103.6 33 3+-*2+' 1520(340) 1682.0 1369 8 4+'-*2'f 6t 3 8.6 7.0 $880 405.5 341 4+%2+/ 1240 (340) 601.4 887 References: (1) JTucl.Phys. A 332, 241 (l97g)and ref.cited therein. (2) Nucl.Phys. 8,237 (1958). (3) Phys. Rev. C26, 685(1982):Nucl.Phys.Symp-B29# 151 (1986)j Nucl. phys. Symp. B31, P16(1988): Can. J. Phys. 67, 1301 (1989). (4) J. Phys. Soc. Jpn. 54, 901 (1985). (5) Nucl. Phys. A249/ 141 (1975). 40 SPECTROSCOPY OF HIGH SPIN STATES IN 92Mo Pragya Singh, R. G. Pill ay and H. G. Devare Tata Institute of Fundamental Research Bombay 400005 Low spin states of positive and negative parities have been studied1-2, arising from the (ng^Pi/z)4 configurations, in the closed neutron shell (N=50) 92Mo nucleus using (a, xn) reactions. In this paper, we discuss preliminary results on the high spin states, populated in two different reactions using heavy ion projectiles produced in the TIFR Pelletron accelerator facility. The reactions used were 66Zn(3°Si,2p2n)92.Mo and 59Co(37Cl,2p2n)92Mo at 115 MeV and at 120 MeV, respectively. The production of 92Mo was observed to be the most dominant channel (approximately 20% of total) consistent with the estimates by CASCADE. In the first experiment a thick target of enriched 2000 1000 - c O o 850 950 1050 1150 1250 1350 1450 151 0 in 10 250 - O tv 1 o-l- — 1 '•— 1 1— —-—1 1 1 1 ' l70° 1800 1900 2000 2100 2200 E nerqy ( keV ) Coincidence spectrum gated on 235, 627, 109S keV y-rays Coincidence spectra were projected from the list data for all the prominent 7-rays. These consisted of 56 gates corresponding to unshifted and 36 gates to Doppler shifted y-rays. The y-rays which were fully Doppler shifted, as seen in the 5 detectors (0 = 15°, 45°, 75°, 105°, 135°), would correspond to life-times shorter than 50 ps, the flight time between the foils. Several new y\s, e.g., 110, 135, 168, 537, 557, 649 and 2065 keV, were observed to be in coincidence with the transitions in the negative parity band (see figure). The 110, 168, 537, 557, 649 and 2065 keV lines were Doppler shifted and correspond to transitions above the 8.8 ns isomer. Analyses for the detailed level scheme of 92Mo based on coincidence and angular distribution data are in progress. ' C. M. Lederer et al., Nucl. Phys. A169 (1971.) 449. 2 T. Numao et a!., Nucl. Phys. A305 (1978) 163. 42 CORIOLIS COUPLING IN DOUBLY-ODD ROTATIONAL BANDS Kiran Jain and Ashok K. Jain Dept. of Physics, Univ. of Roorkee, Roorkee-247667 The study of rotational bands in deformed nuclei reveals a strong Coriolis coupling. Recent two - quasi particle plus rotor band - mixing calculations in doubly-odd rare-earth nuclei carried out by Jain et al./l/ show that the Coriolis coupling as well as the particle-particle coupling is important in deciding the behaviour of doubly-odd rotational bands. We have carried out similar calculations in the actinide region. We have considered only seven , . 234.23 43 Table ! : Summary of GM splitting energies and Newby shifts in actinide region. All values are in koV. Conf i gurati on Nuc1eus EOM EN proton ® neutron KT;KS Cal c ;Expt Cal c ; E x p t l/2C400]®l/2C631] 238KNI p on* - 9; -2. 8 1/2C53O]<8>1/2[6313 234Pa 0;l" 43. 8; 39. 2 236Pa 0;l~ 55. 3 49. 3 238Np 0;l 99. 3; 102. 1 50. 9; 44. 5 3/2[521]®l/2C620] 250Bk l;2" 108. 7; 109.3 - 3/2C5213<8>7/2t613] 250Bk 5; 2" 66. 5; 66. 1 - 5/2£5233®l/2[5013 240A 3;2+ 47. 0; 48. 7 242** Am 3;2" 39. 0; 42. 8 - 238 3;2~ 5/2C5233®l/2C6313 P 52. 5; 52. 3 240* 3;2 59. l; 58.4 - 242*° 3;2 244Am 52. 5; 54. 1 Am 3;2 59. 8; 69.7 5/2E5233»l/2t62O3 242A 2;3" 17. 0 - 244*m 8; 23. Am 2;3 10. 8; 14.2 5/2C5233*5/2[622J 238,. 0;5~ 6. 1; 3.0 -23. 6; -23. 3 240^P 0;5~ Am 23. 9; 8.5 -30. 7; -28. 5 242 0;5 20. -28. -27. 5 244^m 1; 4.8 5; Am 0;5 40. 2; 33. 6 -26. 6; -28. 7 244. 5/2C523]«>7/2[624] Am 6;l" 167. 8; 199. 7 - 5/2[6423«>l/2C6313 238 2;3+ 82. 82. 3 242*P 9; Am 2;3+ 31. 3; 28. 7 _ 5/2C642 3<8>5/2[622 3 238.. 5;0+ 9. 41. 1 -51. -48. 0 242^ 6; 3; Am 5;0+ -59. 1; -61. 3 7/2[6333®l/2C620] 250Bk 4;3+ 75. i; 84. 0 - 7/2£6333<&3/2C6223 250Bk 2;5+ 96. 9; 91. 8 - 244. 7/2C6333&7/2C6243 Am 0;7+ - 12. 2; 32. 7 7/2[633]<8>7/2C6133 250Bk 7;0+ 106. 9;135.7 -25. 0;-24. 7 NUCL:234Pa 29 44 CORIOLIS EFFECTS IN 2qp ROTATIONAL BANDS OF EVEN-EVEN NUCLEI ALpana Goel and A.K.Jain Department of Physics,Univ. of Roorkee,Roorkee Experimental data on two quasiparticle (2qp) intrinsic excitations and the rotational bands based on them are not many. Yet,a recent compilation lists atleast 50 Gallagher doublets and associated rotati- onal bands in many cases.The 2qp states in even-even nuclei differ from those in odd-odd nuclei in seve- ral aspects.The residual interaction splits the fv =JCi(irO|states and puts the singlet member lower than the triplet member, which is opposite to the odd-odd case.The odd-even splitting of K=0 band is also expected to be opposite in sign to that observed in the odd-odd nuclei"; It. is also observed- that 'the residual n-p interaction parameters derived from the odd-odd data are quite different from the interact- ion parameters obtained from the even-even data. Besides the Coriolis mixing which is present in odd- odd nuclei also, additional mixing of AK=0 nature is suspected which mixes (2-n) and (2-p) states. It is therefore important that unperturbed 2qp energies be extracted ' from the experimental data.We have devel- oped a 2qp plus rotor model for even-even nuclei where a nearly complete Coriolis mixing of all the bands is possible.This model is similar to the one developed for odd-odd nucleiz.The difference arises because of the antisymmetric nature of the wave- function , xVz While all the terms appearing in the odd-odd model survive, new additional contributions come to the K=0 rotational bands.These additional terms connect K = 0 ,Ln,-+-x>]and K = 0 ,to+j,+citJJ bands more strongly.An app- lication of the model to the rotational bands in Er which exhibit strong Coriolis mixing in the form of odd-even staggering is shown in Fig.1.It may be noted that the large odd-even effects are reprod- uced very well.These calculations also provide info- rmation on unperturbed residual interaction energy and odd-even shift. 45 Financial support from D.A.E. is gratefully acknowledged . REFERENCES : 1. P.C.Sood etal., At.Data and Nucl.Data Tables (1990) to appear. 2. A.K.Jain etal., Phys.Lett.B209 (1988)19;Phys.Rev C40Q989) 432. I I i K~=1~ f"on2^ 80 jj^g. Caption : Staggering plots for the 2qp bands in Er.The bands are denoted by the K17 values and their 2-qp/2-qn configurations.The notations used for are: for protons ,*}: V*i>"/J , P2.Vz/>,J ' neutrons, 46 DOUBLY EVEN CADMIUM ISOTOPES P.KoMattu and S.K.Khosa Department of Physics, Janunu University, Jaramu-180001, India. In this paper we report on the calcula- tions of the high-spin yract spectra of the doubly 98—110 even nuclei Cd. Apart from the energy spectra we shall also discuss here the results of the calculations of the reduced transition probabilities for E 2 transitions for the yrast states. The calculations presented here are carried out in the VAP - framework employing pairing-plus-quadrupole- quadrupols effective interaction. The details of the input parameters of our model and tne valence space used, are the same as those employed in our earlier work. In Table I we present a comparison of the observed B{E 2; 0 > 2 ) values with the ones 2 computed by using the prescription employed by Ripka . It is satisfying to note that the calculated B(E 2) estimates are in good agreement with the experiments 47 .provided one chooses e ,.-=0.15. It therefore turns out that the VAP prescription, in conjuntion with the pairing plus quadrupole-quadrupole interaction, provides a fairly accurate microscopic description of the observed high-spin yrast spectra in the nuclei 98-110Cd. Table-I, Comparison of the calculated and the observed B (E 2; 0+ • 2+) values in some Cd isotopes. B(E 2; o"48 eZ Cm4 Calculated Nucleus • Expt eeff=0.1 eeff=0.15 eeff=0*2 106Cd 0.368 0.432 0.50 0.410 108Cd 0.386 0.457 0.629 0.430 110 Cd 0.400 0.475 0.557 Oe45O References 1O P.K.Mattu and S.K.Khosa, Phys. Rev. C 39, 2018 (1989). 2. G.Ripka, in Advances in Nuclear Physics, edited by M. Bar anger and E. Vogt (plenum. Mew York, 1968 Vol.1. 48 CORIOL.TS CORRECTIONS I*J QUADRUPOLE MOMENTS OF ODD-ODD NUCLEI Shakti D. Shartna, Aravind Sharma & Praveen Sharma Department of Physics, Panjabi University, Patiala (Panjab) - 147 002. Introduction: Electric Quadrupole moments of Odd-odd Nuclei are reported by experimentalists in different deformed regions of the periodic table. These data deserve special analysis on the basis of collective model. Magnetic moments quadrupole moments and spectral properties are to be simultaneously fitted for optimum adjustments as was done in cases of the simplest Odd-odd Nucleus, the "Deuteron". This simultaneous fit is expected to yield acceptable values of the deformation parameter £ . Theory: In case of deuteron the fit was done using tensorial type nucleonic force, but from our study of high Z Odd-odd nuclei, it is evident that Coriolis coupling dominates over the residual nucleonic interaction in general and many a times it leads to failure of coupling rules . Thus we beUeve that the simultaneous fit in high Z (or medium Z)nuclei should be done using Coriolis coupling. The latter affects the magnetic dipole moments appreciably and thus for best fit value ofJ3 one gets the acceptable decoupling (or partial decoupling) parameter, which can be used to diagonalise a rotating model collective Hamiltonian including the Corioiis perturbations. The eigen vectors so obtained can be utilised to predict the quadrupole moments or other nuclear moments. If Q1 is the electric quadrupole moment of state with parallel alignment of spins of valence nucleons and Q^ is that for the antiparallel spin state, then Coriolis corrected value is Q - Q, xflx + Q2 Y^2 Where "^-fl and "^-T..-, are eigen vectors obtained diagonalisation process. Note that Q = V16 fl/SH (2I-1)/(I + 1) (2I+:OJ (Qc + QpJ 49 Where Q is the quadrupole moment of the core and remaining term in parenthesis [ ] is particle- contribution to the quadrupole moment. RESULTS AND DISCUSSIONS: Foi diagonal isation, the decoupling parameters corresponding to the mixing of Nilsson's Single particle states are taken from J.P. Davidson's book" "Collective models of the Nucleus". The following table gives some of the results in the medium' and high Z nuclei. All the quadrupole moments are in barns. These are the quadrupole moments for ground states of the nuclei NUCLEUS Q Q Q EXP without with coriolis coriolis 0.02 -0.05 -0.06 -0.07 4d 5,Sc 0.10 0.137 0.126 0.119 0.27 0.44 0.40 0.40 8e 35Br tf 0.30 0.230 0.196 0.199 ^Tm'^ 0.32 2.30 2.65 4.62 ta Tm 0.30 0.74 0.55 0.57 It is clear that the values of quadrupole moments for medium and high Z nuclei in general show improvements on applying Coriolis corrections. It may be remarked that these very values ofPgive simultaneous fits for magnetic moments and doublet splittings for the conjugate bands and thus can be accepted as reliable parameters of structure of these nuclei. Inclusion of nucleonic interactions (central or tensorial type) is expected to improve the results. Reference?: 1. S.D. Sharma Ph.D. Thesis "Symmetric and Asymmetric core collective models of Odd-Odd nuclei". University of Kansas Lawrence (Kansas), U.S.A. (1971) 2. J.P. Davidson "Collective modeIs of the Nucleus". The appendix has all details of calculations of Nilsson's Single Particle states reproduced by Davidson's group (1969). 50 STUDY OF Z=64 SUBSHELL EFFECT ON TOE PROTON SPECTROSCOPIC FACTORS IN lbZ lb0GD J.B. Gupta and Satendra Sharma Ramjas College, University Of Delhi, Delhi-110 007 The Pairing-plus-Quadrupole model /I/ is used to calculate the spectroscopic factors for proton stripping involving the even-even Gd, for which the data from (He, t) and ( He,d) reactions are available /2,3/. We seek the effect of deforma -tion and of the subshell gap at Z=64. We use the input parameters as in the study of Gd isotopes earlier/4/ and determine the S values at (|3O,VO). In the absence of pairing.,at P > id the 14 protons would fill the (m=l/2, 3/2) g7/2, d5/2 , hll/2 and (m=5/2) hll/2 orbitals, but with increas -ing deformation, the protons from the up-sloping 5/2 [413] g7/2 and ?/2 [411] d5/2 orbitals would transfer partially to the down - sloping 5/2 [532] hll/2 orbital. The pairing interaction modifies this distribution of the protons in the Nilsson orbits. This effect is evident in the stripping data as also indicated from our calculation (Fig.) To check the need of a larger gap at Z=64 between the d5/2 and hll/2 j- shells, we raised the hll/2 j-shell by 1.0 MeV. The resulting S + are shown by dashed curves. As expected, tne vacancy in the g7/2, d5/2 shells is decreased ?nd in hi1/2 is increased slightly. The effect on the nuclear structure shall be reported elsewhere. Work in part supported by Univ. Grants Commission. REFERENCES: /I/ K.Kumar, The EM Interaction in nuclear Physics (Amsterdam, NY,1975) ch.3 /2/ O.Straume, et at., Nucl. Phy. A266 (1976) 390 /3/ J.C. Tippett and D.G. Burke, Can. J. Phy. 50 (1972) 3152 /4/ K.Kumar & J.B. Gupta, Nucl. Phys.A304(1978)295 51 4 - 88 9O 92 94 N 52 STUDY OF S0(3) WAVEFUNCTJONS IN THE SD(5) BASIS J.B. Gupta and H.M. Mittal Ramjas College, University of Delhi, Delhi-110 007 The Interacting Boson Model (IBM) usually employs the SU(5) basis (n^ n« n^ ) lor the construction of the elements of the Hamiltonian matrix. Then the eigenfunctions of the Hjg^ in the SU(3) limit have a complex structure spread over many n^ valued/I/. Consequently, the identifica- tion ox tne Krr=0+, 2+ p- and V- vibrational bands in the ( A = 2N-4,/M=2) SU(3) multiplet in the nuclei on the SU(3) - SU(5) transition class is done only on the energy basis. In other words, there is no direct prediction of the K-value. Same is true for higher bands. Here we make an attempt to have some insight into this problem taking Dy as an example, where the K=02+» 2-j+ bands overlap and B(E2,0^-2o) is greater than B(E2, 0^-23). Our method consists in the comparison of the exact SD(3) wavefunction (with total boson number N^13, same as for T>y) with those of loSDy, (a well deformed nucleus with R4 =E4/E9 > 3-2), for 2^, 22 and 23 states. We have plocted the square of the (n^ rig n^ ) amplitude of the normalized wave vector in Fig. 1. In 2g there is good overlap, but with some shift of 158Dy wavefunction towards the lower nj values, which implies a contribution of SD(5T symmetry and the K-band mixing effects (20 % K- mixing predicted in DPPQ model /2/) here. Similar shifts occur in 2o and 2<$ states. Further, the large overlap of the maxima/minima in the 2^, 22 (and also 0-^ , not shown) explains the stronger ^- g excitation strength and the small overlap for 22 (and 0i), 2g states explains the weak P~g interaction strength as predicted for exact SU(3) limit, in agreement with experiment/2/. /I/ R.F. Casten, Rev. Mod. Phya. 80 (1988) 389 /2/ J.H. Hamilton, A.V. Rarnayya and J.B. fl be published). 53 J60 c 120- C (0 160 120 ! C Q. —4,0 18 22 54 A LOW SPIN BAND CROSSING IN J. A. Sheikh Daresbury Laboratory, Warrington WA4-1AD U.K. C. R. Prakaraj Institute of physics. Bhubaneswar -751005 Dracoulis et ai [l] have recently observed a mild band crossing bf- tween K = 1/2" and K - 5/2" bads in l75Os and have made a particle rotor model analysis of the bands. They can fit the energy spacings m the bands by assuming two very different moments of inertia for the two bands. But this assumption gives an interaction strength between the bands which is an order of magnitute larger than the interaction deduced from the observed E2 transitions in ike band crossing region. We have done a deformed HF and angular momentum projected analysis of the properties of these two bands and their interaction. Our calculation gives an adequate description of the energy spacings of the bands as well as their crossing and the E2 transitions between the banus. The spectrum of the 1/2" band is shown in the figure. A surface delta interaction has been used in the calculation. V 3- V 33," "l V 2J >t n- n,-_ o \ (,;-.— PH? la the particle rotor model analysis by Dracoulk et aJ jl] one needs different deformations to fit the spectra of K — hj'2~ and K = l/2~ bands; bnt with these deformatioas it is not possible to get the correct E2 transitions between the two bands in the same analysis. In our microscopic analysis we face DO such ambiguity inherent in the particle rotor model. References 1. G. D. DracouJis and B. Fabricius, Phy.Rev.C41,( 1990)2933 56 MULTICHANNEL STRUCTURE Oi1 4He by 3.K. Chikara and V.K. Sharma Department of Physics, Institute of Advanced Studies, Meerut University,Meerut-2:>G_04 In light nuclear systems, the few-body techniques are increasingly oecoming an important tool in various studies .JO as to provide valuable pieces of information about nucleon-nucleon int- eraction, structure of light nuclei,and to under- stand the mechanism of various nuclear reactions. The four-body system is the simplest one in light nuclei and exihibit structure different from three- body system as it has been established that the co-existance of shell structure and cluster stru- cture exists in light nuclei, also the physical interpretation of generator coordinate met bod (SCM) is strongly reminiscent to this idea recently £4 ] . In He nucleus the ground state only proves to be bounded and all the excitations studied experimentally are in a continuous spectrum. In microscopic structure of 4-He, we used the multi- channel structure (i.e. p+%, n+\e and a+d channels) within our G-OM with two-centre single particle basis states. The advantage of consider- ing GCM is that we need not to consider full sub- spaces of various channels out only restrict subspaces will ipve the sajr>e result. The wave function for "hie in (JCK as [' 2 *[ . (1) and f!s are generator coordinates satisfy ing 57 the (2) wit h. H (X In matrix form after using descritization method IhV 0 0 0 where e-9* References 1. V. K. 3 hjir in a, in Developments of Nuclear Cluster DynaF-ics eds. Y.Akaishi ,K.Kato,E.Noto and 3. Oka'oe .(Word Scientific. 19^9 j pr^e 50 2. Y.A.oharma and M. A.Nagarajan; J .£hyz. ^ .Tucl. Phys. JO., 1703 (1984) 58 A NEW ANALYTICAL MODEL FOR EXOTIC DECAY STUDIES G.Shanmugam and S.I.A. Philomin Raj * r Department of Physics, Presidency Coll t e, Madras-600 005 Department of Physics, Madras Christian College, Madras - 600 059 Exotic decay, which is spontaneous emission of fragments heavier than alpha particle from heavy nuclides, has been established experimentally. Many models have been developed to explain this phenomenon and one such is that of Poenaru and Ivascu (PI) (1) which is analytical. In PI model, the inner potential (when the fragment is within the parent) is of parabolic form and changes drastically (at rt) when the fragment just emerges out of the parent completely which seems unphysical. The inner potential was taken as cubic form by Shanmugam and Kamalaharan (SK) (2) and this form is considered to be realistic (3) since it bends at rr The integrals involved were solved numerically by SK model. In the present work, the realistic cubic form is retained for inner potential of the fission model and all the integrals are solved analytically. In PI model, the outer potential (when the fragment is outside the parent) is coulombic, but the .Carrier penetration is at Q' to suit the experimental situation. The SE model (with penetration at Q itself) uses coulomb plus yukawa potential to take into account finite range effect and the calculated barrier height and life time are in good agreement with experimental values. The present work uses an entirely different prescription (with penetration at Q itself) for the outer potential which correctly fixes the barrier height. The inner potential is V(r) = [V(rt)-{V(rt) + E^ {*I^}} - (D rt-ri where r. is the CM distance when the fragment is within the parent and just touching the wall of the parent, assuming that the radiisof the fjagment varies as it emerges out (4). rt is the CM distance when the fragment is outside the parent and just touching the parent (4). Ey is the zero vibrational energy. The left integral can be shown to be : I^=(2/*)(2a)1/2(/93r/3xl023)V(rt)1;2(^=^lp(I,2.) ...(2) V 3 ' 3 2 The outer potential is of the form where a= [ 1 - e (rb - r)] with e ^.003236 Q m and 0 / ii \ 1 KR = .63 £ ZiZc ( 1 ~ETh)Fo ... (5) \Q-eZi Tut?) 1/2 where Fo = arc cos (r4 /rb) -[n/rb - Fig. 1 shows the form of the potential for inner and outer regions. When the two spheres are just touching, the protons will preferentially stay as far as possible from the point of contact due to electrostatic repulsion, compelling the neutrons to stay closer to the point of contact (Fig. 2). As a result, the charge centre will be shifted away from centre of mass. Thus, while touching, the cm distance is rt whereas the distance between charge centres is d > rt. To incorporate this physical phenomenon, a factor a has been introduced in equation 3. a has minimum value at rt and becomes 1 at rb as seen from equation4. i.e. the centre of charge tends to coincide with CM as rb is approached and at rb both coincide. With this prescription, barrier height is achieved at rt itself. The life time of decay is given by T = [ 1.433xlOr21/Ev][l + exp CKL + KB)] ...(6) The calculated values are tabulated below. For even-even nuclides, the calculated values of log s[ \ y 0 5 /r 1 -Ev- d ' PARENT FRAGMENT BARRIER HEIGHT LOG(T/ra) | Present Exptl. Present Exptl Ra-222 C-14 27.35 27.29 9.65 9.43 Ra-224 C-14 30.31 29.81 10.48 10.37 Ra-226 C-14 33.07 32.13 10.22 10.50 U-232 Ne-24 32.48 31.52 11.09 11.70 Acknowledgement: The authors are grateful to Prof. P.Balasubramaniamfor fruitful discussions regarding the solution of inner integral. References : (1) D.N. Poenaru and M.Ivascu, J.Physique 45 (1984) 1099 (2) G. Shanmugam and B.Kamalaharan, Phy., Rev C 38, (1988) 1377 (3) J.R. Nix, Ann. Phys, 41, (1967) 52. (4) B.Kamalaharan, Ph.D. Thesis, University of Madras, 1990. EFFECT OF CENTRIFUGAL BARRIER ON EXOTIC DECAY PROBABILITIES C.Shanmugani and B.Kama Iaharan Department of Physics, Presidency College, Madras-5 .We have recently developed a realistic fission model for exotic decay studies by using finite range Yukawa plus exponential potential for the post- scission region. The shape of the potential barrier In the overlapping region is approximated by a third order polynomial. Later, we have modified our earlier model suitably so as to incorporate the deformations'2" of both the parent and the daughter nuclei keeping the emitted nucleus spherical. Our results were found to compare well with the results of other theoretical models as well as experiments. It has been noticed that after including the deformations, the calculated branching ratios for even A parent nuclei are close to the experimental values signifying the presence of odd-even effect. As we know, in the case of exotic decay of even A parent nuclei, the relative angular momentum of the daughter and the emitted nuclei is zero. But, one has to include the centifugal barrier effects in odd A parent nuclei to take care of the odd-even effect. In this work, we have added the centrifugal term l(l+1)/2|JLr to the potential used for the post scission region in our earlier mode! ( \*- being the reduced mass) and studied its effect on the branching rat i os . 61 Bran ch : n g ra t i o Dec ay 1 Expe r i Wi t hou t Wi th men t al 1 1 Ra -> Pb+ C 4 9. 21 8 .38 8 .68 5l ^ Bi+ 't 3 1 2 .4 0 1 2 . 4 9 1 2.67 1 1 1 . 22 1 0 .50 1 0 .52 233 50? u ~> Pb+ ^*Ne 2 1 2. 12 1 0 .99 1 1 .05 7 3 , ^ T 1 + °Mg 2 1 3. 40 3 . 14 1 3 .19 2 ! 1 4. 1 1 3 .80 1 3 .83 __J It is seen from the table that the inclusion of centrifugal barrier has improved our model by bringing the theoretical values still closer to the experimental results. /I/ G.Shanmugam and B.Kamalaharan, Phys. Rev. C3 8, 1377 (1988). Ill C.Shanmugam and B.Kama I aha ran , Phys. Rev. C4 1 , (1990) . 62 NUCLEAR LEVEL-DENSJTY PARAMETER IN HOT ROTATING LICHT NUCLEI G.Shanmugam, M.Thiagasundaram * and A.Chitra Department of Physics, Presidency College, Madras-5 * Department of Physics, Pachaiyappa's College, Madras-30. The temperature dependence on the level- density parameter has a crucial role to play in the study of nuclear structure in hot nuclei. It can be investigated by mean field theories such as Hartree- Fock method and the Landau theory of phase transitions which usually ignore the statistical thermal fluctuations. But, for nuclei with finite number of particles, it would be nice to include such fluctuations and see the effect on the Ievel-density parameter. Recently, Ormand et al /!/ have considered this problem for the case of ^ Cu, 'IO Sn and l5^ Er. The aim of this work is to obtain the I evel-density parameter for calcium isotopes as a function of temperature and angular momentum using Landau method 12/ including thermal fluctuations 131. According to the Landau theory of phase transitions, the probability the system has to display a given shape characterised by the parameters ( ft Y ) 's given by )/T] (1) where Z = dl exp[-F(p.i )/T] (2) is the partition function and the volume element is taken to be dt = f^jsin 3J j djid/ . The ensemble average of the entropy that depends on ft * can be calculated by the relation S( py y ) (3) The I eve I-density parameter including thermal fluctuations is given = <£S/72T The results obtained for the I eve I -densi ty parameter as a function of temperature and angular momentum for the case of Ca are shown in Table. I\ 0. 5 MeV 1 .0 MeV 1 .5 MeV 0 5. 2026 4 . 2743 4 . 4533 (4. 9 67) (4.2 45) (4 . 413) 8 5.2172 4.2 731 4 .4535 16 5. 2609 4.2 695 4 . 4523 It is seen from the above Table that the I eve I -dens i ty parameter in •4^- Ca remains almost unaffected by rotation at constant temperature but undergoes marked change with temperature. To bring out the effect of thermal fluctuations in the calculations . wwee alsalsoo give the I eve I-density parameter as a function of temperature for zero spin in brackets calculated without considering thermal fluctuations. It is seen that the I eve 1-density parameter remains unaffected by thermal fluctuations analogous to that of heavier systems studied by Ormand et a I /1 / /I/ VV.E.Ormand, P.F.Bortignon, A.Bracco and R.A.Broglia, Phys.Rev C40, 1510 (1989) 121 Y.AIhassid, J.Zingman and S.Levit, Nucl.Phys. A4 63, 205 (1987) 121 C.Shanmugam and M.Thiagasundaram. To appear in Phys.Rev C. 64 SHAPE TRANSITIONS IN EXCITED sd SHELL NUCLEI C.Shanmugam, K.Raanamurthi * and Kalpara Sankar Department of Physics, Presidency College, Madras-5 * Department of Physics, Bharathidasan University, Tr ichy . In our previous work /!/ we have studied the role of thermal fluctuations on the shape parameters in excited light nuclei in the Calcium region. In this work we extend our study to determine the shape transitions occuring in hot rotating s-d shell nuclei. For this we use the Landau theory 121 According to this theory the free energy at w=o can be written to fourth order in B as / 1- 3 J 4- F(T,w=0,ftY) = F0(T)+A(T)B -B(T)B Cos 3/+C(T)p (1) VJfiere the coefficients FO A, B and C depend on the temperature T and P> and 7 are the usual intrinsic deformation parameters. Extending equation (1) to the rotating case with w parallel to Z axis 2 py = F(T, w=0,(i,y )-\ Izz( ft.Y^jw " (2) where Izz = I0(T)-2R(T)6COSY +2I;(T)(?> +2D(T)pSin 7 Where t. R and D are suitably defined, to absorb various numerical constants. Since nuc)el are finite number systems. One should, also consider thermal • fluctuations. Now the ensemble average of P> and 1 are given by J ^ ft(-F/T^ f y|jy and -^ in the following Table, we show sample results for the case of mid sd shell nuclei "^ S i . It is seen from the Table that ^ S i which is oblate with P> - . 5 at ground state drifts towards the prolate state with reduced deformation through triaxial shape when the temperature is increased. Ill C.Shanmugam and M.Th'. agasundaram, To appear in Phys. Rev. C. Ill Y.AIhassid, J.Zingman and S.Levit, Nucl. Phys. A469, 205 (1987). \ T 1 • 5 MeV 3 .0 MeV 0 .4912822 -172.3033 .1506838 -141.5184 2 .491278 -172.302 .1506499 -141.5158 4 .4912653 -172.2983 .1505482 -141.5081 6 .4912441 -172.292 .1503785 -141."4951 8 .491214 2 -172.2831 .1501407 -141.4771 10 .4911756 -172.2717 .1498343 -141.454 66 JOLLiiJ'x'-Lv Jepartment of Physics, Jniversity of llalyani .ialyani, \l2zt Hengal, 741-^36 J'e are reporting here an investigation of the symmetry ^roup of the tine-dependent Schroedinger equation /l/ for nucleons with tvo-body harnonic interaction. \ia are treating a system of particles 01 tv;o types _^p=l,2) with masses II, II in muabers, at positions r , characteristic frequencies w for intra-type interaction and w1? for inter-type ^ interaction. V/e have obtained a very rich symmetry structure of the systea. The sy;mnetry irroup for L protons and il neutrons has C^(^-1)+9NCK-1)+4O 1/2 generators. Time translation, scaling of vavefunction, rigid translation, Galilean transformation, rigid rota- tion and rotation of the centre of mass provide 14 of these generators. The other generators are •'•'-In' ' *'1 "~ '" •L>T** / -•S"' <"*C7 * J r Pi: j^A •-/here II = 1^ + Up = total nurriber 01 nucleons, ;I = -'-I-IT4" V.gA?,,- total .'.ass of system, . = v/avei'u.nction, '^ ^//^T7 67 '.'.ere VjP^ is rotation of the n-th particle o± : 'cy^e p *' ;:- jo'it the -o-th particle 01 the ^a..ie type, '•> is oscillation of the two types^of uarti- n cl-3P - '..'ith respect to aacli other ?.i:d —+-' is oscillation of t'.e 21-th and the '.'.. -•;;: oi' type o v/ith respect -' ;o each oti:er. ,'anajas showed /L/ that for a sir.jle type of .v particles the Orthogonal ^rou^ 0<->.-l'j provides tiu collective decrees of freedom. In our analysis ^.;-nerate txiese aodes. .;e assi :n ^+ to tiis "' jiant resonance .:iode /3/ of ..iuta.al - oscilla- tion of the neutron and the proton iluid^ and -h-^1^ to anotiier collective :.iode describing -• oscillation of each fluid separately. An investigation of the sy^i.aetry jroup for the nucleons ^iovin^ in an average harmonic field has also been ;nade and it has been found that T-" ..jeneratinj the i-iant resonances are absent in this a ppr o y-i nation. References 1. L.T.Ovsjannikov: Group properties of differen- tial equations (J. of ^ritisli Jclu..ibia, UJ7j •:.. V.Vana^as: in Lecture notes in rhysics, no.135, ^d. i:.B..;olff (oprin^er-Yerlaj, Parlin, I^-IU) : j. J'..Io_lisenber.2 . ; './.••ireiner: .'ucloar Jiieory, Vol. I (r.orth-iiolland, A;:isterda.-.'i, 1^70) 68 GENERATOR COORDINATE TECHNIQUE FOR AHTISYT?K!5- TRIZATION OF THREE-CLUSTER WWE FUNCTIONS B.B.Srivaatava and Piyush Sinha Physic3 Department, Meerut University PMeerv.t-250Q05 - The resonating-group method (RGM) has been quite success t'ul for microscopic calculations of nucleus-nucleus scattering- A major difficulty in the application of RGM is that for systems with A 8 the antisymmetrization procedure and calculation of kernal terms becomes prohibitively involved. In ruch cases the calculations can be ;;;a The cluster-model wavefunction is written for the nucleus Be described as alpha-alpha-nucleon system following the usual procedure. Using the following integral representations for the delta functions and a few coordinate transformations this wave function is transformed into a transla- tionally invariant antisymmetrized product of nine single-particle wavefunctions after making a suitable choice for the centre-of-mass wave function- 3 S( r9- ^ )= (^) j exp[ 69 The expr&ssions are somewhat lengthy and are given elsewhere . This form of the wavefunction will allow the use of well-known shell-model techniques for calculation of kernel terms of the RGM scattering equation. Details of the calculations and wavefunction vviil be presented. References 1. W.Sunkel and K.Wildermuth, Phys. Lett 4 0 B (1972) 439. 2. Piyush Sinha, M.Phil. Project Report, Meerut University, 1989. 70 100 INTERPRETATION OP BACKBENDIHG IN Mo IN A CRA11KED NILSSON MODEL WITH PAIRING Tripti Mathur and S.S.Mukherjee: Department of Physics, Baaaras Hindu University,7ARAHASI-221 005. An interpretation of backbending in '^Oio nucleus is given in terms of the crossing of the ground state band with an aligned two quasipartiole band. Experiments done by Gelletly et.al. show a backbend at n£O o 0.4 Me?» However the data does not tell us whether tMs is due to the alignment of neutrons or protons* We have done calculations within the framework of Cranking Nileson with Pairing model for both hu# neutrons gQV,x protons. The Hamiltonian used was: SX A Writing this fiamiltonian in quasiparticle notation and choosing a Nilsson basis with good signature,the Hamilto— nian matrix can be constructed and dlagonalised* This is equivalent to solving the eigenvalue problem: I . x. \r The plot of quasipartiole energy 6 vs rotational frequency *o (Fig. l)t thus obtained,shows a band orossing at H ci c 0*41 MeV for g protons and at h c>o = O.35 MeV for ^y^ neutrons. Hence we conclude that thA baokben&ing is due to the alignment of a pair of g protons* 71 Pig.lr The qua- siparticle energies for neutrons and protons plotted as functions of rotational fre- quency • The fol lowing parameters hare teen used* B - 0.253 0133*^ and A - 4.853 for neutrons and A - 4.292 for protons. References: 1. W.Gelletly et al: 'Nuolear Structure of the Zirconium Region1 p.101 (Springer Verlag) 2. Z.Szymanski: *Past Nuclear Rotation*(Clarendon Press, Oxford) 3. O.V.K.Batoa: SERC School lecture notes Acnowledflesnents; Useful discussions with Dr. C.V.K. Balsa are gratefully acknowledged. One of us (TM) is grateful to C.S.I.R. and U.G.C. for award of JRP. 72 'oTUDY OF Oa-185 AND Re-186 DECAYS J.Goswarny, B.Chand, D.Mehte. H.Singh and P.N.Trchan Pliynjcn Department. Pan jab Univeroi ty ,Chnndl«nrh The radionvclidee Os-185 . (tVz = 93.6 d> and Re-186 (tv,= 3.78d) undergo EC decay to the states of Re-185 ' and W-186 respectively; while the radionuclide Re-186 aleo decays through P emission to the states of Os-186.Earlier measurements_ of H'tiiiinn vny Irilnmi ll«jn and facdliiH porconl.'tp.rft (P /md li Os-185 Re-186 Energy Relative Intensity Energy Relative Intensity (in Kcv j Kev) Present Referenced] ( m Present Ref.HJ 59.7(Re K..J 26.9(7) 25.8(9) 57.9 (W K«.) 1.83(4) 2 .1(5) 61.1(Re Kc.) 46.3(12) 44.7(16) 59. 3 (W K«.) 3.15(7) 3 .7(7) 69.2(Re KpJ 15.5(5) 15.1(5) 61.5 (Os Kat)1.20(3) 1.19(4) 71.3(Re Ka) 4.30il4) 3.84(14) 63.0 (OB K*,)2.05(5) 2 .05(24) 71.4(Re-r)" 0.34(14) 0.31 67.2 (W Kf>,) 1.05(3) 1.22(24) 125.4 0.47(2) 0.43(1) 69.3 (W KQJ) 0.28(1) 0 .32(6) 162.3 0.74(1) 0.69(1) 71.3 (Oe Kp,)0.70(2) 0.71(8) 234.2 0.54(1) 0.51(1) 73.6 (OB Ka») 0.180(5) 0 .179(20) 592.1 1.71(2) 1.64(4) 122.6(W-r ) 0.64(1) 0 .64(2) 646.6 100(1) 100 137 .l(Os-r) 10.0(11 10.0(11) 717.4 5.04(6) 5.09(10) 630 .4(0s-r) 0.0310(4) 0 .0277(12) 874.8 8.05(8) 3.16(16) 767 .5(0s-r) 0.0344(5) 0 .0309(7) 880.3 6.59(10) 6.17(12) 931.1 0.065(3) 0.061(3) Table 2. Percentage feeding to different levels in the decays of Os-185 and Re-186. Level Energy Percentage feeding Level Percentage feeding (in keV) Energy Present Ref.[3] Present Ref[3) Os-185 -- Re-185 Re-186 -- W-186 646.6 00.7( 11) 81.0 g.S 4.UG( VJ) 6.2 717.1 5.37( 15) 4.7 122.0 x.-mi i) 1.7 874.8 6.64( 11) 6.8 Re-186 -- Os-186 860.3 7.21(25) 7.7 P.Fl 74.7 7J.0 931.1 0.054(3) 0.055 137.2 18.9(3) 21.0 767.0 0.055(1) 0.055 References: 1. D.MM11./1 ot ni, run A^'ir,. 74 LIFETIME MEASUREMENT Cl> "ONE NUCLEAR LEVELS USINC A Bal-',-DaF2 SET UP C. C. Doy, B. K. Sinha ,ind R. nhattacharya L>'jn.j institute of Nuclear 1'hysico Calcutta Lifetime ot come nuclear levels have been measured by delayed coincidence! mo the' using an ultrafant BaF_-BaF2 coincidence set up [1J. These jncludo 161 kev S/?/ level of 13JC3, 118 kev 5/2* level and 139 kev 7/2+ levels of i69Tm and 122 kev level 152Sm. These levels have been measured by a no. of workers (table 1). The measured half-life of 161 kev level, an r.ren from table 1, Iiaa a broad range from 85 pa to 219 ps . Thuc it neecvi a precise mea3urcment of half-life of this level which is possible '.it? this ultrafast BaF2-BaF2 set up. This will help in predicting coriect model of the structure of the level. The magnetic moment of the 16J \I:'-' level has been measured by Thomas ct al [4J using IRF method taking r = 276 ± 21 ps measured by Valivaara et al [3] . To confirm this value of fJ it l^ads to remeasura the half-life with the BaF2-BaF2 set up. tor 122 keV level of Sm also the half-life has been measured (table 1) but with a prompt time much longer than the half-life of the level. Thus a correction for finite time resolution was necessary. Since it is possible to obtain prompt time resolution much Ie33 than tiie Siali-life with the present set up no correction for finite time rcoolut i:re will ho needed if such a net up i3 used to romea3ure the hnlt-Jife of thin level. 118 keV and 139 keV levels of Tm have been measured also with a bettor precision at a prompt time resolution of 6U0 pa. ,! Of the two D \ —. ', -—'' NLL 75 T A a L. E - 1 Level and h/2 Prompt time Reference Cascade (keV) 161 koV of 133Cs (85 ± 16) pa 2 276-161 (I'JO ± IS) pa 910 pc 3 (249 ± 46) ps 4 (iao ± io) pc 630 pa Present work 139 keV of 169Tm (291 ± 25) po <177+19U)-lll0+130) (321 ± 14) pa {320 ± 8) po 680 ps Present work 169 118 koV of Tra (62 ± 2.8) pa 5 (177+198)-(110+130) (63 ± 7) po 7 (66 ± 0) pa 680 po I'roocnt work 122 keV o£ lb2Sm {1.44 ± 0.03) ns 8 1408-122 (1.4 47 ± 0.026) nn — 9 (1.40 ± 0.02)no 450 po I'roaent work Referonceo : 1. a, K. Sinha at aJ, NucJ. Inutr. and Notli. A276 1106'J)237 2. W. Flangor et al, Atomkcrnenergje 0 (1963) 453. 3. K. G. Valivanrj at al. Phys. Scripts 2 (1970) 19. 'I. W. Thomas ct al, Nucl . Phys. A 318 (l<)79> 97. 5. A. E. Dlaugrond et al, Phyx. Hev. 120 (1960) 1323. 6. T. Sun3dstrom et ul, Ark. Fys. 26 (196']) 377. 7. R. E. McAdama ct al, Nucl. Phyr,. 82 (1966) 449. a. F. W. Rictiter et al. Zeit. tur. Pltys. 213 (1960) 202. 9. R. M. Diamond ct al, Phyo. Rev. C3 (19/1) 344. 10. W. K. Warburton et ul. Com. Phyn. Communication 13 (197!)) 371. 76 ANGULAR DISTRIBUTION MEASUREMENTS IN 127I T.S.Cheema, D.Mehta and B.K.Axora Department of Physics, Panjab University Chandigarh-160014 197 The states in x^'l below 750 keV have been studied both experimentally as well as theoretic- ally /I/. Castel /2/ has tried to explain some of the B(E2) vctlues on the basis of core-*excitation model whereas Hustgi et al./3/ has succeeded reas- onably in explaining level energies with intermed- iate coupling model. Ward et al./4/ studied angular distributions in 127I using •L60 ions and establis- hed spin assignment 9/2 for levels at 651 and 745 keV. The measured A2 values for 628.6 keV gamma ray suggested a 5/2 or 7/2 spin assignment for 628.6 keV level wher_as no definite A2 values were given for 418.0, 375.0 and 202.8 keV transitions. In the present work, we.report angular distribution measurements in ' 271 and present the measured A2 values and compare these with the ones available in literature. The measurements were made at Variable Energy Cyclotron, Chandigarh using a 3.57 MeV proton beam. The beam current was kept at 100-200 nA to avoid large dead time corrections. The target consisted of a 1 cm. thick pallet obtained from spectroscopically pure KX powder and was placed at 45° w.r.t. the beam direction inside a cylindrical chamber. The gamma rays following Coulomb excitation were detected simultaneously with two detectors positioned at 0° and 90° respectively and data was recorded with ND 76 and ND 100 multichannel analys- ers coupled to each of the detectors. The 64.1 cra^ HPGe detectors had a resolution of 2.0 keV for the 1332 keV gamma ray of °Co. Simultaneous placement of the two detectors and data acquisition avoided the inherent difficlty of charge collection and its normalisation for the 0° and 960 detectors. The photopeak efficiency of the two detectors was found to an accuracy of 1% over the energy range of 77 KJ i'-/ yields at O'"' C:>n_i '/., v/eiL- ;,.:a '.'d tho ar.'julor correlation function ALder et al./5/ i,eo in which the symbols have the usual meaning. The small value of 34 makes the last term insigni- ficant in the above expression and is neglected in the analysis. The experimental determined values of A~ for different gamma ray transitions excited via E2 mode are listed in table 1 below and are compared with those given by Ward et al. JAf. Our value for A2/a2 agrees well with that of Ward et al./4/ for tne gamma ray transition of 745.5 keV energy whereas for 628.6 keV gamma ray transition our value is higher. Table j_ Angular distribution results K Ao/ao (keV) Work ftsf.74/ Present 145.0 .304 - .597+ .06 — 172.2 .359 - .297+ .007 — 202.8 .437 - .133+ .001 — j7b.O .670 - .209+ .007 — 418.0 .712 - .398+ .03 — 628.6 .868 - .251+ .006 - .085+ .01 745.5 .967 + .180+ .008 + .2O3± .01 References /I/ Nuclear ^ata A4(19o8)83 /2/ B.Castel.Can.J.Phys. 46(1968)2571 /3/ M.L.Rustyi,J.G.Lucas and S.N.I.-iukherjee, Nucl. Phy s. ' ,-,117(1968}321 /4/ J.o,^eiyer and R.L.Graham, Phys. Lett. 29b(1969)48) 7 /'of K.Alder, A.uohr, T.P-{uss, B.Mottelson and A...'inther, iiev.Mod.Phys. 28(1956)432 78 CONVERSION ELECTRON, K X-AND GAMMA-RAY INTENSITY MEASUREMENTS IN Cd-111 J .Goewomy , B.Chand , D.Mehta.N . Singh and P.N.Trehrin Physics Department,Panjab University,Chandigarh-160014. The radionuclide Ag-111 (tt/z-7.45d) decays through ft'emission to the excited states of Cd-111. Only a few measurements of gamma-ray intensities are available in literature and they too exhibit inconsistency and large uncertainties.A reinvestigation of this decay through conversion electrons, K X-and gamma-rays measurements was felt necessary. The radioactive liquid source of Ag-111 in dil. HC1 was procured from BARC,Bombay.Sources in appropriate geometry were prepared by drying radioactive solution on mylar backing.The measurements were performed using a Vertical HPGe detector (Volume=28.27mm* x 5.0mm ,FWHM =459eV at 122 keV),two coaxial HPGe detectors ( Volumes = 9Scc and 57cc, FWHM = 1.8 keV at 1332 keV) and mini-orange electron spectrometerCl]. These detectors systems were coupled to 4k channel MCA (ND 66B) through a spectroscopy amplifier (Ortec 572). The efficiency calibration procedure for various detectors have been described elsewhere [1,2]. The calibration uncertainties were estimated to be 2.0% and ±.% for vertical HPGe and coaxial HPGe detectors respectively while for mini-orange spectrometer it is 3% .Ten spectra of long duration were taken with each detector and source combination. Theee spectra were analysed and corrected for efficiency to obtain intensities of K X-rays, gamma-rays and conversion electron peaks.The intensities of K X-rays and gamma-rays are presented alongwith earlier measured results [3] for comparison. The conversion coefficients of various transition deduced, using present conversion electron and gamma-ray in- tensities, have been compared with theoretical val- ues from tables of Hager and Seltzer [4] in table 2. The present results for gamma-ray are, in general agreement with earlier measurements [3] with the exception for 96.7 and 245 keV transitions. Our measurement for96.7 and 245 keV gamma-rays are more reliable since measurements with 96cc and 57cc HPGe detectors are in good agreement with each other. Prcccnt', eonvcrcion cocfficionte ohow good agr-ecnicnl with the theoretically predicted values [3].Present measured values of K X-rays are lower compared to tho evaluated results (4].This difference is mainly due to signifleant difference in gamma-ray inteneltiea of 96.7 and 24£> keV ganiina-rays used in evaluation of K X-ray intensities. K X-reys intensities calculated U3lng the present conversion coefficients, and lnL'jriiclt lee uhow aootl agreement with measured valuee. Table I . Intensities of K X-rays and gamma-rays emitted In the decay of Ag-111. Energy Radiation Relative intensity (in koV) — - - . - - - . - Present Rpfr*rTirrf 't ! 'J3.1 Z.'J.<)(lJ) u.vycju) 26.2 K* 0.54(3) 0.56(5) 96.7 r 1.56(2) 2.99(90) 1U. Jt>( 1U) lb.Olll) 278.3 0.012(1) 0.0091(24) 342.1 100(1) 100 374.7 0.039(2) 0.0'i:i'5) 509.4 - o.oiyf>) (522.6+524.7) 0.053(3) 0.043(5) (619.3+620.3) 0.388(4 ) 0.-12(4) 754.7 0.0026(5) 0.040(8) (865.H866.7) 0.112(3) 0.126(11) Table 2.Internal conversion coefficients of various transitions in the decay of Ag-111. EnerRy of Type of Conver3Lon coefficient Multipolp transition conversion - Assignment Present Keference[3} 245.4 K 0.0536(31) E2:0.0536 M3 :0.761 E2 (L+M+..) 0.0042(16) 312.1 K 0.0152(6) Ml:0.0150 E2 :0.0182 Ml (L+M+..) 0.00162(22) References: l.J.Goswamy et al, Proc. Hucl. Phys. Symp. Vol.32B, P46 (1989). 2.D.Mehta et al, NIM A 245, 447 (1986). 3.R.G.Hager and E.C.Seltzer. Nucl. Data 4 (1966). 4.E.Browne and R.B. Firestone, Tables of Radioactive Ifiotopes (1986) (Wiley, New York). 80 K-CAPTURE PROBABILITIES IN THE DECAY OF 152Eu AND 169Yb USING HPGc DETECTOR K. Bhaskara Rao, Dr. S. Lakshminaranaya and Dr. V. Seshagiri Rao Dept. of Nuclear Physics, Andhra University, VISAKHAPATNAM INTRODUCTION: There are several methods by which the K- and L- capture probabilities (P., and P. ) to the excited states of the daughter nucleus can be determined. The sum-peak method is used initially in the case of simple decay schemes. In the present work it is success- fully extended to the complicated decay schemes of Eu-152 and Yb- 169. There are several reports (1-3) in which the usefulness of the sum-peak method for the determination of PR is well established. The evaluation of PK by this method involves the use of data on fluorescence yields, TC- and total convertion coefficients and absolute efficiencies. EXPERIMENT: The Yb-169 source was supplied in the form of YbCl by BARC, Bombay. The standard IAEA source was used for Eu-^152. Experimental point sources are prepared by evaporating a few drops of the source at the centre of circular mylor foils fixed to perspex discs. The HPGe detector used in the present work is 49.2mm in -rystal length and 44.7mm in crystal diameter. This is coupled with ND600 having 4K channels. The K- electron capture by the parent nucleus and consequent emission of conversion electrons as a competing process to the gamma- ray emission from the excited levels of the daughter nucleus is followed by K-X ray emission. When the gamma-ray and cascading X- ray enver the sensitive volume of the detector simultaneously, both radiations are recorded as a single event. A peak at an energy corresponding to the sum of the energies of these two radiations is observed as a sum-peak in the spectrum. This is obtained by keeping the source at 5mm distance from the window of the detector. As an example the P., value for the 1529 KeV level in ths decay of Eu-152 is obtained by the following relation: Here £, is the absolute efficiency of the detector which is determined by sum-peam method and reported elsewhere (1). Knowing the other parameters in the above equations the P, value for 1529KeV is deter- mined. Similar equations are used to find out P, values for the three excited states in the decay of Eu-152 namely 529KeV, 1233KeV and 1085KeV levels and three levels in the decay of Yb-169 namely 472KeV, 379KeV and 316KeV. 81 The experimental and theoritical values are presented below in a tabulor form. The experimental P.. value for each level is the weighted average of the PR values determined by taking different possible sum-peaks. - value P. - value Isotope Energy Lt Level (Xev) Expt. Theory Expt. Theory Eu-152 1529 0.829(21) 0.832 0.141(3) 0.142 1233 0.840(20) 0.848 0.127(3) 0.128 1085 0.861(79) 0.851 0.127(11) 0.125 Yb-169 472 0.822(16) 0.823 0.151(2) 0.151 379 0.829(23) 0.830 0.145(4) 0.145 316 0.832(16) 0.831 0.146(6) 0.145 The P~ value for the 1085KeV level in the Eu-152 is reported for the first time. There was only one earlier measurement in the case of Yb-169 for the present three levels. The experimental values are in close agreement with the theoritical values within the limits of experimental errors. The P, values are also calculated using present PK values and the theoritical Pi/P* ratios and reported along with the theoritital P. values in the Skmi* table. The large uncertainly in the case of 1085KeV level of Eu-152 may be attributed to the fact that the gama ray intencity involved in the sum-peak area is comparatively less. REFERENCES B.k. Das Mahapatra and P. Mukherjee J. Pbys. A7 (1974) 388 K. Singh and H.S. Sahota J. Phy.Soc. of Japan 52 (1983) 2336 H.S. Sahota, T. Iwashita and B.S. Grewal J. Phy. Soc. of Japan 56 (1987) ?881 82 A STUDY OF INTERNAL CONVERSION COEFFICIENTS M.V.S. Chandrasekhar Rao, G. Sree Krishna Murty, K. Badha Krishna, S. Bhuloka Reddy, G. Satyanarayana, D.L. Sastry and S.H. Chintalapudit Svami jnanananda Laboratories for Nuclear Research, Andhra University, VIS AKHAPATNAM - 53O OO3, INDIA "fr Variable ETr.&rgy Cyclotron Centre, CALCUTTA. As a part of the continuous programme1-2 of work under a UGC project at the VEC Centre, Calcutta, we have carriedout conversion coefficient measurements characterizing 4 high multipole transitions and one low multipole transition. The concerned transitions are of M4 type in117m Sn (TJ* = 14 d), 115mIn (T>s s 4.45 h), E3 in187 Tm (T* = 9.25 d) and HI in the same nucleus. The conversion coefficients were obtained employing 'Intensity Balance, X- ray peak to gamma peak, Sum coincidence and Normalized peak to gamma peak' methods. A high resolution (FWHM =180 eV at 5.9 keV) low energy photon detector was employed for these measurements. The isotopes were studied, in general, in a close geometry while 1B7Tm in a 7 cm geometry. The energy and efficiency calibration of the system were accomplished in the usual manner. The results of these studies are summarized in this presentation. FS = 75,000 * X 1/27 117mSn : The source was produced via I 11BIn(a,pn) reaction at a beam energy 158 keV | of 32 MeV and a current of 200 nA. Intensity Balance method was used to determine ar of the 156 keV M4 ,158+Ka transition. The recorded gamma and sum spectrum is shown in figure 1. After applying the usual corrections for absorption, efficiency etc to the > observed gamma intensities, the err <» value of the 156 keV M4 transition was deduced as given in Table 1, which also includes theory3. The OK value of the same transition was also determined for •P -- the first time using the sum I ' -^ coincidence method in the same 2215 2255 2670 2715 geometry. The same is given in Table 1 Fig. 1. together with the theory. Table 1 shows a good agreement between theory and experiment for err as well as OK values governing the 156 keV M4 transition in the decay of 117mSn. 83 : Produced via 116In(a,a') reaction at a beam energy of 14 HeV and a current of 200 nA. The XPG method was used to determine the OK value of the 336.2 keV M4 isomeric transition. Experimentally the gamma and K X- ray intensities were determined in their final form and coc value was estimated using the standard relationship. The same is given in Table 1 together with the theory3. This result is found to be consistent with the earlier results due to other methods. ie7Tm : Produced via 1BSHo(a,2n) reaction for a study of K electron capture probability. As a byproduct of this study we measured the can value of the 207.8 keV E3 transition and ox value of the 57.1 keV M1+E2 transition using NPG method. The measurements were taken in a 7 cm geometry. The CCL value was measured for the first time. The OK and OL values of the respective transitions are given in Table 1 together with the theory3. The CCL value shows an E2 admixture of 12% in the Ml component for the 57.1 keV transition. CQHCLUSIQM : The present values of internal conversion coefficients governing high multipole transitions are in general agreement with theory except a small anomaly in the case of iismln. The OL, value of the 57.1 keV Ml transition shows an admixture of 12% E2 component. REFERENCES : 1. G. Sree Krishna Murty et al J. Phys. G15 (1989) 1769 2. K. Radha Krishna et al Ind. J. Phys. 64A (1990) 294 3. Rosel et al At. Data and Nucl. Data Tables 21 (1978) 92 TABLE 1 : Energy Transition keV Experiment Theory Sn-117« 4 + ll/2~-^ _*3/2 156 o^ = 48.72 ±1.11 47.88 + ll/2~-^-»3/2 156 aR _ 28.20 ± 1.53 29.6 In-115n H4 1/2" >9/2* 336.23 «R - 0.81 + 0.03 0.87 Tm-167 E;j + 1/2" >7/2 207.8 aK 0.47 + 0.02 0.47 - Ml ?/? > 1 /? 57. 1 a. = 18.34 ± 0.66 19.2 LJ 84 LEVEL DENSITIES AT HIGH SPINS H. Rajasekaran and D. Caleb Chanthl Raj Department of Nuclear Physics, University of Madras, Culndy campus, MADRAS 600 025. Level densities are considered to play an important role in many nuclear physics processes. For example, the different decay channel In fission, the particle decay in heavy Ion fusion products, etc are determined by level densities. In this paper we propose a way to calculate level densities at high spins. The method is based on the Deformed Nilsson potential. We consider Er for our study. Since Er builds its angular momentum by single particle alignment, we consider only non-collective rotation. In our earlier work [1] we have extracted thermodynamic quantities like temperature and entropy from Strutinsky's single particle density of states. The prescription was extended to rotating nuclei with the introduction of lagrangian multiplier a into the single particle density of states[2]. This has been proved to be equivalent to the cranked Nilsson procedure for axially symmetric shapes. 2 2 g(c, The single particle levels for protons (or neutrons) with spin projection mz are generated using Nilsson Hamiltonian. The averaged energy E is given by E = 2 c g(c,cc)de + Tux I (2) where A is the chemical potential that conserves the number of protons and neutrons, i.e. N = IY 1 n ' = -I 2 |f g(e,a) dc n( = (l/2)[l+erf(A-ci-ami/y)] (3) As the smearing width n —» 0, E —> Esheii. The occupation probability (Eq.3) would be 1 or 0. The entropy S of the nucleus is given by S = - Y, [nlnn+ (1-n )ln(l-n )] (4) The temperature is given by T = 5E/3S. 1 he level density ran be obtained by using I •< I p( 1 . 6 ) = exp[ S I /T (!>) The level (Jens 1 t y Is calculated for various deformations and for various angular momenta. The variations of ln(p) vs angular- momentum for1 a few deformations are shown In Fig 1. The fluctuations in level densities is due to non-uniform distribution of spin projections and spacings in the energy level scheme. We thus find strong shell effects in level density. The level density is also deformation dependent. Its variation with deformation at 40 h is shown in Fig 2. References: 1. M. Rajasekaran, D.Caleb Chanthl Raj, R. Premanand and V. Devanathan Phys. Rev. C4JL, 396 (1990). 2. M. Rajasekaran , D. Caleb Chanthi Raj, Nucl. Phys. Symp.32B, (1989) 98. 3. M. Rajasekaran and V. Devanathan, Phys. Lett. 113B.433, (1982). 3iq \ •« 0.0 1 V 1 \ \ — — — — 1 ,.-1 •••\ •••»•-...v- ANGULAR MOMENTUM (O n.1 n.2 0.^ II.. i DFFORMAT ION VALIDITY OF THE INM MODEL IN THE EXTREME LOW MASS REGION H. C. Nayak Dept. of Physics,K.K,Collefee,Berhampur-760001. and L.Satpathy Institute of Physics, Sachivalaya Marga, Bhubaneswar For the last several years more and more exotic nuclei in the n- and p-drip regions have been obser- ved due to increasing precision in the experimental facilitiesO) .This helps in testing various models of mass, predictions •Especially in the low mass region it is always a challenging task for most of the models due to shell and single particle effects.Recently we (2) have successfully developed a model for masses of nuclei, based on infi.nl te nuclear matter mo del (INM) of nuclei(3)«0ne of the remarkable features of the model is that the mean deviation from experimental values in the known mass region is only 1Kev compare- d(4) to several Kevs with the other models«In the present paper we report here the utility of this mod- el even in extreme low mass region* AeJf to 18. Before discussing the results it is worth mentio- ning here that our model recognizes the fact that nu- clei in general possess two basic properties namely the universal liquid like behaviour and the local fe- ature corresponding to sh&Ll, deformation etc. .Based on this picture and witnlielp of generalized(5) Hugen holtz - Van Hove theorem it is possible to obtain re- cursion relations which help us to develope a network of all. nuclei known and unknown both*Ihe parameters of the model are fitted with the known masses once for all and then applied to various regions. In. table 1, we have compared the predicted masses with experiment for some representative series of is- otopes in this region.The agreement is quite good.It remarkable that the model works well even, in this ex- treme low mass region.We find that the local energies play dominant role here as expected because predomin- ant shell effects in light nuclei .It is worth point- Ing here that none of the models(6) based on liquid drop model could work here in this region*The quality of our predictions in this extreme low mass region is comparable to those of Garvey-Kelson, 87 Table 1. Nucleus M.E. Nucleus M.E. Nucleus M.E. Th.-Exp• Th.-E3cp. Th.-Exp (MeV) (MeV) Tie 0.1 7B 1.1 12C 1.6 1.5 8B O.if 13C 0.9 6He -2.6 9B 0.1 lifC -0.6 7 10 He 1.1 B -1.0 15C 0.1 8He -0.8 nB -0.2 16C -1.0 9He 0.9 12B 0.5 1 I. ft f\ r\ 15 0.5 B -1.5 J! U.I 6 lif 16 Li 1.7 B 0.6 F 0.1 17 1 J^L 1.1 -0.6 F 0.9 0.8 8C 0.5 9Li -0.9 9C -0.7 10Li' -0.2 c 0.2 l1Li 1.7 nc -2.2f References :- 1.C.Detraz,Proc.Int. National Conf. Nucl. Phys.Vol* 2,337(i989);U.Strohler et al,Z.Phys.336,369(^990) 2.L.Satpathy and R.C.Nayak, Atomic Data aad Nuclear Bata Tables 39,2Zf1 ( 198&) 3.L.Satpathy, J.Phys.G13,76i(1987) 4.P.E.Haustein,Atomic Data and Nucisar Data Tables 39,185(1988) 5.L.Satpathy and R.C.Nayak,Phys. Rev.Letts.51* f5(8) 6.P.Holier and J.R.Nix,Atomic Data and Nuclear Data Tables 39,218(1988); P.Moller, W.D.Myers W.J.Swiatecki aud J. Treiner, ibid 39,22.5(1988) 88 VARIATIONS OF THE NUCLEAR LEVEL DENSITY PARAMETERS IN DIFFERENT RANGES OF MASS NUMBERS Asok Saha Department of Physics, University college of Science, 92, A.P.C Road, Calcutta-700009 As reported in two earlier communications /I, 2/, the nuclear level density parameter a (data after Baba/3/and Holmes et al /4/) in the range 2pp „ 210ei shows a very goo 89 (data from von Egidy et al /5/) being 2.558 + -9604 HeV and 1.1274 + .4415 MeV respective3.y. Table 1: a values (in MeV~ ) of nuclides compared with those of adjacent nuclides. A = 20 - 75 76 - 109 110-152 153-210 Nuclides Next Next Next Next Next r^ext Next Next higher lower H L. H L H L E - E 3 + 5 + 2 + 3 + 1 + 1 + 5 + 1 + 5 - 3 - 6 - 4 - 11 - 11 - 8 - 13 - (1=6.659) (a=H.639) (a=15.365] (a=l7.741) O - O 4 + 7 + 4 + 4 + 1 -r 3 -f- 3 + 5 + 7 - 2 - 4 - 4 - 5 - 3 - 9 - 5 - (a=5.2Ol) (a=11.183) (a=l4.887) (5=17.386) E - 0 6 + 12 + 4 + 1O + L2 + 16 + i€+ 16 + & O - E 11 - 8 - 10 - 5 - 4 - 2 - 7 - 9 - (a=6.448) (a=11.686) (a=15.672) (a=18.O57) Note: ( + ) & (-) signs indicate number of a values higher-than/lower-than that of adjacent mass respectively. References /I/ A. Sana, proc. Int. Conf. Nucl. Reac. Mech., Calcutta, India (Jan.1989), Pt.A, p.85 /2/ A. Saha/ proc. Symp. Nucl. Phys. (India) 32 B (1989) P83. /3/ H. Baba, Nucl. Phys., A 159 (1970) 625. /4/ J.A. Holmes et aa. At. Data Nucl. Data Tables, lT"(1976) 306. /5/ T. von Egidy, et al, Nucl. Phys., A 481 (1988) 189. 90 THE TOF-I'DST liUCLEON SEPARATION EtfERCZ AND TOTAL BINECKG THEIR CONNECTION M, K, Basu Department of Physics College of Science, Calcutta 700009 The connection between the top-most surface-nucleon separation energy and the total binding energy of a nucleus is of considerable interest to nuclear physicists from the view poiat of study of nuclear forces and sizes. Unfortunately no aiteespt has so far been made to explore m. explicit connec -tion between thesaj hence the present attempt, of course, from phenomenological considerations. Nuclear-oatter density being proportional to the packing (binding) of nucleons inside a nucleus, the distribution of the nucleon-binding energy inside a nucleus is the binding- energy analogue of nuclear-matter density distribution and can, therefore be expressed, on the basis of an exponential densiiy distribution,, by the following. E =EO Exp( -//r) ... (1) where E = banding energy of a nucleon inside a nucleus at a distance r from the centre, Eo and /y. being the total binding energy of the nucelus and the inverse of the pi-nasic compton wave-length = 1*4 fin i.e. range of 2-body nuclear forces and inter-nucleon separation in standard nuclear matter, respec- tively. If E^ « separation energy of the top-most surface- nucleon defining the radius. R = r0A^ of the nucleus, eqn. (1) reduces to ^ =% Exp( -JUR) ... (2) 1/3 or logd^/Ej = (/Uro)A .,. (3) Eqn.(2) is the desired connection the validity of which is to be checked by the acceptability of values of ro's computed from eqn-(3). ro's computed for almost all nucltd e::oept very light ones lie in the ranges (1.45-1.2?,) fin. for even-A and 91 (1,6-1.35) fte. for odd-A nuclei, being in close agreement with values of ro' s obtained from other set-bods. As expec- ted2*' » ib's exhibit also odd-A and even-A effect and ahell-structure effect for isotopes of an elecient. Eqn-(2) is, therefore, the desired connection; but how this connection can be obtained from microscopic consi- derations is the question left to the future for its answer. For perfect analogy with nuclear density, lb in ecp-(i) should have been the binding energy of the nucleon at the centre (r=0) but not the total binding energy of the nucleus; nonetheless, the emergent connection turns out to be correct, 1) M. Harada, Phys. Rev, CIO (1974) 2616. 2) J. M. C. Scott. Prog. Nucl* Phys. J (1956) 157. 3) C, M. H. Smith, A Text-book of Nuclear Physics (Psrgeaon Press Ltd,, 19^5) Page 238. 92 A. 3 an _ j -? -r..j Y. J.T. ^o Je ! ;rt:"' •• • •- ;;hy ,'_ :.;, .' o rt h /J "• '. _ r:: i \ 1. 1 '.' niv:r.;i i •/ , J.iil Ion.:-?: : "j. The spi:ior-L_-p ; '.=,•;;: ;he--Jaip it " e r..at icn, v/hich i.. :i 3i::t ••••": co.-vo ..rv. p. t C'^u;>l--^.J evaaticn 1G stu- -•i-id in t'.i-B non-reiativi^t ic iirr.it. In this li- mit, the pj2udD.:calar part of the equation can be decoupled to give an integral e^.iation in the closed for-n, vi;:., i) (the notations being everywhere the ;:zme as in ref. 1) . v/riting /mz instead of (/yvt1-*- />* ) in 1) the equation car; be reduce ^ to tha '-/ick-Cutkos KV ' .3 eqi.uit ion The eiger^/cU-ue : •• ;ctru:n .~>t '-:1J :: ;::.twn has b-^e otu.lijd by various autii'^r..; in various appro:-"ir:ia- t ions. j'': o: ;3 : t- :.:•••'••- ve t".; " o^ctr!::; tiius ob.aia: ' ' i:: ';;V: ;:OM- celat ivi ;t: c ii.-'it), ::.Jeto r'itaine^ the ^>z terra in t'v; ini.ogral equation (e; 7 ^orturbal: : ri) v.r. i v"."-: ::C: i~. '_o a 3ciiro— .lir.-"\?.r like i •~i \t: on 3) 93 vw_ 0- um this (( ^ ) was obtain:.-;-' v/hich i:3 more like that obtained from >7ic.':-Cutko-;K;y' 3 equ?.ti JO in the extreme relativist ..c limit. Thus T./e apprehended t.nat th3 approximation.-, were inadejuats and calculated the ground state eigenvalue by a perturbativ: approach to the integral equation thus obtaining 'which in the limit y-^o becomes Equation (<-) gives thi:; ratio as v/hich is different :;ro:r. what we obtained a oart from havinq u very oi :7f: /rent cr" Jeyen ^enee. ]. :.. ;eto, Pr-'irj. Thc-or. Phy3. 64 (19^0)1026. 94 K SHELL IONI3ATION FOLLOWING R DECAY LAKSHMI NATARAJAN Department of Physics, University of Bombay, Bombay. Making use of the theory of sudden approxi- mation and the atomic screening constants derived from non-relativistic self-consistent-field wave functions, we have calculated here the probabili- ty of creating a single and double vacancies in the K shell of 15P and -jgS as a result of ft""- decay. As the eletron shake-off probability for a given shell is inversely proportional to (Z- While there \re several systems where the fusion cross sections have been measured in the barrier region /I/, only in a few cases simul- taneous measurements of the cross sections and angular momentum distri- bution have been performed. Measurements of the average angular momen- tum JL and / or L as a function of energy have been performed through the isomer ratios /2/, fission-fragment angular distributions /3/ and gamrna- ray multiplicities /4/. We have used the dependence of the relative cross- sections for different evaporation residues (ER) on the angular momentum distribution in the compound nucleus to derive i.. The measurements 28 32 37 were made using Si, S and Ci beams in the energy range 70-ll5MeV from the 14 UD T1FR peiletron accelerator facility. Vacuum evaporated 2 2 targets (thickness - 30/fgm/cm to 120/ugm/cm ) on. Bi and Au backings were used. The partial cross sections of the ER were obtained by measur- ing the on line and off line gamma-ray intensities with the help of two 110 c«i3 HPGe detectors. The V -ray intensities were corrected for feed- ings from decay chains of neighbouring nuclei. The channels considered are 2n, pn, p2n, 2p2n, p3n, oCpn, ct 2n and 97 shapes. The ratio R is lound to be independent of the shap' out it is a function of JL at a given excitation energy. The 1 was then derived by comparing the experimentally observed ratio R to that given by the calculation. The total cross section as well as the derived J. values for the system Si+ Zn, S+ Ni and CU Co are presented in figure 1. These results are compared in the same figure with correspond- ing calculations on the basis of the coupled-channel model of Dasso et al. /6/ and the model of Stelson /7/. References 3'CI IH M. Beckerman, Rep. Prog. 10 .;-* 20 10 .*•/ in Phys. 2L (1988) 10^7 15 10 11/ R.G. Stokstad et al., Phys. ' No Coupling il • 10 10 2* .3~Couolin9 Rev. Lett. 62 (1989) 399 ••(•' Slclson Model 5 /3/ R. Vandenbosch et al., Phys. 10 20 Rev. Lett. 56 (1986) 1234 X) 10 E M.L. Halbert et al., Phys. 10 b' ° No Coupling Rev. DO (1989) 2558 1a1 "'' 2+ , 3~Coupling 10 *' Stelson Model /5/ F. Puhlhofer, Nucl. Phys. 5 28 Si A280 (1977) 267 10' ?0 •/. .- /6/ C.tl. Dasso et al., Nucl. 10' 15 Phys. A^05 (1983) 381; No Coupling c 10 2 , i~ Coupling 10 Nucl. Phys. A407 (1983) 221 Slelson Modal ILL 5 HI P.H. Stelson, Phys. Lett. 50 55 60 65 70 B20 5 (1988) 190. Fig. 1- Fusion Cross-sections (•) for the three systems. 98 DISPERSIVE CONTRIBUTION TO THE NUCLEUS-NUCLEUS POTENTIAL FOR THE SYSTEM iso+2O9Bi P.Singh, S.Kailas, A.Chatterjee, A.Navin, S.S.Kerekatte, A.Nijasure and B. John Nuclear Physics Division, B.A.R.C., Bombay-85. Recently, Mahaux et al/1/ have shown that vith an energy dependent imaginary part in the nucleus- nucleus potential an energy dependent real term can be obtained through the dispersion relation. The strong contribution of this term at energies close to the barrier can explain the observed anomalies of the optical potential. In this study the energy de- pendent contribution to the real part that arises from the imaginary potential through the dispersion relation is estimated for the system i6O+209Bi. For making these calculations we have made use of the data of Vuigaris et al /2/ at EL=79, 81,82,84 and 86 MeV, in addition to our data reported earlier /3/ at EL=90,95 and 100 MeV. In order to make the data set complete we have measured elastic scattering of 160 from 20 9gi at 83 MeV and the measurements at 80 and 98 MeV were also repeated with better accuracies and these data have also been included in the analysis. Optical model analysis was done using both phenomenological and double folding potential. The best fit parameters obtained using the double folded real potential are listed in Table 1. The dispersive contribution to the real part of the potential at the strong absorption radius (rsa=12.7 fm) was cal- culated using the relation in the so called sub- tracted form oo , y where Es is a convenient reference energy and P is the principal value of the integral and In the present work, we assumed a linear schematic model /I/ and represent W(E), obtained from phenomenological analysis, by linear segments that join the experimental values for the calculation of the dispersive contribution. These results are shown in fig.l by open circles. It can be seen that the part of the empirical real potential arising from 99 the dispersion relation is very important, espe- cially when the energy approaches the Coulomb bar- rier. Only a few MeV above the barrier the impor- tance of this term decreases rapidly. The dispersive contribution to the real part of the potential at an energy corresponding to the Coulomb barrier is ~25% of the real part of the potential. This value is much smaller as compared to the 60% contribution in the case of 1G0 + 208Pb but is similar to the values estimated for 130 + 58,60,64Ni (30%), 160 + ?<>Ge (38%) and 160 + 90Zr (20%) /4/. Similar analysis was also done using imaginary potentials obtained from double folding model. As per dispersion rela- tion, a factor of 2 enhancement in the real part of the potential is expected at energies around Coulomb barrier from the energy variation of imaginary potential. However, experimental values of the real part are much smaller and this discrepancy needs to be understood. Table 1 E Wi TI ai 79 1.98 9.0 1.255 .580 80 1.90 17.0 1. 222 651 82 1.88 35.0 1. 240 .535 83 1.82 46.0 1. 236 559 84 1.79 58.5 1.232 520 86 1.77 65.0 1 .230 530 90 1.72 75.0 1.240 550 95 1.77 75.0 1.201 538 98 1.74 75.0 1.257 497 100 1.75 55.0 1. 212 572 86 94 102 ELQb(MeV) References 1. C.Mahaux et.al. Nucl.Phys. A449 (1986) 354. 2. E.Vulgaris, et.al. Phys.Rev. C33 (1986) 2017. 3. P.Singh, et.al. DAE Symp. on Nucl.Phys.32B(1989) 4. M.Lozano, Phys.Rev. C36 (1987) 452. 100 . f:MPc '-•• rURFI DEPENDENCE OF Ef-4ISSJ0N BARRIERS FOR PRG10N AND ALPHA ...*! COMPOUND .NUCL. E J IN -MASS REGION A=!30 Aruna ,". , A.K.Mohanty. A.Chat tenjee, A.Saxena, O.John, S> ft has been observed that the evaporation spectra of light charged particles (p.alpha) obtained ex- perimental ly are softer as compared to those calcu- lated by using the" statistical model codes.This in- dicates that the omission barriers for these par- ticles are lower than those used in the statistical model codes. Deformation degree of the composite nucleus alone is not able to explain this effect, and the reason for lowering of the barrier is not well understood. A survey of the available experimental data of the difference between observed emission and fusion barriers for p,alpha indicates that the emission barriers iwy depend on the temperature of the com- pound nucleus. A systematic study of this dependence is needed. Therefore, in the present work we have studied the decay of the same compound nucleus at various temperatures. We have selected different projectile arid target combinations which will result iruo the same compound nucleus with a wide range of temperatures. The range of temperatures that can be obtained using the Pelletron beams at TIFR,Bombay is indicated in Tr.tl*; J. Rf ~. c *. i on Evaporated Jni t ial CN Final CN Part i cle Temp. Temp. f+Nb->Sn Proton 2.55 2.55* (1)0 MeV) Alpha 2 41* Proton 2.04 1 77 <70 MeV) Alpha 1 85 Li +Aq-*Sn Proton 1.85 1 54 (54 MeV> Al pha 1 59 H-» In-»sn Proton ) .29 0 49* (10 MeV> Alpha 0 59* * indicates the estimated values.Others are Exptal Table 1 We have obtained the proton and alpha spectra in the foilowinwing .reactions: tNb ~> ,»Sn (at 70 MeV) Hit •lo8Ag -•> "*SM (at 54 MeV) P and Alpha spectra are obtained at various backward angles between 110 deg. to 160 deg. Two sol id state detector telescopes of thicknesses (15 m.m.) and (40 vrn.+Z m.m.> have been used for alphas and protons respectively. The proton detector has been calibrated using recoil protons from a mylar target whereas alpha teilescope is c.alibratod 101 using Th source. llach spectrum has been nor- malised by using Rutherford scattering data obtained I rom a morn tor detector placed at a fixed forward . shows that proton and a!pha spectra f r a m the t w •: a c t. ion1.; studied are similar, c o n f i rm- inn mat '.; i'j i.i.i contribution from :,: roct reuc- t i oriK and a ! i t i •;, i:ons i ui en r. w i fl the fact that f the t C'rnpo IT. "; ur•.: s or thftse two rea'jLions are near', y eoi :a I as, -:\ \ i;. in 7'jbi i: 1. F i'). Z nives the com- r pa i• ; ;on bet •J.'I; '.'II the ;;ut!stica! mode.' code (ALICE) P r PI!! c i. i ons id the expennontal spectra. It can be •it-Mr'i that ti- peak :."'O«! cion of the proton spectrum ; :M t. t Cho. 7, W! moiio! but alpha spectrum is softer by r .v)i...,t ? MeV. he calculated peak position for alphas c : .n F+!Sib syn L n wa j 15'. ] MoiV and fur Li+Ay system was 14.6 McV. whereas in observed experimental spectra these v a 1ues a r H 10.8 and 1.1.0 MuV respectively. Further mea-iuremun t:-; are pl anned to extend the range of temperatures in Gn compound nuclei in order to systematical 1y study the temperaturt e dependence of the emission barriers. References : 1.David 3. Moses et al Z.Phys.A -Atoms and Nuc1e i 520.229(1985). 2.M.Gonin et a I Ph'ys. Lett.B 217.406(1939) 1000c PTO1ON iPECTHA F»MI>(70MIV» *• PR01QX SPECIRA — - FlHi/ I ?0M / *• ALPHA 100;.- 10017 I.Oi- X) o o ai G 10 !'• I'l '• J '•' "' •'(J CM. ir.'i'K'V ( MrV ) cr.f. rr.jf'Oy (Mev) 102 EVIDENCE FOR ALPHA PARTICLE DOORWAY STATE IN 2551 AROUND 44 MeV EXCITATION THROUGH THE REACTIONS 12C (160, 8Be) 2 0Ne* AND 12c (180,«He) 2 Suresh Kumar, M.A. Eswaran, E.T. Mirgule, D.R. Chakrabarty, V.M. Datar, H.H. Osai" N.L.Ragoowansi and Uttam K. Pal Nuclear Physics Division, B.A.R.C. Bombay-400085 In conti nuation of our study( i .2 ) of heavy ion resonances i ;'; i-ho system 160 + 12Q we report in the present work experimental evidence cof alpha particle doorway state -r. >-8£i at 43.8 MeV corresponding to Ec. -i. (160 2C) - 27.0 MeV. 1 The intermediate -"• tructare res f T?_ m.„, (ISI 1 R O + 12C) = 27.0 MeV .; • -'•. 3.tec as i'/rt^r;1 ' ., in our oarlisr work in the /-.-•action 12C •0,4 He) 2*Hg*, was found to decay dominantly t ;.he Ex = 20.25 MeV state in 2 4Mg, wnich has strv tural connection to quartet state of 2 0Ne3 ) . In th>-th*: present work we have evidence of this resonance decaying also to the quartet states(3) the region of 6.7 to 7.8 MeV in 20 m 8 through the reaction 12c (iso, Be)20ft[e#_ A natural carbon target of thickness 70 ug/cm2 was used. For 8Be detection AE and E detectors of 30 urn and 1000 [xm thickness were used subtending a geometric solid angle of 5.3 msr. at 9o to the beam. For alpha detection two telescopes were used at 6° and 16© to the beams respectively subtending a solid angle of 0.42 msr. The data were recorded in two dimensional mode ( AE-E) in a pc based data acquisi- tion system to enable analysis with two dimensional gates for particle identification. Excitation func- tion measurements were taken for the energy 100 12CC'6O.eSe)20Ne" range of E(i60) r 53 to > Elob-63MeV.e,ob=9''2.35" 80- 63 MeV with 1 MeV steps 5 Efficiency(BBe)=!3-15V. with about 25 particle nA '60- beam on target. Since • n 8 Be decays into two alpha particles the consequent O 40 1 f[ ' ' detection efficiency was - 1 calculated by a computer 20- VWll i programme. An example of the 8 Be spectrum is shown 50 100 150 200 CHANNEL NO in fig. l Fig. 2 (a), ng.i 103 (b) & (c) show the excitation functions for E(ieO) 53 to 63 MeV for the reaction i2C(160,a Be)20Ne* for 0+, 2+, 4+ ground state band respectively. Fig.2(d) shows the excitation function in this reaction lead- ing to states in the region 6.7 to 7.8 MeV which have been identified3) as quartet states in 20Ne. Fig.2 (e) sho^;; the excitation function for the reaction 120 (1 60,4 He)24Mg* leading to the 20.25 excited state of 24Mg. Solid lines are through the points of present data and dashed line showing the earlier 'iata1 > for check on the reproducibility. It is observed Ext Si) (MeV) from those excitation functions that the intermediate resonance structure at Ec.ra. =27.0 MeV corresponding to excitation energy of 43.8 MeV in 2 8 Si decays to 20.25 MeV state in 2 4Mg through alpha channel (fig.2e) and also through a Be channel to quartet states near 6.7 to 7.8 MeV in 2 0Ne (fig. 2d) and not to low lying non-quartet states of 20Ne (fig.2 a,b & c). The 20.25 MeV state of 2 4Mg is known to be a 12c + 12C resonance which decays sig- nificantly by alpha emission to quartet structure near 7.4 MeV in 2°Ne3). Hence from the present data it is surmised that the resonance structure at 43.8 MeV excitation in 2 8 Si is an alpha particle doorway state having a large overlap with 20.25 MeV pos- sible quartet state of 24Mg and 6.7-7.8MeV quartet states of 2 0Ne. 1) Suresh Kumar et.al. NP Symp. (DAE) Aligarh (1989), 029. 2) M.A. Eswaran et.al Phys. Rev. C39 (1989) 1856. 3) H. Voit et.al. Phys.Rev. Lett. 30 (1973) 564. Fi/ SHAPE EVOLUTION AT HIGH SPIN AND EXCITATION ENERGY IN THALLIUM ISOTOPES Y.K.Agarwal, C.V.K.Baba, H.C.Jain, A.Roy, M.K.Sharan, R.Varma Tata Institute of Fundamental Research,Bombay-5 D.R.Chakrabarty, V.M.Datar, R.K.Choudhury. B.K.Nayak, S.V.S.Sastry Nuclear Physics Division, B.A.R.C., Bombay-85 Recent measurements [1] of high energy V~ray spectra ( 5 105 Pb case [1]. Also the widths of the split components are "50% larger than in the Pb case at similar Ex and Jma s . In a separate experiment we have tried to dis- entangle the effects of increased Ex and Jmax by studying the ^-ray spectra at Ea - 72 J-!eV in coin- cidence with a multiplicity setup consisting of 13 BGO and 1 BaF2 detectors (^ tot"40%). The fold dis- tribution beyond F^4, agrees with that expected for 'i naxiinuir: multiplicity M~15 instead of VL~"L3 consis- r.ec'. with the fusion cross section. This discrepancy ••„•*:•. be understood if the higher -I' s lead to fission. The F>3 fold gated Y~spectrum agrees with our ear- lier data. The low multiplicity events were con- taminated by- light impurity V-rays and so the cru- cial comparison between low and high fold gated *^~ spectra could not be made. Improved measurements with € tot ~ 75% for the multiplicity array are being planned. [1] D.R.Chakrabarty et.al.,Phys.Rev.Lett.58(1987)1091 [2] Y.K. Agarwal et.al.,Pramana 35 (1990)49. [3] W. Reisdorf, Z. Phys. A300 (1981) 227. . 107 MeV n --- CASCADE •r-i 89 MeV CASCADE C Pro) 2- 84 MeV 1 • 10 15 20 25 E7 (MeV) HIGH ENERGY V-RAYS IN THE FISSION OF 252Cf V.M. Datar+, D.R.Chakrabarty*. Y.K. Agarwal*, C.V.K. Baba* •Nuclear Physics Division, B.A.R.C., Bombay-85 •Tata In.stituc.rj of Fundamental Research, Bombay-5 In a recent investigation Kasagi et.al. [1] have reported a high energy V-ray spectrum extending much beyond the GDR bump (~15 MeV) in the spon- taneous fission of zs2Cf. The V~ray multiplicity was measured to be M 107 lated using the statistical code CASCADE (see Fig.). The calculated spectrum is in remarkable agreement with our experiment. It should be noted that the J- spectrum depends sensitively on the excitation energy distribution in the fission fragments. The Ex distribution used here is consistent with that derived from neutron measurements [3]. The measure- ments of Dietrich et.al.[4] gave a higher yield (a factor of 1.5 to 2) in the GDR region. The upper limit on the yield of ^-rays for E# ~20 MeV to ~40 MeV, was derived from the 38 cm run. The integral counts in this energy region for 1.8x109 fissions is 0±8. Folding the efficiency of the detector with Kasagi's measurement in this region gives an expected counts of "265. This im- plies an upper limit at the l •N. CASCADE o Id' FISGI-N FRAGMENT ANGULAR DISTRIBUTIONS FOE THE SYSTEM i9F+232Th S. !<":-•<. as. A. Navin.A. Chatterjee, P. Singh, R. K. Cnoudhury , A. Saxena, S. S . Kapoor, D. M. Nadkarni , B.K.Nayak,V.S.Ramamurthy* and S.V.Suryanarayana, Nuclear Physics Division,B.A.R.C., Bombay 400 085. *I.P,Bhubaneswar-751 005. Zhang et ai have recently reported/1/ for the sys- tem 19F + 23 2T"n, abnormally large fission anisotropy values in the energy range from 81 to 105 MeV,using mica track detectors. These values are perhaps the largest so far reported at these E/A and fissility values. They have also reported a bump in the anisotropy versus energy plot at E(Lab) ~91.4 MeV. In order to investigate some of these observa- tions by another technique (using silicon surface barrier detectors) we measured fission fragment an- gular distributions in the bombarding energy range of 94.1 MeV to 107.7 MeV,using the BARC-TIFR pel- letron accelerator.Natural Th target and two silicon detector telescopes were used for these 9measure- ments. The anisotropy values A=W(180*)/W(90#) deduced from Legendre polynomial fits to the angular dis- tribution data are shown in Fig.1.The anisotropies are significantly smaller than that of Zhang et al/1/. It is not clear as to why the results of ref.1 using a different technique do not agree with that of the present work.The angular distributions were integrated to obtain the total fission cross sections (0^) .The resultant fission excitation func- tion is shown in Fig.2 along with the data available from literature/1/. Following the procedure discussed in ref.2,the fission fragment angular distributions were calcu- lated using the effective moment of inertia derived from the measured systematics of 0C induced anisotropies/3/ and spin distribution deduced from a fit to the fission excitation function.The theoreti- cal predictions are shown, as continuous curves in Figs.l and 2.At all the energies measured the ex- perimental values of ani-jotropies are significantly higher than the saddle point statistical model pre- dictions and hence are anomalous.This observation is consistent with the entrance channel dependence of fission anisotropies reported earlier/2/. 109 References /I/ H. Zhang et.al., fhys. Lett. B218, 133 (1989) /2/ V.S. Ramamurthy et al.,Phys.Rev.Lett.63.25 (1990) /3/ R.F. Reising et al., Phys. Rev. 141. 1161 (1966) . 19F-232Th 3.0 • Zhang et al o Present work 1.0- . JL J_ 80 85 90 95 100 105 Ecr a(MeV) 103 - °F (mb) io! / ^VB)= 89.5 M«V (Rg)= 11.98 Im / •/ (hu)= 3.70 MeV 10' ~ 7•/ - Wong - Esbtnscn mod*' 0 10 •i ill 80 85 90 95 100 105 FISS1QK OF Au-197, Lu-175 AJID Ho-165 VITH 0-16 IOKS: CROSS SECTIONS AND ANGULAR DISTRIBUTIONS S.H. Iyer, A.K. Par.d?y, ?.Z. Kslsi and E.C. Sharia Ra-Jiechssisiry Division, BARC. Boabay-400085. As part of a systematic prog;aa of work on the fission properties of low Z !2<60) eleaents induced by light (1' and heavy ions, ve have carried out soie leasureients on the cross sections and fragment angular distributions in the fission of Au-197, Lu-175 and Ho-165 induced by 0-15 ions at several boabarding energies above vhe fusion b^riers bsing t>-e BARC-TIFR i4L'D Peiletron accelerator. While studies on the fissicn excitation functions provide information on fission barriers and level density paraaeters, those on fragaent angular distribution provide infornation on the the spin distribution and thape of the nucleus at th? saddle point ^K There is a renewed interest in the seasureaent of angular distribution of fission fragients froa systems of high angular aoaentua and in testing standard tnc-ories for their adequacies in interpreting and quantifying the data *3-6/> |n ^e present work we report a few experiaental results on fission cross sections and fragasnt anisotropies froa the interaction of Au-197, Lu-175 and Ho-165 with 0-16 ions. Ve have sade a preliminary analysis of the anisotropy data and estimated the mean square angular oooentua Targets of Au-197 of about 700 jig/ca^ thickness and oxides of Lu-175 and Ho-165 of about 0.5-1.0 ag/ca^ thickness deposited on high purity silver foils of 10-12 ag/ca^ were used. Fission fragients recoiling in the backward heaisphere were detected in a cylindrical lexan track detector aounted in a specially designed target asseably which acted as a Faraday cup and which allowed seasureaents over laboratory angles froa 90°- 165'. The center-of-mass transforaation was done by assuaing syaaetric fissicu with kinetic energies given by Viola systeaatics. '•' (See Fig.l). The absolute fission cross sections were calculated by integrating the fitted anisotropy function and froi a knowledge of the integrated beaa current ami target atoas. The experiaental anisotropies and cross sections are listed in Table 1 and compared with other available data '3'"' and also indicated in figure 2. A preliainary analysis of the anisotropy data A = U Ve acknowledge the useful discussions we had with Dr. S. Kail as of HPD, BARC. 1. R.H. Iyer, P.C. Kalsi, A.K. Pandey and R.C. Sharaa, Proc. Syap. on Nucl. Physics, 0-38, Vol. 32 B, (1989). Ill 2. R. Vandenbosch *nd J.R. Huizenga, Huclear fission, Acadenic press, H.V. 11973). 3. V.E. Viola, T.D. Thoias and G.T. Seaborg, Phys. Rev. 129 Ho.6, 2710 (1963). 4. B.B. Back etal, Phy. Rev.C. 32, 195 (July 1985). 5. Y. Kondo etal, Phys. Rev.C. 35, 828 (1987). 6. V.S. Raaaeoorthy etal, Phys, Rev. Letters 65, 25 (1990). 7. V.E. Viola etal, Phys. Rev. C31, 1550 (1985). 8. T. Sikkeland, Phys. Rev. 135 B669 (1964). Table 1 Experimental fission cross sections, anisotropies and other relevant paraaeters Reaction Compound E[a[j Uf nucleus (HeVI (=b) ¥(90) Calc. Au-197+0-16 Fr-213 81 17.7 1.76 223 96 420 2.66 592 108 919 2.9 760 Lu-175+0-16 Au-191 81 0.6 3.66 538 96 45 3.87 704 Ho-i65+0-16 Re-181 81 0.012 3.02 364 Fig. 1: Fission fragient angular Fig. 2: Experimental fission fragient distribution of Au-197 + 0-16 anisotropies in the 0*16 induced at 96 MeV fission of Au-197, Lu-175 and Ho-165 1+1.0300529+.04Cos4e+.59Cos69 ..5 X X Q X a 3-10 • X o (a) Au-197 (+ present work, x Ref.3) •0 (bl Lu-175 (•present 4- work) (c) Ho-165 (• present work) 0-50 10 1 1 I i 1 11 1 1 90 135 180 60 115 170 CM. Angle in degrees E, .„., (MeV) 112 '. . A . ^adxar:;: and S.S.Kapc. r t.ar Physics DivisionB.A.R.C., Bombay-400085 Recent measurement of proton and alpha induced fission cross-sections of 235.238U at deep sub- barrier energies /I,2/ have shown large enhancement of the <5~i at deep sub-barrier energies (E < 4 MeV). This enhancement of (ft was attributed to the fission of the Coulomb excited target states. On the basis of this much larger fission cross-secti p.s are expected in the case of heavy ion induced fission of 235U. To test this we have carried out the measurement of 10B induced fission cross-section of 235U in the energy range of 3)6 to 40 Mev (coulomb -barrier — 60 MeV). Although it is well known that there is significant enhancement in the heavy ion induced reaction cross- sections but no measurements have been reported in the deep sub-barrier energy region as the fission cross-sections are expected to be e-tremely small. As shown schematically (Fig.l), the 2 3 5{j target (~400 ugm/cm2) was bombarded with i^B-beam at the BARC-TIFR Pelletron Accelerator Facility,Bombay. The fission fragments were recorded en an annular Lexan Polycarbonate detector of thickness 120 urn (label-A). This detector registered back angle fission fragments from the 10B induced fission of 235U. The boron beam was stopped completely in the 10 mil thick gold backing. Another assembly of 2 35{j target and a similar annular Lexan detector (label-B) was kept just behind as shown in the Fig.l, in order to record the fission events occuring due to background neutrons alone. The complete target-detector assembly was mounted on a copper cold finger and was cooled by liquid Nitrogen. Lexan detectors were etched with NAOH solution and fission tracks were counted using optical microscope. The number.- of fission tracks on the i^B-side and on the B.G.-side along with the measured fission cross-sections after proper correc- tion factors, have been given in Table-1. The measured values are also shown in Fig.2 along with the calculated d"fusion values which have been • btaineci with Wong and Esbensen model using adjusted parameters obtained from the reaction of i 113 TABLE-1 Sr. E Fis.Tracks Fis.Tracks No.of i«B Oii s s i on No. MeV le B-side in B.G. Particles ubarns 1. 41 4616 539 7X101 •* 11.4+1.6 2. 35 3771 662 7X1014 8.&H.3 3. 30 10335 2131 3X1015 5.1+0.6 The observed enhanced fission C.S. could be due to multiple contributions such as direct fusion- fission, fission following Coulomb excitation of the target nucleus and fission following neutron transfer occuring from the projectile to the target. The contribution of the latter is expected to be large at distances of closest approach (as the energy depen- dence of neutron transfer probability is believed to depend exponentially on the wave number and distance of closest approach). The contribution of the latter is proposed to be estimated by conducting similar measurements for medium heavy targets such as 2O9Bi and 2®6Pb where the neutron transfer is not expected to result in fission of the target nucleus. (IOB+I3SU ) — fissio.i cross sections Calculated lusion c.s • Present Measurement c a X) io c o 5 id COLO PINOCll Fig.l 10 30 60 B - Energy (MeV ) fig _ 2 l.Ajitanand N.N. et al. Phys.Rev.Lett. 58(1987)1520. 2.Ajitanand N.N. et al, Phys.Rev. C 40 (1989) 1854. 3.V.S.Ramamurthy et al, Phys.Rev>Lett.63 (1990) 25. 114 MASS-RESOLVED FRAGMENT ANGULAR DISTRIBUTION IN 12C + 232Th SYSTEM AT 72 MeV S.B.Manohar. Ashok Goswami, A.V.R.Reddy, B.S.Tomar, P.P.Burte and Satya Prakash.Radiochemistry Division. Bency John, Aruna Nijasure, S.K.Kataria and S.S.Kapoor. Nuclear Physics Division. B. A. R. C. , Bon lay- 400085. The mass-resolved fragment angular distribution for oc (28,5 MeV)+ 2*2Th and a (38.5 MeV> + 2'|ju system , measured using recoil catcher technique . showed a distinct increse of anisotropy with mass asymmetry - over and above the expected variation from multichance fission. The observed variation of anisotropy can be easily interpreted in the effec- tive transition state model •" , by assuming that both mass asymmetry and K- equilibration is decided during saddle to scission path. Under this assump- tion , if saddle to scission descent is fast, the effect in anisotropy due to mass asymmetry may not be observable. Generally it is believed that for H.I fission reactions the reaction times are rather small due to large 1-values. This had led to the development of pre-equi 1 ibrium mode^for H.I-fusion- fission reactions. Therefore in the present work, we have measured mass resolved fragment angular dis- tribution in 12C < 72 MeV > + 2J2Th system. The measurements were based upon recoil catcher technique for collection of fission products, fol- lowed by gamma spectrometry assay of fission product activity.. An irradiation chamber of cylinderical geometry of length 130 mm and radius of 7.5 mm was usedd in which an electroplated Th target ( /cm > was placed at 45° w.r.t beam direction. The mounted catcher foils covered the angle from 174° to 90° in ten nearly equal steps. A beam of 2C (+6 state,72 MeV> from Pelletron acclerator of intensity 250 nA was used for 24 hour irradiation. After the irradiation, the ten catcher foils were assayed for fission product activity using HPGe detector for 14 days . The measured activity of individual fission products such as (97Zr,99Mo. 105Rh.1X2Pd.1]5Cd and 115 d.slcih'ution. Fit, 1 snows angular d : s :r ' but i or o. Mo and Rh in tha centre of mass system where the dotted curve is the least squre fit W(e> = a + b cos <©>. Fig 2 shows the mass dependence of W(180>/W(90> as function of heavy fragmsnt mass. The observed variation of anisotropy do not show any systematic dependence with mass asymmetry as in case of a induced fission at similar energies. This observation shows the necessity of detailed studies on these lirtes with variation of entrance channel asymmetry to obtain over all better under- standing on saddle to scission decent. In view of this, work on systems such as 12C,16O,19F on252 Th is being undertaken. References 13 S.B.Manohar et ai. Proc. IAEA Symp. on Phys. and Chem. of fission. Gaussig - 105 2.2 1 I i i -QV W(180) 1.8 rl- AM W(90°) • 1.4 y Jt 1.0 —r I 1 I I i i i i 90 110 130 MO 170 120 130 U0 150 MH figl fig.2 116 MEASUREMENT Of" FISSION FRAf-iMFNT ANGULAR CURRFI. AM [IN IN -••:-v--' -:T lt?F, f > REACTION A!" 10T-.-: Fi,-V A1 a k B:• i -; e r i a 7 D. C. B i s w a s, D. M. N a d k ami, V. B.. A m b ekar, R. K . Che liuhur y and S.S.Kapoor Nuclear Pfiysics Di vision , B. A. R. C. ,Bomabay-400085 P . Bhat tachar ya, P.Basu, S. Bh-a 11 acharr ya and M.L.ChatterjeerS.I.N.P.,Calcutta At incident en^gies close to the coulomb barrier the predominant reaction mechanism in a heavy ion colli- sion is complete fusion corresponding to full momen- tum transfer . Contributions from incomplete momen- tum transfer events come from peripheral collisions which include the inelastic scattering or transfer reactions. Recently anomalous fission fragment an- gular distributions have been observed for many fis- sioning systems* . In order to quantitatively ex- plain the measured fragment angular distributions it is necessary to find out the contribution of incom- plete momentum transfer events for these systems . In the present work we have used a multi wire proportional counter (MWPC) to measure the folding angle distribution of fission fragments in »*F+2aaTh at 104.4 MeV. The l**F beam from BARC-TIFR Pelletron was used to bombard a self-supporting target of 1.8 mg/crrr-3 thickness. A solid-state detector with a col lima tor of lmm >; 10mm was kept at 90° at a dis- tance of 17.8 cm from the target . The MWPC was kept at a distance of 20 cm or the other side of the target to catch the complementary fragments . The active area ::if the MWPC was 5.2crn :•: 7.0cm and was position sensitive on both X and Y directions with a position resolution of 0.7 mm un each side . The details of the MWPC used has been de-scribed elsewhere2. The detector was filled with isobutane operated at a pressure of 2 torr. The angle calibra- tion of the MWPC could be obtained on-lin« from the p o s i t :i. c:t n s o f the 11 y 1 o n wires s up p o r t i n g the I'lvtrancf? window of th*^ MWPC . The measured fragment angular correlation is shown in fig. 1 alongwith the •jaus'fii :in fit to the data- \'h t. r i hu I if •< ar> rie;? t e-jr in i nnd from the:1 117 fit is 157.8+0.6 deg and the FWHM of the distribu- tion is 8.1+0.6 deg. Using the Viola systematics for the total kinetic en<2rgy distribution of fragments and for symmetric mass split, the k: .ematic calcula- tions give the folding angle for full momentum transfer events came at 156.85 deg which is shown by the arrow in the same figure. The peak of the measured folding angle distribution corresponds to about 95% of the full momentum, which is expected for incomplete fusuion of projectile and target after one particle removal from the projectile Further experiments are being planned to measure the fragment angular correlations for this system at other energies and other target-projectile systems. REFERENCES: 1.V.S.Ramamurthy et. al Phys.Rev.Lett. 65 (1990)25 S.Kailas et. al. submitted to Phys.Rev. C 2.P.Bhattacharya et. al. Nlli A27.6 (1989) 585-587 CN FISSION 232 T* 400 — i CO 300 t O 200 O 100 1 J U5 150 155 160 165 170 FOLDING ANGLE(DEG) YIELDS . :30JECTILE-LIKE FRAGMENTS IN i2C+232Th AMD ISO £Th REACTIONS AT NEAR BARRIER ENERGIES D.C. Biswas,B.K.Nayak,V.S. Aaibekar,B.V.Dinesh, S.V.S. Sastry, L.M. Pant, D.M. Nadkarni and R.K. Choudhury, Nuclear Physics Division, B.A.R.C., Bombay-40085 Recent studies1) in B,C,O+Th fission reactions have indicated a strong mass asymmetry dependence in the entrance channel dynamics near the liquid drop Businaro-Gallone point. It was found that for projectiles below 12 c, the fragment angular distributions follow statistical model predictions, whereas above 12c, the distributions are anomalous. It is therefore of interest to study in detail the systems of C+Th and O+Th to look for effects of mass asymmetry in other reaction channels. In the present work we have studied the yields and angular distributions of. projectile like fragments emitted in these reactions. 22c and i^o beams of 80 MeV and 90 MeV respectively from the 14UD BARC-TIFR Pelletron accelerator were used to bombard a self-supporting 2 32Th target of 3.5 mg/cm2 thickness. Two detector telescopes^) consisting of gas ionisation chamber(AE) and surface barrier detector(E) were used to detect the reaction products and fission fragments respectively. The yields of various reaction products of Z>2 were measured over the angular range of 70 deg to 110 deg. The fission telescope was placed at a fixed angle of 90 deg to measure the fission fragment yields for normalisation purposes. The gas detectors were filled with P-10 gas at 150 Torr in continuous flow mode. The data of &E and E pulse heights were recorded in the PC-based multiparameter data acquisition system for further off line analysis. A typical 2D-plot of AE versus E in the i2C+232Th reaction at 110 deg is shown in fig. 1. The different reaction products of Z>2 are seen to be well separated from each other. These data were analysed to obtain the relative yields of the various reaction products at different lab angles which are plotted in fig.2 after normalisation to the fission counts in the fixed detector telescope. It is seen that for the C+Th system the yields 119 of various reaction products decrease with increasing scattering angle, whereas in O+Th system the transfer channels leading "to Z=6 and 7 are strongly inhibited at the forward angles. The striking difference in the variation of the yields of the projectile like fragments indicate different mass transfer processes in these two systems. Further data taken over different bombarding energies and covering larger angular ranges will be useful to obtain the systematics of the above behaviour. 78-6 MeV I2C+"2Th 872MeVi6O+"?lh 90 no ' LAB. ANGLE (0) 9 FiS-2 References: 1) V.S Rammurthy et al Phys. Rev. Lett. 65(1990)25. 2) M.N. Rao, D.C. Biswas and R.K. Choudhury, Nucl. Instr. Meth. B51(1990)102. 120 STUDY OF EXITATION FUNCTION FOR ALPHA INDUCED REACTIONS IN NATURAL IRIDIUM FROM 17-55 MeV M.fC. Bhardwaj, I'. Singh, r.A. Rizvi And A.K. Chaubey Department of Physics, Aligarh Muslim University, ^ligarh-202002, India. After the development of variable Energy -Cyclotron, the projectile excited upto very high energies became avaij.ijie and the experimental features of .the nuclear, reactions were studied by several investigators. The high energy tails observed in the excitation function contains important information about the reaction mechanism Keeping this view in our mind, we have measured the excitation function of the ( c<,xn) reactions with x=l-5 for Ir-191 and with x=3-5 for Ir-193. Sample of the element understudy were made from spectroscopic iridium having purity better than 99.99% by the vaccum evaporation technique. The target stack was irradiated at variable Energy Cyclotron CentrefVECC), Calcutta. The lOOcc ORTEC Ge(Li) detector, multi channel analyser and associated electronics was used to record the data. For checking the flux copper foils were used as a flux monitor and a good agreement was found with less than 10% discrepancy. In the present measurements thr uncertainty in the initial beam energy Was ±0.5MeV. The stopping power values are adopted from the tables of Nortli- ^ij'ffe pnd Schilling /I/, which are accurate within 5%. The straggling is neglected. The theoretical calculations are" done using the compound nucleus model with and without inclusion of PE emssion of particles. The theoretical calculation of excitation function by taking the consideration of equilibrium and pre-equilibrium both, are done by using the- GDH model proposed by Blann/2/ and this is represented by the solid line and those which are obtained by taking into consideration of compound nucleus formation onlv, by adopting the compound model of wer;sknpf-I->.'in«/.}/ are represented by broken line in the fi;]ur(:s. Our experimental measurements are shown by the solid brills. 121 "1 I ' 10 i 40 40 50 Ea(MtV) 191 191 Ir Ir {<< , 2n) reaction J f 10 f.' 1 -i b : 1 191 191 Ir (c<,5n) ir (c<, 3n) reaction 191 lr(«<,4n) reaction" reartion i '• • 1 in^_^_ . 193 193 Ir ( °(,3n) reaction Ir { 193Ir(o<,5n) reaction References /I/. L.C. Northcliffe and R.F. Schilling. Nucl. Data Table-A, 7, 256 (1970). /2/. M. Blann. Phys Rev. Lett. 28, 757 (1972). /3/. V.F. Weisskopf and D.H. Ewing. Phys. Rev. 57, 472 (1940) . 122 AND ANALYSIS OF EXCITATION FUNCTIONS FOR a-INDUCED REACTIONS IN 1<55Ho AND 2Oi>Bi B. P. Singh, M. G. V. Sankaracharyulu, M. A. Ansari and R. Prasad Department of of Physics, A. M. U. Aligarh Study of excitation functions for ct-induced reactions provide valuable information on the pre-equilibrium (PE) emission of particles . In a programme of studying PE emission, excitation functions for the reactions Ho(c*,n), Ho(oi 3r Ho(a,2n), 2Op > U{> Ho(a,4n), Bi(a,3n), Bi(o*,4n) and Bi(a,5n) have been measured using stacked foil technique. Spectroscopieally pure thin foils of Bismuth (1.5 mg/cm ) prepared by vacuum evaporation technique and thin metallic foils of Holmium (10.C48 mg/cm )have been used as samples. The stacks of Bi and Ho samples have been irradiated by a-beams of 50 MeV and 40 MeV respectively at the Variable Energy Cyclotron Centre, Calcutta, India. The incident flux for different runs calculated from ^ charge collected2 in the Faraday cup was 10 a-particles/sec/cm .Post irradiation analyses have been performed using a high resolution Ge(Li) detector coupled to the multichannel analyser. The excitation functions for these reactions have been calculated theoretically with and wihout the inclusion of pre-equilibrium emission using computer code ACT . Equilibrium calculations have been performed using Hauser-Feshbach model which takes into account the effect of angular momentum explicitly, while pre-equilibrium component have been simulated employing exciton model . In all the calculations the consistent set of level density parameters have been used. Experimentally meo._^red excitation functions for the reactions Ho(ot,n) and Bi(c 123 exciton number equal to 6(5p+lh) in the present calculations. Projectile independent prescription for two-body residual interaction matrix plement reproduces the experimental excitation functions satisfactorily. Interesting trends in pre-equilibrium fraction with energy have been observed. 5 r * Ho(-'.rt 10 10' 10 t. t-ig.l. Presently measured excitation function (Solid lines are just to ^-uide the eyes) References: 1. M.Blann, Ann. Rev. Nucl. Sci. 25 (1975) 123 2. H,D. Bhardwaj ana R. Prasad, Nucl. Instr. Methods; A242 (1986) 286. 3. W.Hauser and H.Feshbach; Phys. Rev.87(1952)366 4. J. jr. Griffin; Phys. Rev. Lett. 17 (1966; 478 5. B. P. Singh et al.. Accepted for publication in II Nuovo Cimento, 1990. 124 ALPHA SCATTERING FROM 6Li NEAR THE C. Samanta, S. Ghosh, H. Lahiri 5aha Institute of Nuclear Physics, Calcutta-700 064 S. Ray Physics Dept. , Kalyani University, Kalyani 741235 SoR. Banerjee Variable Energy Cyclotron Centre, Calcutta-700 064 Ue have studied the LiC0*. ^ ) reaction at 23 angles, 7° to 70°, using tha 50 P^eV alpha beam from the Variable Energy Cyclotron of l/ECC, Calcutta. The motivation is to investigate which mechanism excites the continuum near the c< -d break-up thres- hold - a topic uhich has many important aspects^). Ua have measured the yield in an one FleV bin from thetf-d break-up threshold (1.47 to 2.47 Fiel'). The . experimental details have been published elseuhere^"', The Impulse Approximation (IA) calculations have been done assuming that the yield near this break-up threshold arises from the quasi-free tuo-body inter- action between the incoming alpha and the bound °< or d-clustar in ^Li followed by an o< or d knockout. ~oth the Plane 'Jave and Distorted '.Java IA calcula- tions show fair agreement uith the trend of the(r«'9-i) measured cross-sections between lab angles of 11° and 30°, For lab angles below 11°, the reaction scans tha low momentum component of the °(. -d bound state uave function and thara is an apparent satu- ration in the measured cross-section in contrast tn the sharp rise predicted by the D'JIA/P'ilA calcula- tions. At angles greater than 30° the reaction probes the large momentum component (q>,7C7 PlaV/c) of the c< -d bound state wave function and hero our calculations severely underpredict the observed cross :.ect ion, Flecause of our choice of br&ak-up uindow at th-a high eject ile alpha energy we nrg scanninn tiiat region of the break-up continuum uhwrd kh'j.1 .-iv-.iilab.le anorgy for th-j broken-up °< ~. c:air i? r.triall. At small ralativ-a "io;n^n;:a (M — i this may in.juoo -j recombination al + d ->^LI, clu 125 strong final state interaction - an affect not taken care of in the Impulse Approximation calculations. To study this effect ue have carried out a O'JBA cal- culation assuming a possible excitation of a virtual stats at the break-up threshold of 1.47 MeV uhichCRga.; doss give a lowering in cross section at foruard angles. However, at large angles (^lab>450), the measured cross section is an order of magnitude larger than both the above calculations. The origin of this large back angle break-up cross section is being investigated. REFERENCES : 1) H. Delitto, 3, Buschrnann, V. Corcalciuc, H.3. Gils, No rieide, 3. Kiener, H. Rebel, Co Samanta and S. Zagromski, Z. Phys. A332, (T9S9) 317 2) C. Samanta, S. Ghosh, S. Ray and 5«R» Banerjee Proc. of the DAE Symp. on Nucl. Phyo., at BARC, Bombay, Vol. 31B (1988) 019 100.0 — PWBA IO.0 I i 1 U» f - *A 0.I o.oi 10 <0 60 JO 100 126 MICROSCOPIC ANALYSIS OF 9Be (cc,a • J9Be*AT E= 65MEV. Subinit Roy, H. Majumdar, J. Chatterjisnd S.K.Datta Sana Institute of Nuclear Physics, Calcutta-730064 and S.N. Chintalapudi and S.R. Banerjee Variable Energy Cyclotron Centre, Calcutta-700064 The folding model has been used successfully in the description of a-scattering from various nuclei /I/. However for very light nuclei, e.g. Li or Be, the data are scarce. Possibility of a—exchange also enhances the cross—section at the backward angles and it often becomes difficult to describe the data in terms of a simple folding model /2/e 0 The inelastic a-scattering data on Be are not many /3,4,5/. We chose to measure the angular distribution of 9Be at E = 65 A4eV, where no back- ward angle measurement exists. The purpose was to investigate how well the microscopic formalism describes the data at the backward angles„ We have used the folding model with reasonable success in our previously reported measurement and analysis of 8§Sr(a,a')«8Sr* ftf and 34S(d,d«)34S* fifm The experiment was carried out at the Variable Energy Cyclotron, Calcutta with an a-beam of E = 65 MeV. The self-supporting target was pure °Be having a thickness of 1.5 mg/cm2. Mo particle identifica- tion was used as the competing reaction Q-values for (a,p) (a,d), (a,t) (a,3He; channels were highly negative. Angular distribution was measured in steps of 2 degrees from 20° to 110° in the lab frame. Fig.l. shows the elastic scattering distri- bution. The so"Id line is a standard optical model calculation. The dashed line is a micros - copic folding model calculation where the real part of the potential was generated from known ground state densities /8/ and standard M3Y potential. In fig.2. inelastic scattering da/dsi. 127 [to the 5/2", 2.43 MeV state are shov/n. The calcu- lation employs DWBA with collective form factor. ;Microscopic calculation with shell model transi- tion densities are in progress. Exchange effects jas also coupled channels contributions will be iconsidered to see if improvement results in the {fit. . A.M. Kobos et al., Nucl. Phys. A425 (1934) 205. . V.N. Bragin et al., Sov. J. Nucl. Phys. 44 (1986) 198. . R.G. Summer Gill, Phys. Rev. 109 (1958) 1591. . R.J. Peterson, Nucl. Phys. A377 (1982) 41. '. M.N. Harakeh et al., Nucl. Phys. A344 (1980) 15. 76/. S.K. Datta et al., Phys, Rev. C39 (1989) 1281; /7/. Subinit Roy and S.K. Datta, Proc. Nucl. Phys.* Symp. 32B (1989) p3. /8/. H. DeVries et al., At data and Nucl. data tables, 36 (1987) 495. i i "! i i i - rrri V. -i /o-i 1. ; ;...;. :— i—i—i—i—j ]_.i_-1. J Zo 80 t&O a-o do 128 ANGULAK DISTRIBUTION OF NEUTRONS EMITTED IN THERMAL NEUTRON INDUCED FISSION OF 235u M.S.Samant,R.P.Anand,R.K.Choudhury, D. M.Nadkarni and S.S.kapoor. Nuclear Physics Division B A R C Bombay 400085. Although neutron emission in thermal neutron fis- sion has been studied in great detail,the mechanism and time of emission of the prompt neutrons is still not clearly understood.There is yet no clear answer whether there are prescission neutrons emitted in the fission process.Recent studies in heavy ion in- duced fission reactions have shown that in many sys- tems the number of prescission neutrons emitted is much higher than that expected from statistical models, thereby leading to the conclusion of long saddle to scission transition times in the fission process.Earlier studies on prescission neutron mutiplicities in 235U(nth,f) reaction have yielded contradictory results /I,3/-In the present investiga- tion, we have measured the angular distribution of neutrons from mass and kinetic energy selected fis- sion fragments to examine the above questions. A back-to-back gridded ionisation chamber was used to measure the fragment energies and angles. A NE 213 detector was placed at a distance of 70.1 cm from the target along the electric field direction to dete^ ^ the prompt neutrons.The experiment was carried out at the CIRUS reactor with appropriate shielding for the neutron detector.The pulse height,pulse shape and time of flight information were recorded from the NE 213 detector in coincidence with pulses from the ionisation chamber. The grid pulses were used to determine the angle of fission fragments with respect to the electric field direction. For a given pulse height at the collector, the grid pulses have a uniform distribution for isotropic emission of fis- sion fragments. The singles data from the ionisation chamber were analysed to obtain the calibration of grid pulses for event by event angle determination. Fig.l(a) shows 2-D correlation of grid and collector pulse heights for one side of the chamber. For a given Vc, the large Vg values correspond to emission close to 900 to the field direction and due to target thickness effects a slight distortion in the grid distribution is seen. This was corrected by suitable 129 normalisation of collector and grid pulses as func- tion of the Vg/Vc parameter and the resulting cor- relation is shown in Fig. l(b). The coincident events were analysed in identical manner,and the neutron angular distributions were determined after normalising with the singles data for each mass and kinetic energy bin of the fragments. Fig. 2 shows angular distributions for the mass pair of 96/140 for various TKE bins. The peaking at 0° and 180° is due to strong kinematic focussing of neutrons due to fragment motion.Contribution from prescission neutron emission appears as an isotropic component in ' the angular distribution. Exact Monte Carlo calculations are in progress to determine the pre and post-scission components required to fit the measured angular distributions.We thank B.R.Ballal and S.R.S.Murthy for providing valu .able help during the experiment. (t) Mt/MH = 96/KO 175 2SI .-:/i.VT •-• 205 170 IS4 • OS ' * *» 2 - 165 * Si 63 «», _ if 160, MO la) 307 3 .«* ***«*. za> '«*«««. ,»x> 2 TKE.15S o _ 20E IM IfO 0 I • I • I • I • ' „ I -1.0 -.8 -.6 -4 -2 .2 .4 6 .8 1.0 Ha ten ^ 5 So SOT 5» Co Cos0LAB Fig.l(a) & l(b) Fig. 2 1. Kapoor S.S. et al, Phys. Rev. 131 (1963) 283. 2. Marten H. et al, Nucl.Inst.Meth. A264 (1988) 375 3. Blinov M.V. et al, Sov.J.Nucl.Phys. 12 (1971) 22. 130 FISSION FRAGMENT TEMPERATURES AND LEVEL DENSITIES IN THERMAL NEUTRON INDUCED FISSION OF 23 50. M.S.Samant, R.P.Anand, R.K.Choudhary ,K.Kumar, D.M.Nadkarni and S.S.Kapoor. Nuclear Physics Division.B.A.R.C..Bombay 400085. Studies of emission spectra of neutrons from the excited fission fragments provide a unique tool to investigate the statistical properties of the neutron rich nuclei produced in the fission process.We have undertaken a program to determine the neutron spectra from time of flight measurements using a NE213 detec- tor. The spectra are measured along the direction of fragment motion and analysed to obtain the centre of mass spectra from fragments of selected mass and kinetic energies.In the first experiment solid state detectors were used to detect the fragments and preliminary results of this experiment were reported earlier/I/. In the second experiment a back-to-back ionisation chamber was used to measure fragment energies and angles.The data corresponding to +100 with respect to the neutron direction were analysed to determine the neutron emission spectra in this ex- periment. The improved statistics in the later experi- ment permitted us to determine the neutron spectra from mass,energy selected fission fragments.The centre of mass energy spectra were fitted by the ex- pression N(rj) = q* exp(-q/Teff ),where q is the CM. energy of the neutrons and X and Teff are the parameters of the Maxwellian distribution.Teff is closely related to the temperature of the residual nucleus after neutron emission and A is found to be close to either 1 or 0.5 depending on whether only one or more neutrons are on the average emitted in the dexcitation process. Fig.l shows the variation of Teff with total fragment kinetic energy for a typical mass pair of MJL = 96 amu and MH=140 amu.As expected the temperature decreases with increasing kinetic energy of the fragments.Fig.2 shows the variation of Teff with fragment mass. In order to explain the data, calculations were carried out using statistical evaporation code ALICE II using shell dependent level densities.The liquid drop level density parameter a=A/k was varied to see the sensitivity of the cal- culations to this par ameter. For each mass bin the average excitation energies were taken to be 131 Ex = V (Bn + n )+Ey where V and Ey are the average neutron multiplicity and average gamma ray energy.The calculations were done to average over various masses and charges for each mass bin. Fig.2 shows the results of the ALICE calculations for two values of the level density parameter 'a*. The calculations in general explain the neutron emission spectra from fission fragments with a=A/7. However some disagree- ments for light fragments of ML < 100 amu,ead heavy fragments MH = 128-132 amu are evident,which need further investigation. Tetf 155 165 17.5 185 145 155 165 175 185 TKE 2.00 EXPERIMENT ••• 1-60 ALICE II CALCULATIONS -—a=A/10 a=A/7 1.20 0.80 0.00 i.i.i.i.i.i 70 90 110 130 150 170 FRAG. MASS NO. l.M.S.Samant et al.Symp.on Nucl.Phys.Aligarh(1989)058 CROSS-SECTIONS FOR THE 46Ti(n,2n)45Ti and 50Cr(n,2n)49Cr REACTIONS AT 14 MeV NEUTRONS P.M.Dighe, CR.Pansare and V.N.Bhoraskar Department of Physics, University of Poona,Pune-7, ABSTRACT This paper reports estimated and measured values of the cross-sections for the nuclear reaction 46Ti(n,2n)45Ti and 50Cr (n,2n}49Cr induced by 14 MeV neutrons. The cross sections were measured relative to ^Al (n, oC ) ^4Na reaction employing activation method. Cross sections were also computed theoretically using the stastical model and ALICE CODE and compared with the experimental results. INTRODUCTION : Cross-sections of these reactions have been reported by a few workers but a large uncertainty is observed in the reported values. The International Nuclear Data Committee-'- has therefore recommended measurement of cross-sections of these reactions because accurate data is needed for fission and fusion reactor technology. EXPERIMENTAL : Neutrons of 14 MeV energy were produced employing D-T reaction in our laboratory. Each sample was prepared seperately by packing the enriched isotope of the element alongwith an aluminium foil (99.9 %) in a polyethylene bag. Samples were irradiated with 14 MeV neutrons of flux - 10^ n/cm^/sec. The irradiation time was set equal to 30 rnin and 90 min for 50Cr and 46Ti respectively. Nuclear reaction ^ hi(n,ac) ^9Na was used foe monitoring the neutron flux as the cross- section of this reaction is well defined and covers a wide range of the half life of product nuclei. The induced gamma-ray activities of produced isotope 45Ti(0.511 MeV, 190 %) with half life, Tl/2 = 3-06 h^s and 49Ct (0.511 MeV 185 %) with half life T\/2 - 5.79 min were recorded separately with HPGe detector coupled to a 4096 channel analyser. The measured values of the cross-sections are in agreement with the theoretically estimated values. The results are given in the table I. The theoretical calculations were carried out using ALICE CODE2 and semiemperical model3.The results are accurate within +_ 5 % . Theoretical results obtained with semiemperical relations are closed to experimentally measured results. ACKNOWLEDGEMENTS : Thanks are due to B.R.N.S.,D.A.EU, Bombay for financial support to the project. Table I : Cross-sections values in mb for the nuclear reactions. 46 Nuclear reactions Ti(n ,2n)45Ti 50Cr (n,2n)4<9Cr PRESENT WORK Experimental 47.0 + 4.0 28.0 + 2.0 ALICE CODE 58.0 26.0 Semi-empirical 50.0 30.4 model EARLIER REPORTED values ExpeLimental 50.4 + 8.0 26.4 + 8.3 31.0 + 8.0 27.0 + 6.7 28.3 + 3.0 Theoretical 54.0 — REFERENCES : 1. INDC (NDS) 1611 GT/INT(87)-7, 1984. 2. M-Blann VCID-20169 (1984) and IAEA-NDS-93 (1988). 3. Pearlstein, S. Nucl. DATA A3 327 (1967), U.S. Atomic Energy Commission Report No. BNL-897 (T-365) 1964. ION-ION POTENTIAL FOR VARIOUS FORMS OF NN INTERACTION. R.C. Mishra, Madhup Seth, V.S.S.D. CoUjge, Kanpur and Ravi Datt Godiyal, Ashok Kumar, D.B.S. College, Dehra Dun. In the present paper we have calculated ion-ion potential for various forms of NN interaction. These interactions are used for the calculation of fusion cross sections of 12C+12C reaction at the centre or mass energy, Ecm = 28.20 MeV /I/. Peak of fusion cross section curves is observed at the above energy in all the cases of NN interaction. Dynamical calculations of ion-ion potential are dependent on various factors such as (i) impact parameter (or entrance channel angular momentum), (ii) incident energy (iii) initial relative random orientations of the colliding clusters. There- fore, nature of ion-ion potential is expected to be different depending upon the initial conditions of dynamics. In the present work, two (incident energy and initial relative random orientations) out of above three factors are kept con- stant in calculating ion-ion potentials for four different forms (Ml, M2, M4 5 M8) of NN interaction /2/. The ion-ion potential is obtained in analogy with double folding model procedure of obtaining real part of the optical potential. In double folding model, the ion-ion potential is given by V(R) = jp^) ? ^? Subsitution of the value of NN interaction '2/ results in the ion-ion potential as, Al A r r J m V(R) = I I - V (1 - ----] expl- (~r- -) ) 1=1 j=Al+l ij o Fusion cross sections in the present reaction are calculated purely in classical equation of motion approach (CEOM) /3/ considering nucleons as classical spinless particles. The initial velocity of clusters corresponding to Ecm = 28.20 MeV is 1.5 fm/NS. The critical impact parameters which lead to fusion for Ml, M2, M4 8 M8 forms of potential are 5.2, 5.2, 5.0 8 5.8 fm respectively. Figure shows the plot of ion-ion potentials with respect to the separation of centre of mass of colliding clusters (RCM) at the end of each time step (T = INS) of collision event. It 135 is clear from the figure that all ion-ion potentials have approximately the same value upto Rcm = 14.6 fm. This separation (RCM) is reached in the 2nd NS of the collision event. Nuclear part of ion-ion potential in case of Ml, M2 6 M4 forms of interaction is ineffective upto RCM = 7.8, 7 8 6 7.7 fm, respectively. This distance is reached in the 5th NS of the collision event. In case of M8 form of NN interaction the ineffectiveness is upto RCM = 8.2 fm which is reached in the 6th NS of the collision event. Attractive range of NN interactions (Ml, M2, M4 a M8) starts from RCtf = 7.0, 6.9, 5.6 and 7.3 fm which are reached respectively at T = 9.0, 10.0, 7.0 and 11.0 NS of collision event. The maximum attraction corresponding to above forms uf interaction is 8.9, 22.7, 40.2 and 9.6 MeV which is obtained in the 18th , 28th, 29th and 24th NS of collision event respectively. The variation of ion-ion potential with respect to RCM at different times of collision event shows that reorgnization of nucleons takes place during the entire process of collision. This reorganization of nucleons is massive when the nucleons of colliding. nuclei are in the attractive range of NN interaction. The reorgnization of nucleons is responsible for the shape oscillations of the fused system. References : /I/ R.C. Mishra and Y.R. Waghmare, Proceedings r of the International Con- ference on Nuclear Reaction Mechanism, SINP Calcutta, 1989. I /2/ H.S. Koehler and Y.R. Waghmare,Nucl. Phys. j)6 (1965) 261, Y.R. Waghmare, Phys. Rev. B136(1964) 1261. - -46 /3/ S.S. Godre and Y.R. Waghmare, Phys.Rev. C36 (1987) 1632. 1 -32 -• 136 TEMPERATURE DEPENDENCE OF NUCLEON DRIP-LINE J.N. £3 Variable Energy Cyclotron Centre 1/AF, Bidhannagar, Calcutta-700064 D. Bandyopadhyay and S.K. Samaddar Saha Institute of Nuclear Physics 92, A.P.C. Road, Calcutta-700009 and N. Hudra Department of Physics, Kalyani University Kaiyani, West Bengal Therrrj^dynamic models with assumptions of liquid-gat phase equilibrium or metastable equ- ilibrium (~ero total pressure without any ext- ernal vapour) have been found very useful in predicting limiting temperature s''1" in finite nuclei. With further constraints that the che- mical potential of neutrons (^ ) and protons ( M-p ) must be 137 asymmetric nuclear matter in the self-consistent mean-field approximation with addition of Coulomb and finite size corrections. The role of temperature on the p -stability line is to move it towards a region of a little high neutron-proton asymmetry. The accompanying figure shows lines of limiting temperature and limits of stability as a function of temperature for nuclei with N = 126 with varying charge number. The hatched area is the region of stability. From the figure, one can find that very exo- tic nuclei that may not be stable at zero or low temperatures may become stable at higher temperatures. At first sight, this looks counter-intui- tive; the reason is traced back to the lowering of equili- brium density at higher temperatureP 22,0 that decreases the kinetic energy and also dilutes the A repulsive density- dependent part of the interaction. References : 1. S. Levit and P. Bonche, Nuc. Phys. A437 (1985) 426 2. D. Bandyopadhyay et al., Nucl. Phye. A511 (1990) 1 3. J. Besprosvany and S. Levit, Phys. Lett. 3 217 "(1989) 1 138 JL PARAMETRISATION OF DISTRIBUTIONS OF FUSION BARRIER A. K. Mohanty. S. K. Kataria Nuc.l ac-r physics division, D. A. R. C. , Bombay 4OOO85. and V. S. Ramamurthy InsLlluLe Of Physics, Bhubaneswar 751OOS. Th£j fusion cross sections of heavy ion collision near and below the couJomb barrier are still not well understood inspite or extensive theoretical and axporimental efforts. The compound nuclei.-; spJn distributions of the fusion cross sections art? far more sensitive to the mechanism underlying sub-barrier fusion then excitation functions alone . The wej1 studied theory, accounting for the observed large sub-barrier fusion cross sections are based on coupled channel approach where the coupling to the low lying collocUvw states is included explicitly [11. This coupling spJiIK tho single barrier into a distribution of barriers which can bo approximated by a gaussian distribution. The wj dth of this distribution can be related to the deformation length, deduced from collective model analysis of data on elastic scattering experiment or else they are obtained from published BCE.'O values T?J3. In a recent study it has been pointed out C33 that, best fits to the experimental fusion cross sections are generally obtained with distributions whi ch aru rather flat and are characterised by a. sharp cut-off vaJue at the low energy end. Furthor tho low energy cut-off barrier has been correlated with the separation oiiergios of the valonce neutrons and associated with tho distance at which merged potentials just allow neutrons to flow botweon the nuclei. Therefore, it has been concluded that fusion initiated by neutron flow is the principal enhancement mechanism and that coupling to the collective staU-s plays a secondary roJe. In this work, we have shown that, it is possible to fit fusion cross sections by using a large number of Lruncalotl gaussian distributions of barrier heights with tho saw average value but with tho different widths. It is also in fig. 1, that tho gaussian distributions of smaller 139 width, which can be related to the luclear deformation longth, gives higiiei- spin values than a flat distribution of large* width, though alJ give nearly same fusion cross sections. Tho quality of fit to fusion excitation function is; same for all shapes of barrier distributions as seen from fig P.. for widely different value of cr parameters of truncated gausslan distributions. Therefore, tho shape of spin distribution of the barriors which fits the fusion cross sections can not be obtained uniquely. As a result of present calculations it can be concluded that it is not possible to deduce the fusion mochanjsm from analysis of fusion cross section alono and there-fore, are in contradiction to the conclusion of Stelson ot. al . t3] that one needs to invoke the neutron flow as the dominant mechanism for sub—barrier fusion enhancement mechanism. In addition, the present study brings out that tho comparison of average spin values <1> against the experimental datas for the fusion channel has more descrimi nation on the underlying reaction mechanism. 1. M. Uokerman, Rop. Prog. Phys. SI C1O88D 1O47. P.. W. Reisdrof et. al. Nucl. Phys. A 438 C1985D 212. 3. P. II. Stelson. Phys. Lett. B 2OS C1Q88D 1QO. I'. H. Stol son et. al . Phys. Rev. C41 0 9903 1584. 90 MeV 96 MeV 98 MeV io3 3 10 m - JTt E I— I1 2 D 10 - SIG = 30 MfV .o / SIG» 10 MeV SIG = 6 MeV (l> / 10° I io' -^ i i i i i ill i i I i 90 95 100 105 107 10 IS 20 25 30 SIG (MeV) 140 PL-NET-RATION I HR0U6H TTME DEPENDENT BARRIERS 3.K. Kataria, PA'.S.SsKtry, A.K.Mohanty Nuclear Physics Division and K.V. Bhsgwet, Solid State- Physics Division B. A, R. C, Bombay-400085 The shpnrption and pniission of charged particles by a nucleus is generally ca i. cul ated under the an pi- ox i ma t :i on of a st a t :i c con 1 omb pot en t i a 3 bar r :i er .. In the casa of a deformed nucleu1;, one usually employs adiabtic approximation under which harrier penetration is taken as rn average qiiant.it y over all the incidRnt. orientat i on? e t c „ The va .1 :i d :i t y o f ad :i ah t :i c: aprox irnat ion i.e. the assumption of slowly va.ryi.nq collective.- variable e»g. nuclear shape & I f consistent, potentials, we have studied the problem of penetration through a rectangular tirrn dependent potential without making any ad i ah tic approximation or a sum ing that. the magnitude of the time 'J^penrlent part is small, V- vV,-!-V* Cos wt -a In earlier sturli.'^s of traversal times for tunnelling throu9h this model pot en t i a .1 , Bi> I: t :i I•;er and I.andauer o b t a i n e > i a n a I y t i r. a 1 e :•: p r e s v:i i. o n f o r t r a n s m i s s i. o n coefficients at incident energy Ffr as well as for transmision on through bands at F. ±. hw snergies by making assumptions on the magnitude of V, and i.iiiicri modulation quanta energy Tiw, and limiting themselves only to emission and absorption of only one quanta. In this study, WP have calculated the reflections and transmission coefficients with the inclusion of higher order si'13 bands with the energies E ±. nhw (n ,' t J (. ...:..I 141 t. •;! • i i.'S:/; :i on fen T in, ', u.:o < *• o - v -1". i" :i I • :i Y i < i the' t r anr-iiii : >'•- .1 (MI oi- o.)i- t i.; (ps '.-/hi'in I).av: • 11 :J- if jr b<'.'~\ n -mr)i"Jn 1 "it 1.on MI tin I. a, and vi •. i"i <.:•:•:'<:,'• thn > \,: :> '.-,'-, .1 (• r § o f ri • iiiodu 1 a t :i on quan t a dut-Mi'i '•. i):-i 111' -iv^r-i'-il. in Mi'-: 1. n t' j.r -ic t i. on rsqion), but. one h/•:;••• :invi'-it thr- c ! if; i-• J PM I'l-^tr.irKR obtained ! • y i!','l fc':l 1 i. n-'-i '.:'>n'J! '<: < >•!)•'> at Ui:-: i T •• n 1 n • 1 • •* r • i.--"'.r->, nww'.r ira I. I. y » I "h;-< 11 L.i r. 1 >_ -1 :i (. -j .1 solution to thr: pr o!:< 1 pin ypre oh t a :i ned in two differ ;nt way-j irnJ Ui:;y 'j^r^ chsrk^d .=iqainst the I :i m i I 1 iici H'-tri J H t i ( We? have' ai->f > ] :i ed I h j ;:- prccpdurK to srt- tliR i n f I '(••-•: n •':••?. of I 1. in---1 -d:ii-);''ii>"Jt;nt b-'jr r i. ;-rr on !. h>7 eni'"i \ he f.'nl iarif <-:nie n t factor of tht? total t r ariBmi !->ir>i on factor 13 1 ar «"!:.-.'-„; t at n--?.-ir HHO -barrier ennrqia-;, and fen above' harrier encirqiufi one finds large contr ibut 1 on t o 1. hH S I. I I" banrls r ••?.c> 11 1.1 i nq i ri w idsn :i nq of thv cibr.er ved c-.pprtrd. In t lit:7 <•? mi !=><=. i on protest, thf? rriod u I a t x on i-a f ri 111 n t 1 <~ 1 n br> rnt r a I. a t ed w i t hi t h&. cnllfLtivt iTiodf'f. of thcj (;';:c. .1 t prl n in: .1 RUS and this it can L-'^arJ to Rntianc:-- •.< I liriii-vuoii •»+" part icltis at. far below ariti much above I *. -- - • r i(--:i t-'iipi Fip I vr Fiir ec: I .. I'i.. Hu (. ( i k< 'I' '.u n l I'. I • .'.:':'.. t .. \\. I !-.-:» UQC •.::(!'I .. I,, i, .. • 1 i 1 v 1 !• ' 1 i< I ;' '•/. I'!.)-/. :'h , .. .1 1 •:;•/.• v I /., 142 A VARIABLE-HEIGHT PARABOLIC BARRIER FOR HEAVY ION FUSION Zafar Ahmed, NUCLEAR PHYSICS DIVISION, D.A.R.C, BOMBAY-400085 During the current decade, many theories have been put forth to explain dramatically high fusion rates of heavy ions below the Coulomb threshold. Saving the optical model calculations, it has mostly been a question of incorporation of the internal degrees of freedom of the colliding nuclei in various possible ways [1]. Static deformations, collective surface vibrations, neck-formation and nucleon transfers are the various internal states of the fusing nuclei which have been accounted for. However, a simple formula that can systematize the fusion rates both below and above the Coulomb barrier remains elusive in the literature. The present work is one step in this direction. In the language of the barrier penetration, it becomes an interesting excercise of invoking another coordinate in the fusion interaction [2]. When the fusing nuclei apDroach each other their shape and the surface profile of their density distribution changes (collective surface vibrations). Consequently, apart from the sepration, x, of the nuclei the intrinsic coordinate, y, makes the fusion interaction two- dimensional, a saddle-point (NECK) is formed [2]. This saddle point directs the nuclei towards a set of barriers and the net penetrability is obtained as some relevant average over y.We have schematized the neck-formation by a simple amenable 2-0 potential: V(x,y)=V 2 1/2mw x +1/2mwQy +gy+"h /2mItQ 1(1+1), x=r-R and calculated the "net penetrability in sudden-limit-approximation [3] (nw>>nw ). interestingly, our findings mimic a parabolic barrier of variable height (V.+gy) and the net penetrability (T,) is simply the height- averaged. We obtained: Tl = 1/(pH-ul) ln[{Hexp(p-u H/M+expf-vuj)}], 2 2 where «1=(2u/iiw) {V +n l(l+1)/2mR -1:), p=2nV /fcw, -Y-2UV /nw. V and V are the parameters appended to the usual one dimensional models (V^.tiw.R^. Mostly V =V suffices; when V =V =V ,V1 is related to the surface vibrations as V^g/fn72mw ) (then gHHeV fm becomes the free parameter). Further V can also be related to the standard deviation of the surface viorations. This formula would be useful in fitting the fusion rates and in providing their connection with vibrations. We present a few instances of the 1W°B *W8 s8*? and (f 143 f o (4) W. Reisdovf et al. Nucl. 4 -^— Phya. A438 (1985) 212 SL-^ (5) F. Viderback et al. Phys. 58Ni(6) ReV. C25 (1977) 954 I ml Vo = 97.9 MeV (6) M. Bekerman et al. Phy. Rev. Ho = 8.30 C25 (1977) 837 • . 4iw = 4.0 Vj = 4,0 MeV (7) M. Beierman et al Phya. Rev. = 10.0 MeV C23 (1981) 15B1 ) M.L.H^IbeU- JfJ. PKys. R^.Ci4O 100 2 J9' 10 1QQMo <0] 15 2D Lio' 140.0 MaV O+ °Pb (5) Vo =76.3 MaV 11.0 fm Ro = 12.25 fin 4.0 MeV .1 =4.0 MeV 1-10 12.0 MeV V. =4.0 12.G MoV 100 127. S r •^ "Sn (4) {.. 56Ni • 64Ni (7) Vo = 1Q7.83HBV ' '"' Vo » 96,0 MeV Ro = 11.29 fm Ro » 8.20 fm tw » 4.0 MeVj •frw ». 4.0 MeV V1 » 9.5 MBV 1 5.0 MBV V2 » "9.5 MeV I JO" V? s 5.0 MeV 120 T02.5 110 1 . i Ec.m(MeV) 144 DIRiXT CLUSTER-TRANSFER REACTIONS USING THE QUANTUM MECHANICAL FRAGMENTATION THEORY. Heaiant Kumar and Raj K. Gupta Physics Department, Panjab University, Chandigarh-160014, India, In some light heavy-ion reactions, the probability of direct cluster transfer is observed to be as large as for a single nucleon. The measured angular distributions in C-13(He- 3,He-4)C-12 at sub -Coulomb energies show /I/ that both the transfer of n OJ 3e-9 from C-13 target to He-3 projectile are equally probable. In another reaction /2/ of 0-16 + Al-27 at incident energy above the Coulomb barrier, the production rate of Be-8 in outgoing channel is found to be very lars;e ( 1/3 of alpha or C-l^ ), arising due to alpha-particle t °er from the projectile nucleus 0-16. Thus, in these reaction -?re is an increasing evidence of competition between the frt \tion and fusion processes Targets / projectiles, rather the compound nucleus , are observed to be fragmented. I, other words, here the fragmentation of target/ projectile seemsto play the same role as cluster transfer. It is from this point of view that we have used here the quantum mechanical fragmentation theory (QMFT) /3/, to study these direct cluster -transfer reactions. In the QMFT, fragmentation potential V (^ ) is calculated as the sum of two experimental binding energies, Coulomb and proximity potentials and the stationary Schrodinger equation in mass asymmetry coordinate °? = (A, - A2)/ (A, + A2 ), is solved at fixed R^ = R f + R2 . For the kinetic energy part of Hamiltonian, we use the classical model of KrSger and Scheid /4/. The temperature , 0, effects are included by using Boltzmann like occupation of exited states. C-13 ( He-3, He-4) C-12 : This reaction is studied at incident energies below the barrier and hence the probability of fomation of compound nucleus and its eventual decay via He-4 + C-12 channel ( indicated by the calculated fragmentation potential of 0-16) iri very small. Alternalively, the calculated fragmentation potential and yields ( fig.l) for the target C-13 show the two equally probable decay channels n +C-12 or He-4 + Be-9. In the first case, the emitted n when absorbed by He-3 forms the re.si dual He-4, whereas in the second case again two-possibilities arise : (i) Be-9 combines with He-3 to form C-12 or (ii) He-4 145 combines with He-3 to form Be-7. The second possibility , however, seems improbable since V (v[ ) for the compound nucleus 0-16 does not show any minima corresponding to Be-7. Similarly, for another reaction Mg-25 (He-3,He-4)Mg-24, we predict equal probability for transfer of n and Ne-21 cluster. 0-16 + Al-27 : The intrection barrier for this reaction is far below the incident energy of 0-16 beam used /2/. Thus, the compound nucleus Sc-43 can decay immediately. Also, the target or projectile can undergo fragmentation at large incident energy used in this reaction . However, the binding energy of Al-27is much larger than that of 0-16 and hence 0-16 can fragment more easily . Further evedences for projectile decay comes from the favourable Q-values of this reaction. The calculated V (TJ) for 0-16 shows He-4 and Be-8 as the most probable fragments . The calculated V(^ ) and yields for Sc-43 show that He-4 and Be-8 can be tran^fered from projectile to target and their yields are in ratios of 1:30 at 0 = 3 MeV and this ratio increases as 0 increases, leading us in the direction of the experimental data. Concluding, the QMFT is shown to give atleast a qualitative interpretation of the recently observed direct transfer of clusters in light heavy ion at both below and above the Coulomb barrier energies. 13 C {9*3MtV) 10V-r s. POTENTIAL 10" 5 io 5 10 Most Numbrr Mass Number Fig.l Fragmention potential. Fig.2 Mass yields. References 1. S. Kumar et.al., Proc. Symp. Nucl. Phys. 31B (1988)017; M.A. Eswaran et.al.,Proc. Symp. Nucl. Phys. 32B(1989)P33, 2. M.E. Branden et.al, J. Phys. G: Nucl. Phys. 12 (1986)391. R.K. Gupta et.al., J. Phys. Coll.(Paris) OS, 45(1986)477. 4. !i. Kroger and VI. Scheid, J. Phys. G: 6(1980)L80. 146 CONSERVATION OP CHANNEL SPIN IN TRANSFEfi REACTIONS: V.S.Mathur, Department of Physios, Banaras Hindu University Varamasi-221005. In the three-tody treatment of transfer reaotions of the kind A * a(b©x) » B(A®x) + bx one treats the partioles A,b,x as cores and uses three«body Alt Grassberger and Sandhas (AGS) equations to describe the system. The cross section of the process j -» i oan be read- ily expressed in terms of the reaction amplitude.,whieh is just the matrix element of thf» AGS operator between the ini- tial and final asymptotic states. The AGS equations are first reduced to a set of one*- dimensional .integral equations by the use of \X) angular momentum basis for representation and (ii) a separable app- roximation for the two-body t-matrix. The reaction amplitude can then be expressed in terms of the on-shell solutions of these integral equations. It turns out after detailed angir- lar momentum analysis that the reaction amplitude contains a factor £•( Jjf ^ . 5£ Ac 1 VCj MK.) ( ^ *lj *j «Aj \ Wj ^ ). Thus, in order that this amplitude be non-zero,&&e spin Jj of the initial bound pair coupled to the spin sj of tha initial free particle must fire rise to the same ohannel- spia K • as the spin J^ of the final bound pair coupled to the spin s^ of the final free particle. This inference of Conservation of Channel Spin (K. » Ki) hinges, of course, on our assumption that the two«»body t-matrix is essentially se- parable/ its non-separable part being negligible. It is of interest, however, to test the truth to this conjecture on the basis of experimental data. Let us oonsider (d,p) and (d,n) reactions on even-even target nuclei (Jj =0). Since the spin of the deuteron (s^) is one.the initial channel spin £•: is 1. Since, according to this hypothesis/the final channel spin should also be 1, the spin of the residual nucleus should be 3/2 or l/2,(the spin of the outgoing particle (p or n) being 147 l/2)-Thue, according to this hypothesis, stripping reac- tions leading to residual nuolei with spins other than l/2 and 3/2 would not be permitted* On examining the data on (d,p) and ld,n) reactions on l6 12 48 6 0 and (d,p) reactions on 4°Cav C, Ca and Li, we find that although reactions leading to residual nuclei with spins other than 3/2 and l/2 are not ruled out/the differential oross sections of reactions leading to spin states 3/2 and l/2 dominate over all others. From this one can infer that the two-body interaction %$>•• essentially separable 4 has 1. small non-separable component. The data is reproduced in table 1. TABLE 1 Reaction and deuter* .State of resi References -on Lab, energy. dual nucleus 0.0 50. Oliver et. 12 MeV 0.5 150.0, Nucl. Phys.l27ra7 «0(d,n)l7F . 0.0 P. 2 » ditto Ed - 7.73 MeV •0.5 249.0 . 4Li(d,p)7Li 9.3 " Schiffer et al Ed B 12 MeV -O.98 6.8 . Phys. (1967) 0.0 4.0 •> Schmidt Rohr ex. Sd - 11.8 MeV 2.0 17 • o „ alvNuol.Phys.li K - 2.5 10 • o .. () 77 4| Ca(d,p)**Ca Ex » 0.0 25.0 Roy and fiogaards E Ed - 5.5 x " 2.03 23-o Nucl. Phys.Al60 (1971) 269 (d,p) -0.0 Vj 21.3 Schiff«r et.al. rt =12 MeV 21.2 Phys. 148 -JUIVALENT LOCAL POTENTIAL •-R NUCLEON + 160 SCATTERING 0,0. Sharma and H.M. Singh Deptu, of Physics, Meerut College, Meerut and E,,3. Srivastava Deptt. of Physics,Meerut University, Meerut In the r&sonating group formulation, the optical potential for nuclear interaction consisis: of a local potential V^(r), also known as the direct potential and a nonlocal potential rep res- ented as ^ ' Jor the nucleon-nucleus scattering (when the nucleus is described by a harmonic oscillator shell model wavefunction) the kernel function K(r,r') has been found to consist of three diffey- rent angular dependence /l/ of the form ^TCt ^"^ 1 = 1,2,3* According to Thompson and Tang these terms correspond to different exchange processes* In Born approximation, the kernel function term corresponding to knockout exchange process gives a Wigner type of equivalent local potential while the other terms give rise to Majorana type of equivalent local potential. Since odd-even depen- dence of the equivalent local potential is quite weak for ttv: nucleon + 16o scattering /2/, the terms other tnan the knockout kernel function teen have very small contribution for nucleon + 16Q elastic scattering at medium energies. Therefore, in the present investigation an equivalent local potential Ve (r) has been constructed from the nonlocal knockout kernel function of the resonat- ing group calculations for the nucleon + 16Q elastic scattering. The two-nucleon potential used in the present investigation consists of a sum of three Gaussian terms including a weakly repulsive core and different singlet and triplet range. The calculated potential Ve (r) is energy- dependent. Fig. 1 shows Ve(r) at Eiab= 40 MeV* It is 3-~'~n from this figure that the calculated 149 Ve (r) has a repulsive core of radius 1.6 fro. The repulsive core radius is not very sensitive to the energy value for medium energies. Pig. 2 shows the total local optical potential (sum of V^ and Vo) for nucleon + 160 scattering at 40 MeV, assuming a hard core of radius :.6 frn. Eape- rimental optical model potential is also shown for comparison in this figure. /I/ D.JR. Thompson and Y.C. Tang, Phys. Rev. C 12 (191b) 1432. /2/ D.R. Thompson etal, Nud, Phys. A 270 (1976) 211. 150 MEASUREMENT OF 14 MeV (n,nV) REACTION CROSSSECTIONS USING CYCLIC ACTIVATION H.M. AGRAWAL* Department of Physics G.B.Pant University, PANTNAGAR 263 145 Cross-section dat- for (n,n'/) reactions leading to short- lived isomeric states are of considerable theoretical and practical interest. 14-MeV neutrons can excite compo- und states with high spins and thus become a useful tool to investigate the so-called yrast traps. The (n,n' Y) crosssections ^re often quite high, a good elemental sensitivity in NAA is obtained; especially when the dominant (n,2o) reaction leads to a comparatively 'ong- lived radio r.iv:lide. Since the source of 14 MeV neutror.s a D-T reaction target - is depleted within hours for open generators through some hundreds of hours for sealed neutron tubes, short-lived reaction products have always been preferred in fast NAA. The motivation of the present work was to measure the activation crosssections with high precision for four (n.n'lQ reactions leading to short-lived reaction products. Samples of Ag pure metallic foils and of Y and Yb in powdered form were used in the present work. The purity of the material was better than 99%. For cyclic irradiation of samples an intense neutron generator KORONA is used. KORONA consists of a high intensity, concentric, sealed neutron tube with a compact arrangement of an annular ion source, a cylindrical target and the irradiation terminal of a fast sample transport device /I/. Cyclic activation and measurement are possible with a minimum cycle period of 5 sec. For the Y -ny spectroscopy of activated samples, a Ge(Li) detector with a relative efficiency of 17% is used at a distance of 56.5 mm. During the first few seconds of short lived nuclide analyais, the counting rate can easily exceed 2.10 cps. Therefore, a special electronic unit determines the pile up and dead time losses and corrects the registered pulses in the memory of the multichannel analyser by incremenatine; not one but a variable, loss dependent weighting factor 121. 151 Employing the well known excitation functions of reactio- ns [90Zr(n,2n), 93Nb(n,2n)j and (58Ni(n,p), 58Ni(n,2n)] the neutron energy at the centre of the cylindrical target of KORONA was determined to a median at 14.6 MeV and a FWHM of 0.6 MeV/3/. For the neutron flux monitoring, a long-counter is used. The long counter has been calibrated via the well known cross-section 27 of the reaction Al(n,c<). The time dependent fluctuatio- ns of flux were corrected for cyclic activation and measurement with the code ZYKLA. The resuJts are given as follows: Half life Ey I* Measured Reaction (sec.) (KeV) (:%) cross sec- ction (mb) 89Y(n,n'/)89mY 16.1 909 99 .1 451±22 44.3 93..1 4 .67 294±12 109. . ,,.109m Ag(n,n7) AA g 39.6 88.-04 3 .6 292±12 11.4 389 88 .38 18.5+1.2 Significant improvements in the knowledge of cross-secti- ons are achieved for the above reactions as a result of this work. References /I/ H.U.Fanger et_ aj_., J. Radioanal.Chem. 61, (1981) 147. 121 R.Pepelink et^ aJL Nucl.Instrum .Meth. 226 (1984) 411 /3/ H.M.Agrawal and R.Pepelink (under nublication) * It is a great pleasure for me to thank Dr. R.Pepelnik (GKSS Research Centre, West Germany) for his keen interest throughout this work during my stay there as a guest scientist. 152 n,2n ) GBQSS SECTIONS AT 14.0 MeV N. L. Singh Physics Ofipartment, Faculty of Science,M.S.U.BAiSODA and S.Mukb.3rjee: A.V.Kohan Bao,L#Chaturvedi and J.BamaHao Physics DepertmentsB.HeU. Varanasl - 221 005 (n,2n) czoss sections have been measured l24Snf136Ba 142,150Nd at 14#0 MeV using mix der technique and high resolution HPGe detector (2.0keV FWHM for !332keV photons). In order to achi -eve the smallest possible statistical error of the fall energy peak area, it is essential to measure the activity of activated sample at smaller distan- ce from the detector and at the same time samples should be in bulk amount* In these cases self scat- tering and self absorption effects in the target and pile-up effect in the detector become a major source of errors. This requires a rather precise knowledge of these errors experimentally* It is therefore worthwhile to look carefully above effects to improve the reliability of measured cross-sectio -us by simulation technique /I/. 14.0 MeV neutrons were produced with AN 400 Van de Graaff accelerator at Physics Department, BHU, Varanasl using 3H(d,n)*He reaction at 250 keV duetron energy. Element under investigation homogeneously mixed with aluminium and pressed in the form of pellets of dlameer 2 cm. and thickness 2 -3 mm. each. Before Irradiation how -ever, relative efficiency measurements are made for a predetermined target-detector geometry using thin uniform disc source ofl52gu having same diameter as the target. The source is carefully intersp- erced between pellets and spectra are recorded at each position. To get an idea of the extent of attenuation for various photon energies, the above experiment is repeated wifch the 152Eu disc source alone in the above position without the absorber pellets/1/. Spectroscopy data used to Identify the product nucleus was taken from the table of Isotopes/2/. The cross sections measured are condensed in tab- -I alongwith some earlier values. The errors in the present cross section measurements are the root mean 153 square errors and are composed of the following ; The error in the relative photopeak efficiency of the detector(3$)• the error in the photopeak area (3£), the errors in weighing and mixing of sample (2%) and of the monitor cross section (£) TABLE-I s (n,2n) Cross Section at 14.0 MeV Product Present Previous Refe- nueieus Ty Er(keV) Value Value rence ^ tftb) rtb) 81 74As I7.79d 596 903 i 1016 1GC 3 1170 1+1 + 117 4 123m,, 40.0ai 160 574 Sn +_ 52 347 23 5 547 6 135m 28.7h 268 1035 + 94 1149 80 Ba 7 1020 1+1 + | 98 3 141m+g 2.5h 1127 1639 +152 1700 6 Nd 1910 139 9 1692 1+1 + 120 10 149Nd 1.73h 211 1673 +150 1679 118 9 160 1906 1+ 1 + 10 iffiJ?BKB»CBS : 1.J.Rama Rao et.al Nucl.Inst.and Meth.Bl?. (1986)368 2.Lederer and Shirley,Table of Isotopes,7th Edn. (1978) 3.P.V.Hao et.al, Phys. Rev. 03,(1971) 629. 4.P.Rama Prssad et al,Nucl.Phys.Al38 (1969) 85 5.SiM. Qaira,Hand Booic of Spectroscopy V.III, Florida (1981) 151 6,R.Pepelink,Nucl.Instr.and Meth.340/41 (1989)1205 7.Wen-deh-lu et al,Phys. Rev.Cl,(1970) 350. S.ti.L.Das et al. J.Phys.G: NucT.Phys.6 (338091045 9.An Jong Do et al. J.Phys.GiNucloPhys.l0 (1984)91 10.S.M. -jalm^Mttcl.Phys. A224 (1974) 319 154 PARAMETRIC STUDY OF NEUTRON EMISSION SPECTRA 2as FROM FISSION FRAGMENTS IN U(nth, f) USING ALICE CODE K. Kumar, M. Samant, R. P. Anand, R. K. Choudhury and S. S. Kapoor, Nuclear Physics Division, BARC, Bombay-400085. Energy spectra of neutrons emitted from various frag- ment masses 1) in the thermal neutron induced fission of a3=U have been analysed to obtain information on the fragment temperatures. The observed spectra are super- position of several evaporation components at different temperatures on account of wide range of initial ex- citation energies of the fragments as well as succes- sive de-excitation due to multiple neutron emission. These spectra are usually represented by : N(rj)= n, expC-n/T.^) (1) where rj is cm neutron energy. Le Couteur and Lang2> have derived analytically for cascade emission of neutrons, the values of As5/ll and T.#f Z 11/12T ( T being the temperature of the residual nucleus after one neutron emission). The validity of the above assump- ar| tions for X d Tm* + needs to be studied for the case of fission fragments which are produced over large range of masses with varying shell corrections and binding energies. In the present work, we have used the statistical code ALICE II with shell dependent level densities 3) to calculate the neutron spectra over wide range of mass ,charge and excitation energies of thp fission fragments. These spectra were fitted with eq(l) to determine the X anc' T.<>#> parameters. Fig 1 shows the variation of \ and R=T/T«## with the initial ex- citation energy for typical fragment masses. It is ob- served that for all the cases X shows a decreasing trend from 1 to .5 as excitation energy is increased. The behaviour of R however, is stro'gly dependent on the fragment mass. In the closed shell region, for low fragment excitation energies R is much less than unity and even at Ew=25 MeV it does not reach the expected value ofrvl2/ll. This shows that the prescription of Tm.pf = l 1/12T does not hold good in the closed shell region of A~132. We have applied the present calculations to determine T.ff from the calculated spectra and compare with the 155 measured fragment temperatures in ^^^U fission. Table 1. shows the values of experimental and calculated Tm** for several fragment masses. The calculated values are in good agreement with the data except in the closed shell region, where the temperatures are underestimated even after inclusion of shell effects. The reason for the discrepancy in the shell region needs further invest igat ion. Table 1: comparison of experimental and calculated lm*r A E~ -I—- T— A E~ 84 9.4 .35+.03 .32 133 9.9 .72±.O7 .43 87 8.9 .51+.04 .59 137 9.6 ,69±.O5 .52 90 9.8 .54+. 04 .60 140 11.2 •. 78±. 05 .66 95 10.7 .68±.O3 .81 144 10.5 .77±.O6 .67 99 11.0 .75±.04 .82 149 7.9 .59±.O5 .52 102 15,0 .70±.03 .76 152 12.9 .69+.07 .66 106 15.9 .88±.O8 .81 156 17.8 .83±.O9 .69 110 21.3 1.02±. 10 .89 114 23.0 .99±.2O .99 REFERENCES: 1) M. Samant et.alr DAE NP Symp32BC1989)0-58 2.) Le Couteur and Lang, Nucl. Phy. 13(1959)32 3) S. K.Katar ia, V. S. Ramarnur thy and S.S.Kapoor, Phys. Rev. C18(1978)549 A= 87 A = 33 U"5(n.f) ~ Z = 34 Z = 52 A=152 •••• 2 = 60 M — — -y •— _»-2 . * T/reff - •• 0.5 • - 1.0 • * A • * •*** 0.5 i i i 1 . 1 1 10 20 10 20 20 E*(MeV) 156 OF A UtoT\T P IN THE (p,p'y) REACTIONS C. Singh* and D.C. Tayal Physics Department,N.RrE.C.College,Khurja-203131 A knowledge of population of nuclear magnetic substates through feeding in the course of nuclear reaction processes provides insight into nuclear sub-structure and reaction mechanism character- istics. Any nuclear scattering or interaction process differentially populates the magnetic sublevels M that make up the residual nuclear state of spin J (where M = -J to + J i.e.(2J+l) substates labelled by the magnetic quantum number M). The underlying theory to evaluate the relative population of each substate in an ensemble as based on the formalism of Davons and Goldfarb/l/ has been presented by Litherland and Ferguson/2/ and quantitatively delineated by Poletti and Warburton/3/. Using this approach, Sheldon et al./4/ have incorporated the evaluation of magnetic substate population into his statistical compound - nucleus distribution code f'CINDY11, It provides theoretical calculation of relative population P(M) for each magnetic sub- state (+M) comprising the residual nuclear state J in percentage. Our findings for the magnetic substate populations P(M) are presented in a tabulation form for the low lying excited levels in the residual nuclei fed by (p,p'y) reactions with odd mass nuclei (A = 45-61) at E = 1-5 MeV. /I/ S.Devons,L.J.B.Goldfarb, in Handbuch der Physik, edited by S.Flugge(Springer,Berlin), Vol.42,p.362, /2/ A.E.Litherland,A.J.Ferguson, Can.J.Phys.,39, 788(1961). /3/ A.R.Poletti,E.K.vVarburton, Phys.Rev., 137, B595(1965). /4/ E.Sheldon,V.C.Roger, Compt.Phys.Commun..6,99 (1973). ^Permanent address: Physics Deptt., D.A.V.College, Muzaftarnayar-251 uul. 157 Resi. Level Level Incid. Mag.Sub,Population P(/«J Nucleus Energy Spin / 5x Energy D } £* rn flab *^2' PV'2 P\ 2> [MeVl j FMeVl FPercentaqel 45Sc 0.376 3/2- 1.0-3.0 23.5 26.5 4.0 23.7 26.3 5.0 23.9 26.1 0.543 5/2+ 1.O-5.O 16.7 16.7 16 .7 47AH Ti 0.159 7/2" 1.0 13.4 13.0 12 .3 11 O2 2.0 13.5 13.1 12 .3 11 .2 3.0 13.6 13:1 12 .3 11 .0 4.0 14.4 13.7 -12 .1 9 .8 •1Q 5.0 14.9 13.9 12 .0 9 .2 49Ti 1.382 3/2" 1.0-5.0 25.0 25.0 51V 0.320 5/2- 1.0 15.6 16.4 18 .0 2.0 15.5 16.4 18 .2 3.0-5.0 15.3 16.3 18 .4 0.928 3/2" 1.O-5.0 25.0 25.0 b3Cr 0.564 1/2- 1.0-5.0 50.0 1.006 5/2" 1.0 18.2 17.0 14 .8 2.0 18.2 17.1 14,• 7 3.0 18.9 17.a 13<,9 4.0 19.6 17.4 13 .0 5.0 20.0 17.5 12,,5 55 Mn 0.126 7/2- 1.0 13.1 12.9 12,• 4 11 .6 2.0 13.7 13.2 12,.2 10 .9 3.0 14.1 13.4 12,,2 10 .3 4.0 14.2 13.5 12,.2 10 .1 5.0 14.5 13.7 12.,1 9 .6 57Fe 0.136 5/2- 1.0-5.0 16.7 16.7 16,,7 0.367 3/2" 1.0 28.0 22.0 2.0 28.2 21.8 3.0 28.7 21.3 4.0 29.4 20.6 5.0 29.6 20.4 j9Co 1.099 3/2" 1.0-5.0 25.0 25.0 61Hi 0.067 5/2- 1.0 18.1 17.0 14. 9 2o0 18.3 17.1 14. 6 3.0 18.8 17.2 14, 0 4.O 20.0 17.5 12. 5 5,0 20.3 J7,6 1?. o c. 2bo 1/2" l.G-O.U 5o.O 158 STUDY OF THE SPECTRUM OF Se FHOM THE 7;5As (p, n)' Se REACTION G.P.S.Sahota, V.K.Mittal,S.D.Shanna,H.S.Sahota G.Singh",S.S.Datta* and I.M.Gcvil* Deptt. of Physics,Punjabi University.Patiala-147002 •Ueptt, of Physics,Panjab University,Chandigarh-16014. A pruton beam of 4.0 Mev from the Chandigarh cyclotron was bombarded on As target. As a result the Se* nuclelta was formed.The levels of ' Se* upto 1.7 Mev were excited in this way.The lifetime of a number of levels were calculated using the Doppler shift Attenuation technique. Using the 1> 0 angular distribution of the emitted gamma rays at 0°,30 >45 , 60° and 90" angles, the J^ values were assigned to a number of levels.The level scheme poses a problem. The large quadrupole moment of Se suggests deformation &O, 0.35 or even more. But the positive and negative parity states in spectrum upto about 2 Mev or so could not be explained satisfactorily.The positive parity spectrum seems to be a decoupled base band or a sequence of rotational states or the states of the odd valence proton under excitation, which are easily available to it according to the Nilsson Scheme of single particle states. The negative parity bands are based on >i f 55OJ and 3/2 C541J-These are Coriolis coupled. These perturbed bands are generated on an approach based on effective moment of inertia parameter under Coriolis perturbation. Theory: The collective model Hamlltonian can be diagonalised including the Coriolis terms and the mixing of available Nilsson states. The diagonalisation yields '-A %=• -i± 159 RESULTS AND DISCUSSION: The negative parity bands are generated using the above model. The results are compared with our experimental values.The spectrum is quite well reproduced on the basis of particle state 3/2- £54]~J .Eaarlier we also tried the states 3/2-[532^ 3/2-L52lJ , 3/2-£512] & 3/2-£5Ol]but with no good success. Thus the state is 3/2- £54lJ .It is also justifiable from the fact that the energy of the prticle is minimum in this state for deformation /?~ 0.35. So this is the first available state to the particle which could generate the spectrum well. It may be noted that the Coriolis effect goes on increasing with spin as the same increases resulting in an increased moment of inertia at higher spins. The rer.ults tally quite well with our experimental results upto about 2 Mev or so.The discrepancy is about 100 Kev for the spin 13/2.at energy 1.7 Mev. Similarly the band head at K=J£ has the rotational sequence coupled to the band with K=3/2* This spectrum too is well reproduced with the same deformation parameter. Thus it la evident that the model based on effective moment of inertia works quite well in predicting the spectral properties. Once can also predict Coriolis affected magnetic dipole and Electric quadrupole moments usinR EJ^en vectors obtained on diagonalisation of the Hamilton;an. The only defect of fhis approach is that one can not estimate the unperturbed moment of inertia parameter for the system. Here we used the lowest energy gap for estimating the same aa the coriolis pertubation is the lowest in this case. 160 PHASE ' "TS IN ALPHA PROTON INTERACTION AT 40 MSV. S- Karmakar and S-S.Dasgupta Department of Physics, Burdwan University Burdwan-713104. Angular dist ourions of the Proton differential Cross-section.y In alpha proton scattering have been measured in different angles at 40 MEV.alpha at V-E.C-C* '••,--cutta. The aim of the present work is to improv- -:ho accuracy of (i) Cross-section measurements .l) (ii) The phase shift analysis of most availati. oroton alpha scattering data at this energy. A set of phase shifts iff determined through search using reasonable starting values. The results are compared with ontical model (2). The phase shifts are also determined from an effec -tive range expansion (3) and comnared. The theo- retical ohase shifts obtained from non-local separable potential (4) are much differed from experi mental nhase shifts* These comparisons are shown in table- 1» References s- 1. S. Karmakar, DAE SymDOsium on Nucle- -ar Physics, 1988 " oC-P interaction at 40 Mev." 2. G.R. Satchler et.al. Nucl.Phys- A 112 (1969)1. 3. M.W- Kermode, Nucl. Phys. AlO4(l967) 49rApnendix A-2. 4. J. Barguil et.al* Muovo Cim<.-r;to. Vol I A. N 2(1971) . 161 T A B L E -I The Best-fit Dhase shifts from searches are shown with calculated phase-shifts obtained from different theori- tical ao^roach for comnarison. Phase Shift in deqrees. OQ «>I Optical Model. 116.2 59.1 •108.9- 1.3 2.0 Effective Range 116.07 57.57 108.05 1.01 1.43 theory* Non-local 113.9 60.0 110.7 1.0 2.0 Separable Potential Best fit 118.74 65.17 111.98 2.78 4.38 from + .68 +1.26 +.91 +.57 Searches. +.57 162 ALPHA I.1LUCLD EXCITATION FIMC TIOtf^ FOR S R.P.Gauum* , M.K.Dhardwaj, H.Siagh and A.K.Chaubey Department o£ Physica h Muslim University ,Aligarh 2o2 002 Excitation functions of alpha induced silver isotopes have teen extended to 50 MeV/1/ using stack -foil technique. The three independent irradiations were made- to cover tne entire range of the available energy* The total charge collected during the irradi- ations was monitoned vith Faraday Cup. Ihe (CX , 3n) reaction of 109 Ag produced the same product uurleus as produced by the (o( ,n) reaction of 107 Ag, Above the theshoLd of *09 Ag(ot,3n) rearrtion the mjasur^d cooss -section is the sum of 1()7 Ag (ot tn) and 109 Ag(0(,3n ) reactions. Similarly (o(,2n) rea- ction with 109 Ag Iead3 to an iaomerjc st^te of 7.6 min anc1 the g • ound state of 2.1s days. Th^e iaomeric state decays to the ground state. The me' surement of this reaction could be eone after th complete decay of isomeric state. Hence our measurement is the total cross- section. The (Ot ,4n) reaction on Io9 Ag produces the same product as Io7 Ag (o( t 2n) . Belcw threshold of 109 Ag(C(. , 4n) the ccoss section is only c?ue to Io7 Ag (o( , 2n) .Abo'/e threshold the cross 3ection is the im of these tvo reaations, The cross section of these reactions have been separated using theoretical calculations, The measured excitation functions have been tested theoretically on the basis of Biann/2/ hybrid mode7, using the latest computer -ode Alice/3/. It is observed that pre- equil ibriurn process ia more pro- nounced in high energy tail portion and the experi- mental data are well reporoduced quantitatively only 163 when P.£# emission of -particle is also into account. The comparision of the results is shown in Fig-1, Sig-2, for 109 Ag( , 4n) l09In and 109 Ag( #3n) Ho In respectively. The initial excition number 4 (2p + 2h •»• o h) gives best reproduction tOOOr- Authors are grateful to Dr. S.K, Chintaipudi and VECC personnel for their co-operation during % 100 the experiement. o Prsunl «ork • Mlso*lld«f on<3 Mumst EO and P£ (COH mo 50 E. (MsV) Pt»nnl «o/* 8i>nop «l ak Fuk.unma it at EQ anu PE ! JOM moail) £0 'inj PE (Hyond Tiodd EO ,,L M 40 10 References t £„ (MeV) 1. R.P.Gautam, Symposium on Nuclear Physics 1986, Vol. 29B (1936), 245. 2. M.Blann and J .Bisplinghoff. ALIC£/LIViiR MORE 82 report U C I D- 19614 (1982). 3. M.Blann, Phys, Rev.Letter 27 (1971)>337 164 EQUIl.'' ••: JM AND PRE-EQUILIE*RIUM EMISSION OF NEUTK \ND PROTONS IN ALPHA-INDUCED REACTIONS ON ANTIMONY B. P. Singh, H. D. Bhardwaj and R, Prasad Department of Physics, A. M. U. Aligarh, India * D. S. N. College, Unnao In reactions initiated by few tens of MeV alpha particles, the reaction mechanism is considered to proceed through an admixture of equilibrium (EQ) and pre-equilibrium (PE) emission . The relative contribution of these processes is still not well known. With a view of studying PE-.-mission we report the measurement and analysis of excitation functions for the reactions Sb(a,n), 121Sb(a,2n), i21Sb(a, 4n) , Sb(o<)3np)> i23 Sb(«,n), Sb(a,3n) and Sb(a,4n). Excitation functions have been measured using stacked foil technique in the energy range %. 30-60 MeV. Experiments have been oarried out at VECC, Calcutta, using a-bean of 60 MeV. The post irradiation analyses have been performed using high resolution Ge(Li) detector coupled to the multichannel analyser. The excitation functions in the past have mostly been analysed on the basis of statistical EQ decay m^del. The analysis of t.ie EQ component in the present work has been made with statistical Hauser-Feshbach (HF) model and PE contributions are simuls'.ed employing e x citon model (EM). Theoreticii calculations have been performed using the computer code ACT with the consistent set of level density parameters. In all the calculations the initial exeiton number n - 6(5p+lh) is found to give £D-:I| reproduction of the data. The best fit valii'- 'if the parameter FM , used in the ca leu la t i •'.ri :•; of matrix element for two-body residual .: f -:- r:>o t i on;: , is fourr! to be projectile :;.']•; . . ... ^ !.,.,•; .,•... ;.-.; ,!,;.i..;i- ;. ., jtudy Id-- efff'-t "t" , • •• 165 i L'U i i • Him; nave bet-n done for J ipoit- and higher • i r? r rv: 1 t i po 1 es , however, the inclusion of higher m.: i t : p,. I e s .Joes not affect the calculated • • r ."ISG - y. ••••: t urn s to any significant extent. A considerable amount of pre-equilibrium •'••') f.r ib'; r ion is found in the present analysis. 1-1 :•• equilibrium fraction FR, which is the measure or relative strength of PE component has been ••ilculated using computer code ACT. FR has been pioUed HS a function of a-particle energy for I •£ t . 1 -S 3b „ i. n figure 1 As can be seen from this figure VR increases very rapidly with the increase in bombarding energy 10 0.9 06 0-7 ,0-6 0-5 0-'t 0J i) 0- I_L_1 _I_J l_l_t._ i i i 10 20 30 U0 50 00 i. Variation of pre-equ L • ibriurn fraction as a function of bombardincj energy. R*r f or eri' 1. H M «nn; Ann. Rev. Nucl. Sci. 25 ( 1975) 123 2. W. M' user and H. Feshbach; Phy Rev.87(1952)366 3- J. I Griffin; Phys Rev. Lett 17 ( 1966) 478 166 EXCHANGE EFFECTS IN ALPHA SCATTERING FROM 6Li Subinit Ray and C. Samanta Saha Institute of Nuclear Physics, Calcutta - 700 064 Recent experimental data on Li (o<,°< ) Li at E - 50 MeV, taken at the Variable Energy Cyclotron Centre, Calcutta, /1»2/ show anomalously large backangle cross sections for both the ground ftate ( 1*, 0.0 MeY ) and the first excited state ( 3+i 2.1 £j JfeY ) excitation of 6H ( Fig. 1 and 2 ). Calculations with phenomenological optical potential with reasonable parr.aeters fit the elastic data upto Qc^10°/2/o 7? Since Li has a pronounced o<+d cluster structure (spe- ctroscopic factor ~0.73) with very low binding energy ( 1.47 Ms. )» we have investigated the effect of the elastic transfer of alpha cluster to resolve the back angle anomaly. The calculations have been done with the same phenomenologi- cal optical potential parameters in which the elastio and transfer amplitudes have been added coherently. Details of the calculations and the results will be presented, • To get a more fundamental understanding of the problem, microscopic calculation with appropriate " cluster " knock-on exchange terra is needed. 167 REFERENCES j /1/ C, Samanta, S. Ghosh, S. Ray ans S#R, Banerjee, Proc. of the DAE Symp. on Nucl, Phys., at BARC, Bombay, Vol. %\B (1988) 019 C, Samanta, So Ghosh, M* Lahiri, S# Ray and SO!R, Banerjee, Submitted to Phys* Rev, C, /3/ G.R.' Satchler and W#G» Iwe, Phys. Rep» (1982) 163, /4/ P.A. Bicniller et al, Pbys, HOT. ^ (1972) 591 /5/ J.C Bor^stroa et al , Huol. Phya. A^gJ, (1979) 459 % . 185" MeV jB= O . 69 10 "" - l 60 + Experimental data point3 — Microscopic calculation with 0«58 163 DWIA 3-BODY COUPLING MODEL CALCULATIONS FOR 140 MeV H(OL , The model developed earlier to account for the 3-body coupling in the final state of knockout reaction has been applied to D(a ,<%p)n reaction (Ref. 1) at 140 MeV. In this reaction the residual nucleus is light and hence recoil effects are expected to be large. This reaction may be called Peripheral 3-Body Coupling Model ( P3BCM ) because in this model the coupling term is treated almost exactly in the peripheral region of the nucleus. It is mainly in this region that the knockout reaction is localized. The final state 3-body equation is written down in this model ( see Fig.l for nomenclature ) as: which can be compared with the following conventiona equation for the so called Kinematic Coupling Model (KCM): In both these equations the normal 3-body coupling term (- k- V . f ) is replaced by ^V^+LV^ -lTaC£bc) and ( 7ffc k _.k, „) respectively. It is clear from Eq.(l) that this T-^body model equation becomes exact when at least one of the distorting optical potentials go to zero as is the case when the reaction is localized in the peri- pheral region of the nucleus (see Fig.2). This is in contrast to the KCA Eq.2 which does not become exact in any region of the nucleus. The DWIA results calculated using Hulthen deuteron bound wave function and both of these final state prescriptions as also the plane wave ( PW ) formalisms are presented in Fig.3 for the 140 MeV D(cx ,a p)n reaction. The calculated results shown in this figure are normalized to the cross section at the peak position (~108 MeV). It is seen that the shape of this energy .sharing distribution is IK-.: :••:,:•:, iijcci !r; the P3BCM [IIV-.U-I:,!!^!. The; I'W distribution is rather wide and the KCA results are also somewhat wider as compared to the experimental data. 169 Table 1. FORMALISM P.W. K.C.A. P3BCM Peak rrpss section mblisrZ. MeV) 305. 116.6 91.6 It is to be remarked from Table 1 for the absolute cross sections that magnitude-wise also while the PW results are about 7.3-times larger, the KCA results are~2.8-times larger and the P3BCM results are-2.2-times larger than the experimental value. Thus through these calculations for the first time the 3-body coupling contributions to the knockout reactions are evaluated and it is shown that the inclusion of the 3-body coupling contributions improves fits to the data for the 140-MeV D(ct ,ot p)n reaction. 1. A. Nadasen et al. Phys. Rev. C19 (1979) 2099. 2H(a,ap)n 50-7 E =1A0MeV 50 initial state a f/X1 *\ 30 / \ — / t HiO / i1 ; 0i \ \ 5 \\ v 3 i n - ' /' 1 —) DWIA( P3BCM) ~ — -) DWIA (K.C.A.) _ 5 - i\ i — -) P.W -.2 i i i 80 90 100 110 120 130 Fig. 2. Ea(MeV) Fig. 3. 170 an RELATIVE ENEHGY IN ad BREAK-UP S.>:andal and S.S.Dasgupta Physics Department , Burdwan University,Burdwan713104 In a break-up reaction with three outgoing particles .he relative energy of final particles plays an important role. It frequently happens that the relative energy of two outgoing particles is so small that they interact among themselves vevy strongly, These interactions , known as final state interactions (PSl) and often it influences ••prreciably the reaction cross-sections, which helps to •.:nderstar.dtho 'reak-uD reaction... Relative energy of two outgoing particles depends on incident energy, energies of final particles and correla- tion angles(l, --'). It has been seen in CXd break-up that (Xn fingl r.tate in teraciions favour prefered proton angles. : ir.erratical calculations show *.hat for given energy and r-ngles (Xn relative energy becomes lowest at highest proton onergy (Fig. l) i.e.0(n relative energy primarily depends on third particle energy. Our experiment done at VECC , Jelcutta at 45 MeV incident Gf-particle energy show the triple croc--coctions enhanced at this kinmatical P3I TQ^'ion (3) . Data having been taken at two pairs of angler i .-. >>ot:i the cares enhancements coincide with the highest vroton energy (Fig.l). The region of observed enhancement oen not •, however, coincide with phase space enhancement:: • Ion/-; the TC according to phase space calculations of of.!. ." dot^ilod calc\;l'i"tion of arc projected ph'ir.e sjaco j-c-uired for this purpose is alroady underway (4). 0.7.ChI::er., iJucle. Instr. i l.'ith::. 37 (l?65) 240. :•?.:• .Warner, H.W.Bercaw, Nucl. Phys. 109 (1968) 205. \. ]'o. , 3.J. DanfTuptn , D..:cn , T. Roychowdhury, 3.N. .'hL'.t.nl aoudi, i:;.R.p,aner.ier;. Ind.J.Phys. 64A ( H.Ai-hc, Nucl. Instr. & Keths, 20O(lQ8?)36l. 171 t -10 2 0 30 En (MeV) ;. 1. T1rcal-up n coincidence at ^-tic locus ( broken lines ) and an rela- " r:rjorim -o.'-.r,.' or; it« • p - >' ri.: F'if-.l locu;: haa enhancements of cr'.s at t. - r^~ion of minimum Ccn velative 172 LorE ;TERFERENCE EFFrrr: N int PRIOR FORM DWBA L/ F LIGHT ION "! ;V. 7 C pr?rAK UP RF-ir/; " IC-NG D.N. Bast; Variable Energy Cyclotron Centre 1/AF Bidhan Nagar, Calcutta - 700 064. Recently published triple differential cross sections for elastic break up of 156. MeV lithium—6 incident on lead—208, measured for large relative energies between the fragments ( >f> MeV) have been analysed in the frame of prior form DWBA approach (1). Real transition potentials with small depths and large radii and diffuseness parameters have been used to provide reasonably good fits to the conspicuously structured shapes of the experimental curvys. However, the effects of Coulomb forces were not taken into account in any manner for these calculat i ons- The prior form DWBA T-matrix (2) for the ractions of the type a + A->b+x-t-A is given by T = < x l > x ': V\ +\T +vT +vr :x v> > a. k bA bA xA KA O. a. where X and X denotes the distorted waves a a for the centre of mass motion (of b+x system) of the initial and final states and [ — y X (p ' \f •• v ! X '/> ?j n V: bA y.A o. -i The modulus squared of the T-matri:< which is proportional to the cross-section is given by 173 2 !ri = + 2. Real part of and one observes that even if the Coulomb term is small, the Coulomb—nulear interference term (viz. the third terns on the right hand side of the above expression) need not be small if the nuclear part aolne is sustantially large. Detailed prior form analysis of the above ir.ent zoned lithium—6 break up data have been analysed including the Coulomb potential. Due to long range nature of the Coulomb forces the radial integration has to be performed upto 200 fm for convergence. For the nuclear part same set of the transition potentials of reference (1) have been used. The normalisation has to be changed from 0.7 to 0.55 to fit the same data when Cou omb is included. L (M«V) Results show that the inclusion of the Coulomb potential affects the calculations by its strong interference with nuclear transition potentials and suggests that for better fits to the data some adjustments in the previuosly (1) searched nuclear transition potentials are necessary. Calculations Are in progress with the modified real nuclear transition potentials. Refe ren ces 1 1) D.K. Srivastava, H. Rebel rind N. Heide Nuc. Phys. A506 (1990) 346. 2) Frank Rybicki and N. Austern Phys. Rev. C6 (1972) 1525. 174 DETERMINATION OF ROOT-MEAN-SQUARE RADIUS OF NEUTRON ORBITS FROM EXACT FINITE RANGE ANALYSIS OF SUB-COULOMB Ct,d) REACTIONS H.S. Sudheendra, M. P. Sathyavathiamma and N.G. Puttaswainy Department of Physics, Bangalore University, Bargalore-560050 A study of sub-coulomb (SC) single nucleon transfer reactions offers a simple and direct method of determining the root-mean-square (RMS) radii of valence nucleon orbits. At sub-coulomb energies[1], the calculated cross section depends weakly on the optical model (OM) potential but is very sensitive to the size of the orbit of the transferred nucleon. If the spectroscopic factors relating the levels in the target and residual nuclei are known, the cross section can be interpreted essentially in terms of the RMS radius of the bound state (BS) wave function. The (t,d) reaction on "*°Ca, *aTi, 52Cr and 5*Fe have been experimentally studied by several investigators[2-5] at energies below the Coulomb barrier; however, in these studies, only zero-range DWBA calculations were performed and hence the RMS radius deduced depended on the value of the normalization constant. In our calculations, we have carried out exact-finite-range DWBA calculations using the code DWUCK5C6]. The projectile form-factor has been deduced from a fit to electron scattering cross section (on 9He) at small angles[6]. The OM param- eters and the spin-orbit potential depth have been chosen from earlier work[2-5]. To determine the target BS wave function, the depth of the Woods-Saxon (WS) potential has been varied to reproduce the experimental binding energy of the state. The calculated cross section (dc/dO)DW is related to the experimental cross section through the relation (dcx/dO).xp = Gg(dc/dO)DV , where G is the target spectroscopic strength and g=1.5 is the projectile spectroscopic strength. The values of G are again taken from earlier work[2-5]. Finally the radius parameter of the WS 175 potential ro is varied (with ao=0.65 fin) to reproduce (dc/dO)^xp. The RMS radius is then determined from the BS wave function generated in this manner; these values are tabulated in Table 1. Table 1. RMS radius and bound-state parameters deduced for fp-shell nuclei. RMS radius Nucleus nlj EB G (fm) (MeV) (MeV) (fm) Our Earlier work work "Ca lf7/2 8.3628 0.80 53.65 1.258 3.98 — lf7/- 8.1424 0.32 51.81 1.157 3.99 — 2Pa/2 6.7 609 0.61 54.39 1.187 4.31 4.42* 53 Cr 2Pa/2 7.9410 0.529 55.05 1.187 4.24 — 2Pt/z 7.3769 0.40 55.62 1.199 4.28 — 6.9347 0.337 51.93 1.232 4.07 — 55 b Fe 2p3/2 9.2980 0.66 55.89 1.193 4.17 4.17 aRef.3. bRef.5. The values of RMS radii deduced for the f?//2 levels in 41Ca and 40Ti compare very well with the values of 3.99 fm and 4.042 fm respectively deduced from magnetic electron scattering[7,8]. The financial assistance received from the University Grants Commission is gratefully acknowledged. The authors wish to thank Dr.C.R. Ramaswamy, Dr.M.C. Radhakrishna and Mr.V.P. Darshan for their help in calculations. References: - 1. R. Chapman et al., Nucl. Phys A 316 (1979) 40. 2. L. J.B.Goldfarb .ejb ai- , Nuc 1.Phys A_I8_5_ (1972) 33*i 3. P. Woods et al. , Nucl. Phys A_36_3_ (1981) 322. 4. 0. Bing et al., Nucl. Phys A 257 (1976) 460. 5. M. Hyland et a_l- , J. Phys.G: Nucl. Phys 6 (1980) 261. 6. P.D. Kunz, Private Communication. 7. S.K. Platchkov fii al., Phys.Rev.Lett. 6J, (1988) 1465. 8. S.K. Platchkov ejt ^1. , Phys. Rev. C_J>5_ (1982) 2318. 176 1 C0U.LJ.-i3 CO .trUCi ION I'O JSLAS'I'IC &<-C< U. Da3 and P.iw Bera Physics Department, Visva-Bharati, Santiniketan - 731235 The We shall represent Vs by a deep local potential and compute the«-« elastic scattering phase shifts by including the Coulomb effect rigorously. Our app- roach to the problem will be based on a generaliza- tion of the phase-function method C3J (PM> for non- relativistic potential scattering. We work with a Gaussian tf-tf potential C41 which is independent of both angular momentum and energy and examine the eff- ect of Coulomb distortion of the nuclear scattering phases. In figs. 1 and 2, we portray the variation of the scattering phase shifts S^Ck^ C6is£*O or Sfclo} as a function of JS tM . All phase shifts sta- rt at the threshold (KCMO) with YitTT . Here r)t is the number of redundant states. For the 177 results are somewhat improved compared to other ex- isting results ^ -~. ; Y —• — »2 -I •— - — in •ri | | | I | | 1 I I | 1 I | | f | | 1 1 0 4 3 12 16 20 24 28 36 40 nk 9 13 16 20 24 28 32 36 4O Keferences 1 "J,L. Hill and J.A. V.'heeler, Phys. Hev. 1102 (1953) 2 K.;.vildenauth, W.Hcclure, Springer Tracts in Mode- rn Physics 41. Berlin,Heidelberg,ifew York : 1966 t>. i'1. Jalogero, Variaole Phaje Approach to Potential oca tiering (Academic Press, New York: 1967) 4. ii.iiucK e t~al, Nucl.Pnys. A2?5,246 (1977) 5. V.G. Neudatchin et al, Phys .Lett o4B,581 (1 971) 6. L.»-ia the litsch and v/.Pleassas, Proc. in 8th Int. Gonf. on WucLear rorcts,Jraz (Berlin Springer 197 b) v 7. .<,r .i3aret; t et al, uev ..-lo-j .Phys .55 11 55 (1983) 178 PHASE-FUNCTION METHOD FOR HULTHEN-HODIFlED SEPARABLE POTENTIALS . A.K.Jana' and U.Laha . Physics Department, Visva-Bharati, Santiniketan-731 23b . Physics Department, RIT,^ Jamshedpur-831 014 In the recent past one of us (UL) [1] adapted the phase method [2] to deal with Coulomb plus nonlocal separable potentials and derived a closed form expression for the scattering phase shifts. In this note we propose to present the results of a similar investigation by using a Hulthe'n potential in place of pure Coulomb interaction. The Hulthe'n potential has often been used as a model for screened and cut off Coulomb interactions [3J. Since the effect oi screening should invariably affect the theory and interpretation of data relating to charged hadron scattering, it is expected that the analysis of this report will be of interest to a wide variety of physicists. Incidentally, one may note that pure Coulomb potentials never really occur in nature. For example, in the famous Rutherford experiment the Coulomb field of the gold nucleus was completely shield at a few A by the atomic electrons. The Hulthen potential r/a r VH (r)=V0 e- -/(l-e- A), a>0 (1) behaves like a Coulomb potential at small values of r whereas for large values of r it decreases exponentially. The potential in (1) allows analytical solutions of the Schrodinger equation for s-wave only. Therefore, in the following we snail deal only with the s-wave scattering and omit the subscript 1 = 0. In close analogy with our work in ref. 1. We have derived closed form expression for the scattering phase shift fe^ClO for a Hulthen distorted rank n separable potential and specialzed the result for Hulthe'n plus Yamaguchi pot ent ial \/ y( T, r') . For extremely large values of the screening length'a' the 179 Hulthe'n potential VH goes over to the Coulomb potential Vo . It is well known that [4] all objects derived from a screened Coulomed potential do not have an "Unscreening limit". Thus it will be interesting to examine under what limiting conditions 6HyCh) will reproduce the Coulomb-Yamaguchi phase shift bc>C^-) given elsewhere [1]. To that end we observe that the "unscreening limit" Q.->OQ defined in an appropriate manner. Ue demand that as a—>> co and Vo —9 0, their product aV0 remains a Constant and equal/, to 2*2 fc. with 2, the Sommerfeld parameter. In this limit we have found &HVCfe) to go smoothly over to S^^fe) » the Coulomb Yamaguchi phase shi ft. Ref erences [1] G.C.Sett, U.Laha, and B. Talukdar, J. Phys. A: Math. Gen. 21, 3643 (1988). [2] F. Calogero, Variable Phase Approach to Potential Scattering (New York : Academic 1967). [3] J.Lindhard and A Uinther Nucl. Phys. A 166, 413 (19 7 1) [4] F.U.Ford, Phys. Rev.B 133, 1616 (1964); F.U. Ford, J. Math. Phys. 7, 626 (1966). 180 ON INTEGRAL REPRESENTATIONS OF THE COULOMB FUNCTIONS A.K.Jana and B.Talukdar Physics Department, Visva-Bharati, Santiniketan 731 235 In the recent past Maximon [1] derived a number of new integral representations for the s-uave Coulomb funtions written in terms of Uhittaker functions[2] fl^ u (Z) and U|/^(Z). Unlike other published integrall representations [3] Maximon has sought to factor out the effect of Coulomb parameter ( "T, ) from their radial dependence. As a result, only functions of r that appear in his expressions are of the form of non-Coulomb functions. This novel feature makes the results of Maximon particularly well adapted to rigorous calculations of Coulomb and Coulomb-diS"torted scattering amplitudes. In this work we deal with the representation for u w , **- (Z) and try to demonstrate its usefulness for Coulomb half-shell scattering. Our approach to the problem consists in showing that Maximon's expression for U ^ ^ (Z) provides a natural basis for writing the momentum-space Jost states[4,5] and that the half-shell T matrix can be written directly in terms of these states. Admittedly, by working with the result of ref.l we could treat only the case of s-wave scattering. But for the Coulomb problem treatment of higher partial wavesis equally important. In view of this we seek a generalization of the result of Maximon for arbitrary angular momentum. Ue achieve this by making use of a supersymroetry inspired ladder operator[6] for the irregular Uhittaker function. Ue perform a check on the results obtained by us and use them to construct closed form analytical expressions for higher partial wave momentum-space Jost states. Our result for the s- and p-wave Jost states in momentum-space are given by 181 with a=(p- k -it )/(P+ k +i£), e In terms of Jost states, the 1-wave half-shell matrix is written as CUT/2. %. CKh) -C- where fc ia the on-shell and p? an off-shell momentum. The quantity $ Ck) is the ordinary Jost function. In the above we have dealt with the integral representation for the irregular Uhittaker function. One may be interested to obtain the off- shell Jost function by working with the integral representation for the regular solution. Such an attempt is beset with inordinate mathematical difficulties. Ue shall discuss these in some detail. Ref erences [1] L.C.Maxltnon, Report GUU/DP/TR-82 /1 [2] R.G.Newton, Scattering Theory of Waves and Particles (Springer Verlag, New York, Inc. 1982). [3] H. Bateman, Higher Transcendental functions (McGraw Hill, New York, 1953), Vols 1 and 2. [4] R.Jost, Helv. Phys. Acta 20, 256 (1983). [5] H.van Haeringen, J. Math. Phys. 24, 1152 (1983). [6] U.Laha, C.Bhattacharyya and B.Talukdar, J. Phys. A: Math. Gen. 19, L4 7 3 (1986). 182 .CALCULATIONS 0? TENSOR ANALYZING POV/ER IN BACKWARD - (p,d) ELASTIC SCATTERING USING ANALYTICAL WAV3 FUNCTION FOR DEUTERON D-STATE V.N. Pai* and R.J. Kulkarni Department of Physics, University of Bombay, Vidyanagari, Bombay-400 093. Backward (p,d) elastic scattering has been the subject of extensive experimental and theoretical work for many years now. The excitation function at 180° exhibits a monotonous decrease with in- creasing proton kinetic energy and is broken by two structures: the first being centred around Tp=500 KeV, One of the mechanisms in the interpretation of this structure is the one-nucleon-exchange (ONE) mecha- nism. The JNE is the nost elementary process for the understanding of the backward tpjd) scattering. Nakanura et al/1/ have recently proposed an inter- pretation of the backward tensor-analyzing power in terms of the ONE model. The one-nuclaon-exchange involves an expression for RL(Q) which is signifi- cant in the calculation of the tensor analyzing power in the ONE model: = 4lF ^ r where Q = ^(q - pi); pL = four-nomentum of the in- cident proton and q = four-momentum of the exchnnged nucleon. It is well-known that thp existence of the D-wave is absolutely essential for the unaerstanding of the tensor analyzing power T°>oe *n tne 0?iE model: Our aim in this paper is to focus attention on the nature of the deuteron 3 and D state wavp functi' ons, which ire an integral o irt of thn calculations of tb.p tensor analyzing power T^J3^ '.'e havo evalua- ted T9Qeusing a new set of analytical wave func- tions for the deuteron, recently nnoo^od by Anton- Certov et il/ki/. The analytical for.a oi" th,ay 400 057. 183 t? •— where the parameters in the wave functions are given in Table I of ref. /2/. ,7e have used the specific wave function "YLS®* with 8% PQ and with a variation for thp S-state wave function within 3 fin. The numerical calculations were carripd out using the H4SL subroutine DCADRE, based on Ronberg quadrature, v;ith a cut-off value at p=15 fin. The re* suits are shown below: \ 2. 3 4 ^ONE OWE j yl • x 0-5 1. 891 »o. i-o ' 0- 3?6 •vQg - 0' 8?J \'5 0->(0d ** 0 184 A STUDY OF ELASTIC 0t + 4°Ca SCATTERING WITH ALAS Ashok Kumar, S.R. Verma and V.K. Bhatnagar, D.B.S. College, Dehra Dun and O.D. Sharma, Meerut College, Meerut The elastic a + Ca scattering seems to be most widely investigated case from both experimental and theoretical point of view. Recently^much attention has been given to the phenomenon of the anomalous large-angle scattering (ALAS) of a -particle with the selected light - and medium weight nuclei. The elastic scattering of a + Ca at energies ^30 MeV provides a good example of it. Numerous explana- tions were put forth for ALAS, but then it was shown to be explicable in terms of simple potential scattering provided the absorption is "relatively weak and the real potential is deep with appro- priate shape /I/. For this purpose, the full scattering amplitude can be written as, ft e ) = fB( o ) + fx{ e ) where, the barrier wave amplitude f ( 6 ) and internal wave amplitude f ( 0 ) display very different behaviour. As ,such5 the outer barrier scattering oB = |fB( & )| has the characteristics of strong absorption scattering at forward angles, the inner barrier term a = |fT( 6 )j contributes mainly at large angles, while the interference between fR and fT provides complicated structure at intermediate angles. Here, the real part of a + Ca potential is calculated microscopically and is supplemented by phenomenolcgical weak imaginary potential for absorption effects /2/. In Fig.l, solid-line curve is the calculated real potential along with the empirical potential of Michel and Vanderpoorten and the other twc /3/ . The DCS have been calculated at Elab = 29.0, 39.6, 42.6 and 104.0 MeV as shown by solid-line curves in Figs, i and 3, respectively. At these energies the experimental data c^ Michel and Vanderpoorten a: 29.0 MeV /4/ , Th. Delbar et al . at 39.6 and 42. c MeV /5/ and Bernstein et al. at 104.0 MeV /6/ are available for comparison. The agreeem^nt :r satisfactory in full angular range. 185 References : /I/ Ashok Kumar, Pramana (1990) (to be published). /2/ V.K.Bhatnagar, Doctoral Thesis, Garhwal Univ. (1989). /3/ W.G. Love, Phys. Rev. C17 1Q+2 (1978) 1876. /4/ F.Michel and R.Vander- ^ poorten, Phys. Rev. C16 (1977;~ 142. \ /5/ Th. Delbar et al. , Phys. =- Rev. C18 (1978) 1237. 10+1 /6/ A.M.Bernstein et al., .Phys. Rev. C32 (1985) 1208. Hi** p I I 40 Ca(o,O)40Ca I 10** - 04.0 HeV 7 io<} - - v 10* D \vIf* : 11 * I* rv. O V \i -i- D • \r "' 111'1 i ' V )U }U loeg) 136 32 ?ft ELASTIC SCATTERING OF S PROJECTILE FROM Si TARGET AT Elab = 135 MeV. Ashok Kumar, Ravi Datt Godiyal/ K. Eswaraiah. Madhup Seth, D.B.S. College, Dehra Dun and R.C. Mishra, V.S.S.D. College, Kanpur The elastic scattering angular distributions of the 32S beam on 28Si target nucleus had been analysed earlier by Mermaz et al (1983) taking into account the alpha exchange between the two identical colliding cores /I/. The six parameters had been readjusted to best fit the data-points on the full angular range- Recently, Bilwes et al (1988) /2/ has produced experimental data of 32S elastic scattering on 28S.1 and other s-d shell nuclei on a large energy scale and an accurate theoretical interpretation PRE been given in the frame work of the folding model by use of the complex effective interaction of Faessler et al (1981) /3/. In this analysis renormalization coefficients for the real and the imaginary parts of the optical potential are introduced to reproduce the data but the renormalization of the imaginary potential is unphysically large. Thus, it seems reasonable to develope a new microscopic approach in the double- folding model and to test it at higher energy away from the pure Coulomb scattering. In the present investigation, a simple microscopic method has been applied to calculate DCS for 32S -r 28Si elastic scattering. The direct potential from the single-channel resonating group method (RGM) equation for the real part oE the nuclear potential is used. The oblate and prolate configurations have been considered for 28Si nucleus /4/ while the open-shell 32S nucleus is made spherically symmetric by using filling approximation /5/. Thus, the real part of the nuclear potential is calculated using reasonably satisfactory two- nucleon interaction and antisymmetrized shell-model wave functions for 32S and 28Si . It is not multi- plied by any arbitrary factors in the DCS calcula- tions, as has beer. done in most earlier calculations of double-folding model. The imaginary part is assumed /6/ and renormalized by a small 187 parameter equals to 0.5, which is quite reasonable. In Fig.l, solid-line curve shows the detailed behaviour of calculated DCS over the full angular range at 135 MeV while experimental data of Bilwes et al /2/ are restricted to around 70°. The agreement is reasonably good. References: /I/ M.C. Mermaz et al. , Phys. Rev. C2J7 (1983) 2408. /2/ B. Bilwes et a.., Nucl . Phys. A484 (1988) 174. /3/ A. Faessler et al., Nucl. Phys. A359 (1981) 509 /4/ Ashok Kumar and B.B. Srivastava# Can. J. Phys. 66 (1988) 813. /5/ V. Maruhn - Rezwani et al. , Phys. Lett. 67B (1977) 134. ' /6/ L.F. Canto, Nucl. Phys. A279 (1979) 97. 10u 28Si(32S, 32S) 28Si Elab - 135 MeV 10" ,-8 20 kO 60 80 100 120 140 160 180 fic m (degree) 188 FOLDING MODEL ANALYSIS OF S + S AT 160 MeV Ashok Kumar, K. Eswaraiah, Ravi Datt Godiyal/ D.B.S. College, Dehra Dun, P.K. Bhatnagar: • Hindu College, Sonepat and B.B. Srivastava, Meerut Uni- versity. 32 Among the nuclei of the 2s-ld shell, S is particularly difficult to study as the findings of Hartree-Fock calculations with or without pairing for the ground state range from oblate to prolate, from axially pear shaped to triaxial, depending on the choice of the n-n interaction and other details of the calculation /I/. Thus, the open-shell nature has made microscopic calculations rather impracti- cal. To avoid this problem, we apply here natural dynamical generalization of the filling approxima- tion /2/ by considering 3/5 magnitude of the unfilled Id shell, thus resulting in a spherical ground state for 32S nucleus. The unproi ^ed variaticnal wave function for arbitrary symmetric even-even nuclei has been constructed from A- particle state into N = A/4 orbitals, each occupied by four nucleons with antialigned spins and isospins (S = T=0) having the same width parameter B = 0.2822 fm'2" in all the Lhr.ee directions /I/, ct>32 = A.7 exp[-( 3/2)(r_i - Rjf-J fl^s^t..), is an with i = 1,....,A; j = 1, , N and A^2 antisymmetrization operator. Here, i and } label the nucleons and the orbitals, respectively and ti . denotes the spin-isospin state of the nucleon. There are 19 variational parameters in our 32- particle calculation. Using the above wave function, real part of 32S + 32S optical potential is microscopically calculated in the douole folding model /3/. The imaginary part is assumed /4/. The sensitivity of the calculated results is tested by computing DCS (solid-line curve) at the highest available energy 160 MeV /5/. The agreement is fairly good in Fig.l. The dotted- line curve shows the result when complex nuclear potential is switched-off . Hence, folding model potential plays a significant role in describing 32S + 3 2S elastic scattering. 189 References : /I/ W. Bauhoff et al, Phys. Rev. C22 (1980) 861. /2/ V. Maruhn - Rezwani et al, Phys. Lett. 67B (1977) 134, • /3/ Ashok Kumar, Doctoral Thesis (1983) Meerut Uni v. /4/ L.F.Canto, Nucl . Phys. A279 (1979) 97. /5/ B.Bilwes et al., Nucl. Phys. A484 (1988) 174. 32 3 2 32 10- i S< V S> S 10- Z b 100 10-1 10-2 10-3 10 0 20 40 60 80 100 120 140 160 (degree) m 190 CHARACTERISTIC FEATURES OF ELASTIC SCATTERING OF IDENTICAL NUCLEI Ashok Kumar, Ravi Datt Godiyal/ K. Eswaraiah/ D.B.S. (P.G.) College, Dehra Dun and P.K. Bhatnagar, Hindu College/ Sonepat. The elastic scattering of two identical nuclei 40Ca + 40Ca at various energies is discussed in the present investigation. One direct consequence of indistinguishability of projectile and target is that the differential cross section is symmetrical about 0 = TT/2. Another important consequence is the appearance of interference between the two unsymir.etrized amplitudesf( 8) and f( TT - 0 ) . This is most strikingly displayed at low energies/ where the scattering is primarily due to Coulomb field. And one obtains highly oscillatory Mott cross sections instead of the monotonic Rutherford cross sections as evident in Fig.1/1/ • d0 ( 9 } 1MM 22 It is noteworthy that the oscillations in the angular distribution seen in Figg. 1 and 2 are a quantal interference effect due to indistinguish- ability and must not be confused with the diffraction like oscillations that may appear for non-identical nuclei. At the bombarding energy is increased above the Coulomb barrier, absorption is increased in Ca + Ca elastic scattering which damps out the Mott oscillations. This occurs because the Rutherford amplitude f_( 9 ) is dominated by Fresnel - like amplitude . It suggests that inter- ference effect is greatly reduced. This has been confirmed both theoretically and experimentally as evident from the damped - oscillatory pattern of the angular distribution at hioher energies in Fig.2. The full-line curvec represent the simplified microscopic calculations of Eswaraiah et al /2/ and the solid dots are the experimental data taken from ref. 1. 191 References : /I/ G.R. Satchler, Direct Nuclear Reactions (1983), Oxford University Press, New York, 400. /2/ K. Eswaraiah, Ashok Kumar, Ravi Datt Godiyal and B.B.Srivastava Symp. on Nucl. Phys. (India) 3_2B (1989) P9. 40 40Ca *«• Ca = 101 MeV I b 10 |- J 20 30 40 50 60 100 120 192 EVIDENCE OF THRESHOLD ANOMALY IN S + Ca ELAS- TIC SCATTERING ABOVE THE COULOMB BARRIER Asnok Kumar, K. Eswaraiah/ Ravi Datt Godiyal and Madhup Seth, D.B.S. College/ Dehra Dun, R.C. Mishra, V.S.S.D. College, Kanpur and B.B. Srivastava Heerut University The existence of a polarisation potential at energies near the Coulomo barrier due to a rapid decrease ot the absorption at these energies is called "threshold anomaly". This phenomenon is quite familiar in nucleon - nucleus scattering /I/ and in heavy-ion systems it was reported for the first time in the 32S + 40Ca -lastic scattering /2/. There exists suitable data of Gutbrco et ai for this system at three incident energies 100, 120 and lbl.5 HeV /3/. Bilwes et a! have recently measured elastic scattering of 32S + 40Ca at 90 and 110 Mel /4/. The anomaly behaviour seems to be due to couplings to quasielastic channels that produce an attractive polarization potential at enemies near the Coulomb barrier. Recently., the data have been analysed in terms of the double-folding model using the coupled - channel approximation for inelastic scattering. The energy dependence of the renormalization coefficient of the folding poten- tial has been confirmed at these energies and is consistent with the dispersion relation /5/. Similarly, in the present investigation the real part or cfre nuclear potential is microscopically calculated in double-folding model. The energy- dependence of the calculated real potential is crudely acnieved by e>dvurting an exchange - mixture parameter u around 1. The imaginary part is treated phenomenoiogicaJly and renormalized by a parameter Aj . Tne ideal situation of getting parameter fret potentials is not yet reached be* it is encouraginq to have reauced the number ol *•*#£ parameters to only :..... In rig.l, the DCS fits obtained by rciuino r.ctential analysis near the Coulomb barrier ar<: rr:. as good as expected from the coupled •r.M'irir:-.-. ••.icuiations. The lack of a good fit near •"'ouia'.'ir Larrjer ,nay reflect the inadequacy ot acc^untirc for t n "• polarization potential by only a 193 renormalization coefficient. However,the present investigation is found to give satisfactory description away from the threshold. References : /I/ C. Hahaux and H. Ngo, Nucl. Phys. A378 (1982) 205. /2/ A.Baeza, et al., Nucl. Phys. A419 (1984) 412. /3/ H.H. Gutbrod, et al., Nucl. Phys. A213 (1973) 285. /4/ B.Bilwes, et al., Nucl. Phys. A484 (1988) 174. /5/ J. Diaz et al., Nucl. Phys. A494 (1989) 311. b 0 40 60 BO 100 120 6C m(degree) 194 SOME ASPECTS OF BARRIER RESONANCES B.M.Jyrwa,B.Sahu,C.S.Shastry Physics Department North—Eastern Hill University Shillong-793003 The characterisation of resonances and their important in nuclear scattering.Generally, in potential scattering sharp resonances are associated with long lived positive energy states generated by potential pockets.In the analytic S—matrix theory resonances are characterised by complex poles of partial wave S-matrix in the lower half of complex k—plane having small imaginary parts.In heavy ion collision the effective potential for a given partial wave has a potential pocket situated in the absorptive region of the interaction and has a barrier due to large Coulomb potential.Resonances may originate due to the pocket or the barrier top states.In this paper using an exactly solvable smooth^ finite range barrier type potential V(r)=VO/(Cosh^ar) we examine the properties of the barrier region resonances. In the case of the above potential the analytical expression for the resonance energies and width has the form 2 7 E =CV (1-a /4V )-4a (n+3/4) 3 ~? 1 f? *"* "P 1 /*? R T R -i4a V. (1-ct /4V^> 195 It can be verified that this transition is —1 /2 proportional to tVoa> which in turn is inversely proportional to r for small a.We believe that these properties characterise the general features of barrier resonances, and give additional aspects not dealt with in earlier works * . It may also be noted that when a potential pocket is dominated by an absorptive imaginary potential,the width of the resonance generated by the pocket is of the order of the imaginary part of the potential.This can be verified in model calculations.For example,in the case of the potential V(r)=-iW ,r =v0, a References 1. W.A.FRIED and C.J.GOEBEL: Ann.Phys.1O4, 14P(1977) 2. D.M.BRINK:Semi-classical Methods for Nucleus -Nucleus Scattering,(Cambridge University Press, Cambridge London,(1985)). 196 ION-ION POTENTIAL IN PSEUDONUCLEON SIMULATION MODEL R.C. Mishra/ Madhup Seth, V.S.S.D. College/ Kanpur and Ravi Datt Godiyal, Ashok Kumar, D.B.S. College, Dehra Dun Present study is made for calculating ion-ion potential in case of 12C+12C reaction in pseudonucleon simulation model /I/. In this model each nucleon is taken as composed of number (NB) of pseud onucleons. These pseudonucleons (pseu- doneutrons and pseudoprotons both) are classical spinless particles and are interacting via a suitable two-body interaction /2/. The motion of these particles is governed by CEOM approach /3/. The ion-ion potential for the system under study is calculated for Ecm = 28.20 MeV. The peak of fusion cross-section curves is obtained at the above energy. Dynamics of the ion-ion potential involves three factors, (a) impact parameter, (b) incident energy and (c) initial relative random orientations of the colliding nuclei. In case of pseudonucleon simulation it is not necessary to average the impact parameter for number of relative random orienta- tions /4/. Therefore,for a particular energy other two fac- tors are constant for fusion reaction. The method of calculation of ion-ion potential is given in the other paper /5/. The relation used is given finally as Al.NB A.NB r. V(R) =11 - V [1 ± ) exp[( ± i=l j=Al.NB+l ij 0 Two cases of pseudonucleon simulation namely, NB = 5 and 8 are taken for 12C + 12C fusion cross sections. The value of critical impact parameter which determines the fusion is 5.4 & 5.6 fin, respectively for NB = 5 & 8 case. Results which are drawn from the ion-ion potential at different centres of mass (RCM) are summarised in the following lines. It is noted that ion-ion potential for the present system has same value from RCM = 20.0 to 9.85 fm. The separation of 9.85 fm is reached in the 4th NS of the collision event. The values of ion-ion potential for NB = 5 and 8 differ from 5th NS to the last of the collison event. At T = 5.0 NS, RCM for NB = 5 case is 7.93 fm and that for NB = 8 case is 8.03 fm. The maximum repulsive value of the ion-ion potential for NB = 8 case is 6.2 MeV which is obtained in the 5th NS of the collision event and that 197 for NB = 5 case is 6.9 MeV at RCM = 6.7 f m, obtained in the 6th NS of the collision event. lor.-ion potential for NB = 5 case changes its nature from repulsive to attractive at RCM = 6.7 fm in the 9th NS. On the other hand the above potential for N3 = 8 case changes its repulsive nature to attractive nature at RCM = 6.1 fm in the 8th NS of the collision event. Remarkably it is noted that nature of ion- ion potential is oscillatory from the 10th NS and this conti- nues upto the last (T = 30.0 NS) of the collision event in both the cases of pseudonucleon simulation. In the conculsion we can say that qualilative nature of ion-ion potential in both the cases is almost similar. Variations in the quantitative nature are seen from the 5th NS. These variations are prevalent after 10th NS of the collision event. At this time separation between the centres'of the mass of the two clusters is ^ 6 fm. The massive reorgani- sation of pseudonucleons is responsible for prevalent quantitative variations of ion-ion potential. It is also noted that the value of ion-ion potential reduces for NB = 8 case than that for NB =5 case during corresponding timings of collision event between 10th NS to 30th NS. The value of ion-ion potential for NB-1 case is much higher than that for cases NB = 5 and NB = 8 during the above interval (10th to 30th NS) of the collision event. References : /I/ R.C. Mishra and Y.R. Waghmare, Proc. DAE Vol 30B (1987) 212. /2/ H.S. Koehler and Y.R. Waghmare, Nucl. Phys. 66 (1965) 261; Y.R. Waghmare, Phys. Rev. B136 (1964) 1261. /3/ S.S. Godre anJ Y.R. Waghmare, Phys. Rev. C36 (1987) 1632. /A/ R.C. Mishra, S.S. Godre, Y.R. Waghmare and V.S. Ramamurthy, Proc. DAE Vol. 2^B (1986) 237. /5/ R.C. Mishra et al. (Communicated for DAE Sympo., 1990). 198 FUSION SPIN DISTRIBUTIONS IN THE MACROSCOPIC MODEL OF NUCLEAR SHAPE EVOLUTIONS. S. V. S. Sastry, A. K. Mohanty. S. K. Kataria Nuclear physics Division D. A. R. C. . Bombay - 40000S and V. S. Ramamurthy Institute of physics, Bhubaneswar - 7S100S The role of nock degres of freedom in the enhancement of sub-barrier fusion cross section has been studied recently tl). In this study it was also seen that this model gives rise to much broader spin distributions along with enhancement of fusion cross sections, although no quantitative comparison against the experimental data was carried out. In inu present work, we have applied this model to the enhancement factors for mean <1> values as a function of the entrance channel fissility parameter X and compared it against the available experimental data. A strong correlation has been seen in the enhancement factor and the fissility parameter X as both are related to the width of the enhancement in the fusion excitation function. In macroscopic model of nuclear shape evolutions, we have shown earlier Cl] that the fusion barrier has three distinct regions depending on tho bombarding energy domain. In region I, bombarding enorgy E is hi ghor than tho cm , barrier .tho systom soes tho frozen density potontial barrier V . Out if E falls in tho II region, thon tho 01 <-m systom fusns by tunneling through an onorgy dopondont potential barrier due to neck formation. In tho III region, fusion takes place by penetrating an adiabatic fusion barrier V which is less than V . This difference C DZ Dl V -V 3 in two barrier heights which gives rise fusion enhancement has been taken from tho model calculations tl] for different systom with entrance channel fissility parameter X . We then calculate the fusion cro'js section as well as average <1> values for those systems using the proscription givon In rof [2) 1 . o. the onorgy dopondonco of tho bjrrier shoulo bo oxprossod as a function of rolatlve 199 kinetic energy at the interaction barrier R8 for a given 1 value. Fig.l shows the plot of E -V for different fissility parameter X . where calculated values of <1>'<1>,D have all the features of the experimental results for the ^i^^ system . A more realistic parametriration of this model fusion barrier will improve the abovo quantitative predictions. *nd results for many other systems will be presented. 1. v. S. Ramamurthy. A. K. Mohanty. S. K. Kataria and G. Rangarajan. Phy. Rev. C 41 C19QO3 27O2. 2. A. K. Mohanty. S. V. S. Saastry. S. K. Kataria and V. S. Ramamurthy. Phys. Rev. Lett. 63 C1S9O3 1096. (Ce»- VtJ 1 200 PROXIMITY EFFECTS IN MOLECULAR CONFIGURATIONS IN LIGHT NUCLEI C.Shanmugam and M.D.Padmini * Department of Physics, Presidency College, Madras-5. * Department of Physics, Quaid-e-Mi I Iet Govt.College for Women, Madras-2. The occurrence of molecular configurations in symmetric and asymmetric heavy ion col I isions has been studied by us earlier /1/ by choosing the elliptic lemniscatoid parametrization of Royer and Remaud 111 incorporating the neck degree of freedom. In this work, we take into account the nuclear proximity energy and study its role in the formation of nuclear molecules at higher spins. The two different reacting nuclei are represented by the two halves of different elliptic Ieminiscatoids joined by a neck of radius 'a' (Fig 1) st and s^, are the two interconnected parameters defined by sL = a/C^ (i=1,2) where is the elongation of the nucleus 121 . The potential energy of the system is given by E =E where TOTAL Ru) %*t > rotating liquid drop energy is the sum of the volume. surface, coulomb and rotational energies and w the nuclear proximity energy arising out of the nucIeon-nuc I eon force inside the crevice. FollowingBlocki et al 13 1 the proximity energy is given by ^ where ' is ihe surface parameter, h is the transverse radial distance varying from a minimum of 'a' to a maximum of hj ,j D(r) is the distance between the elements of the surface, b is the surface width (=0.99fm) 201 The following systems have been studied by us Symmetric reaction partners:- i ) C+ C (ii) ^0 + 0 (iii) Mg iv) Si+ Si (V) * Ca+ Ca II Asymmetric reaction partners:- (i) C+ He (ii) 0+ C (iii) Mg+ He In all these cases the proxirr.ty effects are found to lead to the appearance of competing minima in the potential energy curves at low and medium spins and the first minima fall below the second giving rise to deep necked molecular configurations. Fig (2) illustrates the existence of a second minimum when proximity energy is included and the absence of such a minimum when the proximity energy is not considered, in the case of 'aC+ '*0 —>2 Si However, whether the second minimum will still persist if the neck is smoothened by taking mu I t i dimensional parametrization is to be investigated. /1/ C.Shanmugam and M.D.Padmini, Phys. Rev.C40, 1273 (1989). 121 C.Royer and B.Remaud, Nucl.Phys. Amm, 477 (1985) 13! J.BIocki, J.Randrup, W. J.Swiatecki and C.F.Tsang, Ann of Phys. 105, 427 (1977). ts Si -10- J-iS, 1 202 12 1<5 icS ANALYSIS OF C + 0 AND O + 0 RESONANCES S. Datta*. U. Abondanno , N. Cindro + Physics Department, University College of Science, 92, Acharya Prafulla Chandra Road, Calcutta - 70C C09, India. * Djpartimento di Fisicc dell Universita Trieste, I.N.F.N. (TRIESTE), via A. Valerio 2, 34127 Trieste,Italy. # Rudjer Boskovic: Institute, Zagreb, Yugoslavia A complete and updated compilation of resonances in C + 0 and 0 + 0 systems have been made [11. The compiled resonances were analysed in terms of the Morse [2] and anharmonic oscillator [31 potential approaches. In both the cases the calculated curves fitted very well with the experimental data. Effective Morse potntials were also calculated from the fitting parameters. Figures 1 & 2 shows typical fit curves for 0 + 0 system and the affective potentials for the C + O system respectively. The parameters are explained in ref t 11 . REFERENCES : 1. U. Abondanno, S. Datta, N. Cindro, Z. Basrak, G Vannini; J. Phys.G15, 1845 (1989). 2. L. Satpathy, P. Sarangi, A. Faessler; J. Phys G12, 201 (1989). 3. N. Cindro, W.Greiner; J.Phys.G9, L175 (1983). (contd. ) 203 5 10 15 r (fm) vs > Fig.2 The effective CM potential (full curve) assumed n value of of the 1 204 QUASI-MOLECULAR STATES IN C12 + O16 SYSTEM Pradip K, Sahu, F. Saraagi and L. Satpathy. Institute of Physics, Blmbaneswar-751005,India. The understanding of the mechanism of quasi-molecular resonances observed in heavy ion collisions has been challenging problem since the discover in C12 -f C16 collision by Bromley et.al.[l] in I960. The diatomic-like rotation il-vibrational picture of these states proposed ear- lier by Satpathy et.al.[2] for (712 + C12 system has been found, to be quite successful in accounting about 50 states. Using Morse-type bond- ing potential they hr.e described the mechanism of the quasi-molecular states in the frame v. or]t of a quantum mechanical two-body problem.The rotational-vibrational characteristics of the spectra appear in a very nat- ural way as solution of Schrodinger equation.The low lying states of the spectrum are found to be bound states, while the high lying ones are the resonances of the bonding potential. The effective potential between two ions is taken as a combination of the Morse potential and a constant, 201 I VeJf(R) = A + B[e(- ) -2e(-" )]1 with x = &jg*, where A, B, /?, and Ro are the four constants.The general eigen value expression us- ing the approximation due to Flugge for the centrifugal potential can be written analytically in terms of the four parameters of the poten- tial. The values of the parameters are determined by fitting the data of the resonance ene gies.Here we apply the same model to describe the resonances of the asymmetric C'12 -I- O16 system, ^he values of the pa- rameter obtained by fitting are A = 16.724,5 = 15.99, p = 1.122, and Ro = C 6457. The depth and the range of potential are 16.7 MeV and 16fm respectivly. For an asymmetric system both the even and odd angular momentum states are possible, for which calculation has been carried out. We performed two sets of calculation. In the first set, we use the eigen value expression the Schrodinger equation obtained under Flugge approximation. These arc presented ;w solid curve: in Fig.J(a) and 2(a),where the solid dots arc the experimental data. In the second 205 set we exactly solve to Schrodinger equation by numerical method and determined the bound and resonances which are plotted as solid curves in Fig.l(b) and 2(b). All the known states (35) are well accounted for. The impressive agreemeat bearsout the validity of the diatomic-like molecular picture of the resonances proposed earlier£2.] References [1] D.A.Bromley et.al. 1960 Phys. Rev. Lett. 4 365 [2] L. Satpathy et.al. 1990 J. Phys. G: Nucl. Part. Phys.lG 469 , 1986 J.Phys.a-Nucl.Phys. 12 201 206 NUCLEUS-NUCLEUS COLLISIONS AND THE VIBRATIONAL MODEL Z.A. Khan Dept. of Physics, A.M.U., Aligarh-202002. According to Glauber theory the scattering amplitude for describing the excitation of a target nucleus^A by the proiectile nucleus B with cm. momentum K is given byl) where f(q) is the NN amplitude and k is the inci- dent nucleon -nomentum corresponding to the pro- jectile kinetic energy per nucleon. In the following we apply eq.(l) to study the scattering from the collective nuclei for which the target wave function, under the adiabatic approximation2/, may be written as: where <&> and % describe respectively the intrinsic and the collective states of the target. Substitution of eq.(3) into eq.(l) gives The operator "X(£)may be expanded in a series following the ref.l). The result upto second order in the scattering amplitude is: '-9 ••? * . y. c»») -x %oi h) -t- y. ,c fc 3 It may be easily seen from eq.(5) that the long range correlation responsible for the colle- ctive behaviour is mainly described by the first term 7.o0?) . The second term V^tt), on the other hand, describes mainly the pair-correlation, A present in the intrinsic state <^,y . Thus '/L,(~£) may be considered as a correction to be added to 207 the uncorrelated part ?•„. _ . Now following ref.^), it may be shown that the scattering amplitude (with only first term in eq.(6)}describing the excitation of the target from the ground state 'y^s Icc'y to t\ o one-ohonon state vl/*~ J-+ iV;is oiven by: R rp _ where s--rd and , with some minor modifica-p% tions, have similar"" expressions^ as given in ref.i To consider the,. effect of X,o£)in eq.(7), we further follow ref.- ') in which it is assumedAthat the contribution of the deformation term in K|('^)j because of its higher order in the NN amplitude, may be neoiected. In view of the above and follovi'- inn ref.3) one can evaluate %, d"£) in a relativ- ely simple manner. Obviously, in this situation, the contribution of '/..<''£) would be simply added to the phase function •/,, . The coulomb effects are included in the fo:-i > ttion by following the approach of Ahmad4). Using the above for mi; l tion, we are evalua- ting the elastic and ine.- .-tic scattering of 1.37 GeV a-particles on -' 'c and Ca isotopesp . Thic analysis is expected to provide some usefufll information about the effects of coupling between elastic and inelastic channels, the two-body correlctions, and matter distribution. References: 1. Franco V and Varma G K 1978 Phys. Rev. C18 349. 2. Ahmad I 1975 Nucl. Phys. A247 418. 3. Khan Z A and Ahmad I 1984 J. Phys. G: Nucl. Phys. 10 135. 4. Ahmad I 1978 J. Phys. G: Nucl. Phys. 4 1695. 208 SUPKRDEFORMATION AMD HOCLEON EMISSION SPECTRA OP 28Si M. Rajasekaran and T. R. Rajasekaran Department of Nuclear Physics, University of Madras Guindy Campus, Madras 600 025. The recent explosion of interest in the high 6pin behavior of strongly elongated (superdeformed) nuclei is well justified by the special nature of these states. The search for superdeformed structure in nuclei i.e. deformed states with >2: 1 ratio between major and minor axes, and the neutron and proton emission probality in these nuclei have been a topic of great interest einceRthe observation of states for the nuclei l ^Dy and Si [1,2] We use the statistical theory of the hot nucleus incorporating the deformation degrees of freedom, and collective rotation of the system to evaluate e neutron and proton emission from Si. 2tf observed that stable superdeformed minima for • Si having 5=0.5 and at M=2Qfi. It is confirmed by the experi- mental results of Kolata [2] and theoretically by Faber [3] using the Nilesion Strutinsky model. The neutron emission spectra at high spins for Er has been studied by us [4J. Here this formalism £4] is used to evaluate nucleon emission from light nuclei. The grand partition function is given by ii The conservation equations are given below : i t Where 6t (w) are energy eigenvalues for a given w. The excitation energy ie gr"= g» jr efcoy 7\i , The neutron/proton emission probability 0$(E) ie = C pi\J) E T1(E) with 0 = E*- S - E - Erot where P(U) is the level density of the residual 209 nucleus. S and E are the neutron/proton separation energy and outgoing neutron/proton energy respectively. The transmission probability T1(E) = 1 for neutron and for proton T1(E) < 1. Fig. 1 ehows the angular momentum versus the collective rotational frequencyRw It is observed that the ground states of Si is in nearly spherical (oblate shape) up to M=13n. The stable superdeformed minima is observed at M = 20 -fi with S =0.5 and £>= 0°. Fig.2 shows the neutron emission spectra for M = Oft, 15ti and 20tt. Fig.3 shows the proton emission spectra for M = 0ii,&ft and 15ti. The suppression of^(E)is due to the vanishing for E<4MeV References: [1] P.J. Twin et al., Phys Rev. Lett. 57, 811 (1986). [2]J.J.Rolata et al.,Phys Rev. Lett. 61, 1178(1988). [3]M.Faber, Phys. Scr. 24, 189(1981). [4]M. Rajasekaran & T.R. Rajasekaran et al.,Phys, Rev.Lett. 61, 2077,(1988). 2 3 w(M.;V) Fig. 1 Neutron Emission spectra Proton Emission spectra '"'Si 12 3 4 5 6 cul HIM I mrtiiv I (Mf;V) l (III I litrlliy I (McV ) Fig. 2 Fig. 3 210 IMPORTANT ASPECTS OF FRAGMENT ANGULAR MOMENTUM IN MEDIUM ENERGY FISSION H.Naik, T.Datta, S.P.Dange, C.N. Patra and Satya Prakash Radiochemistry Division, Dhabha Atomic Research Centre TROMBAY, DOMBAY-400 085 TNTRODDCTION:- [n low energy fission, angular momentum of fission fragments arises due to the pre-scission bending mode oscillation for non-linear scission configuration as well as due to the post scission Coulombic torque between the separating fission fragments, tn medium energy fission as the fissioning nucleus has relatively higher angular momentum and excitation energy, statistical excitation of various collective rotational modes e.g. wriggling, tilting, bending and twisting contribute to the fission fragment angular momentum. Thus determination of fragment angular momentum in medium energy fission provide information afcout the effect of entrance channel parameters viz. excitation energy and angular momentum of the fissioning nucleus as well as show the influence of the collective rotational degrees on fragment angular momentum. In order to investigate these aspects in the present work fragment angular momenta for I were deduced from the radiochemically determined isomeric yield ratios in the 33.2+0.2 MeV and 44.2+0.2 MeV alpha particle induced fission of U. EXPERIMENTAL:- Stacks of natural Uranium target foils (75um thick) wrapped in aluminium catcher foils (25um thick) were irradiated for 5- 6 minutes at the 88° variable energy Cyclotron at Calcutta using an alpha particle beam of energy 50 MeV. After the irradiation the front aluminium catcher foil of each Uranium metal foil was dissolved and iodine was separated radiochemically . Standard aliquots of purified iodine samples were counted for the gamma lines 271.9 keV and 847.0 keV of 1 * I metastable(m ) and ground(g") states and 1260.0 key of bI respectively. To correct for the precurssor contribution in [ activity *Te(210.0 keV) and ' bI were followed in unseparated sample. 13bI was used as fission rate monitor in both separated and unseparated samples. Independent yield of I m-state from 271.9 keV and for g-state from 047.0 keV were calculated using decay and decay- growth equations respectively. The independent isotneric yield ratio of • f from present work and for L earlier determined from this laboratory at these two energies along with the value in low energy fission for same compound nucleus Pu are given in table 1. From the isomeric yield ratios fission fragment rms angular momenta (. "f [ and [ were deduced using spin dependent stastitical moc analysis . The 3UMC. values obtained for C and I in medium energy from present work along with the values for the same in low energy fission are also given in the same table 1. DISCUSS TON:- tFrom table 1 it can be seen that for the same compound nucleus ( Pu ) the •TRMq for both I and i are higher in medium energy fibsion (i.e. in U(«,f)) compared to low energy fission (L.e in Piifn ,f)) indicating the pffr-ci of entrance channel excitation energy and angular momentum. Higher fragment angular momentum in medium energy fission arises because of the tilting mode 211 (due to the input, angular momentum) in addition to the statist :.ral population of other collective rotational mode:; e.g. «;i.ggl i:•,.;, bending and twisting. In order to test the validity of of atJtistic.il equlibration of these collective rotational degrees fragment an'j:;l;:r momentum were theoretically calculate! as prescribed by Me •. r •:-.''••• > et.al."", according to which the variance of fragment angular mo-.rT.: nm is given as: o 2 = o2 J, TM where o'].„._,, V*'R variance momentum arTsing due to tilting, doubly degenerate wriggling random (i.e. twisting and doubly de-jenorai e bending) modes, calculation was performed for deformed fragment where deforir.-* • :.»n parameters were deduced on the basis ;>f scission coniigura'.j.on . Th-.- •1~..~ values obtained for " I and " "l are also given in the lahl withiS-n bracket. It is seen from the table 1 that in the case at '"I theoretical as well as experimental values are in close agree-rac-r.;.. However there is a discrepency in the case of L. This may he a manifestation of the residual single particle effect due to the spherical 82n shell in the corresponding fragment (-'35 n , ::.•:;!, probably this is the reason that even the experimental Jr, c of "*; is lower than I. In other words it seems that at medium energy fission there is a residual manifestation of spherical 82n shell along with the influence of collective rotational degrees that are in statistical equilibrium . AKNOWLEC"^MENTS:- The authors wish to thank to Dr. P.R. Natarajan, Head of the Radiochemistry Division, BARC for his keen interest ?.nd encouragement during this work. REFERENCES — 1 .Rasmussen.J.O., Norenberg, W. , Mang, H..T. : Nud . Phys . A; 05, flJ.r>[ ;"•". 2.Wilhelmy,.T.B. ,Chifetz.E. ,,Tared,R.C. .Thompson , S.C. , Bowman, H.R. , Rasmussen,J.R. : Phys. Rev. C^5, 204 1 (1.'l7.?). .1. More t to,L .G. , HchmiU, R . P. : Phys. Rev. :^_l\, ?.CM (1900). 4 .Dange.S.P. , Naik, H. ,Datta,T. ,Reddy, A.v.R.,Prakash,f;., Raman i ah, M . v : Radiochemica Acf.a.: 19, 127 (1986). 5 . Vandenbosch.R, Huizenga, J . R .: Nuclear Fission. (Acad. Press. fJ. Y ; " •"''': fi.Naik.H. .Datta.T. , Dange, F.. P . ,Guin, R . , Pi; jar i , P. K. , Sahokwndu , ".. M . , Prakash, H . ; (TCJ be communicated). T.nJ,E: -1 Fission)ag I '.'iiner i r Yi fid '.i •' :> 13?, IT. . ' 1 /_ system (MvV) I i I C ",c, 10.01 I 0 "if.-; 10"! | ; V). I ! I • 1 ", , ?0 r, | o 7". »o or, | n I ' ! ?T .7 I o i(.\o.()•', ! o (.-..• I i 212 SIMPLE FORMULA OF HEAVY-ION POTENTIALS WITH SPIN- DENSITY TERM IN ENERGY DENSITY FORMALISM — s-d AND fv^SHELL NUCLEI Rajeev K. Puri and Raj K. Gupta Physics Department, Panjab University, Chandigarh-160014, India. In energy density formalism of Vautherin and Brink /I/ , the ion-ion potential is defined as/2/: V(R) = /[ H(P,r,JT> - HjCP^r,,^) - H2(pijC Jo) ]dr (1) = Vp(R) + Vj(R); VP(R)= /[ H(P,r) -H,(P,,c() -H,(P2,c2) ]d? = 2ffR$(s) (2) Vj(R)= J [ H(JT ) - H.CJ",) -H2(J2) ]dr (3) Here we have calculated Vp by using proximity concept and Vj after having generalized spin density J*" for nuclei with valence particles (or hoies)/2/.The universal function §(s) of proximity potential, calculated for some 160 cases (Fig.l), is indeed universal since all the points are foccused around the mean behaviour represented by (for Skyrme force SII ): f-2.64 exp f 0.3250 ( s - 0.2) ] for s > 0.2 ' )sl-2.64 + 2.15 ( s - 0.2) for s £ 0.2 (4) Similiarly, Vj (R) cannot be seperated into the geometrical factor and universal function as it depends upon the shell structure. However, Fig. 2 shows that it can be parametrized if one knows the analytical expressions for four points; (i) repulsive maximum Via (ii) position RJfi of VJ-Q (iii)the distance RJO where spin density changes sign from repulsive to attractive (iv) the limiting value RJI, where V7 is zero (we take VJu=0.003 MeV). We have plotted Vj-afor lfc>0 reactions involving s-d + s-d and f?/2+ f7/2 nuclei as a function of P/P<> , by defining a new coordinate P, called the "Particle Strength" , P =Z™7rfJA+1> -C(^1)-3/4l"--rj(J+1)- ?(P+D-3/4] (5) with scaling factor Po=0.9549. We find a simple relation VjB = m P/Po (6) where m= 1.3375 and 0.94 for s-d and f7/shells, respectively. Similiarly, for RJ^,RJ-0 and R^, we obtain RJft = a +b (Ar \3) (7) RJO = c +d (A . i\2) (8) H RJL ~- x +y (A,.Aa) ,3 (9) where a, b, c, d, x and y are 4.58, 1.11X10 , 3.58, 8.70X 10"* 12.77+0.5, 1129 and 5.77, 4.75X10~\ 4.52, 3.776X10~\ 16.77, 8621 , respectively, for s-d and f«7/2SRells. Then, in terms of these four points ,the explicit expression for Vj (R) is: 213 V-jyj exp [ N (R - RJ6 ) for R » R^ (R) = (10) 2 M [ R - R^] for R S /5 with N= In (0.003/VX3)/(RJt-RJft) and M = - V-Sa/ ( RJo- RJft)* Comparison becween the exact calculation (eq.3) and the analytical calculation (eq.10) is illustrated in Fig.2. We notice that eq.(10) is an excellent simple representation of the spin density potential. In case of Ar -34 + Ar-34 system, we have also snown ( dashed line), that a change in RrLby ±0.5 fm, which changes V^by ±0.001 MeV, does not affect the fit at all. Finally, we have also calculated the interaction barriers 2 by adding the Coulomb term Z,Z2e /R to eq.(l) ( V(R)= Vp+ V,-). This is again parametrized by simple expressions as /2/: V6 = 0.845±0.20 x +(1.30+0.25) XIO* x (11) with x = Z, Z2 /(Ai*+i* ) •iO 3 6 Rs= 7.359+3.076X10 (ArA2)-l. 182X10 +1.567xi6(Al'kJ (12) These expressions are used to calculate the fusion cross- sections for a large number of reactions using the sharp - cut off model. Our results are found to be in nice agreement with experimental data ( for detailed see Ref.2 ). •——r~ • Skjr»« tore* 5II . - S4 / \^Hl+ H. • E HA, • - \ \ k 00)) /I7 9 Fig.l Universal Function. ll(lm) Roforonoos: Kig.^ i'ipi n-den.si f:y potentials. 1. D. Vauthorin and D.M. Brink, Phys. Kev. C5 (1972)626. 2. R.K. Puri, Ph.D. Thiosis ,1990 (l)an.jab Uni vorsi ty,Chandigarh), 214 ALPHA-CLUSTERING TRANSFER EFFECTS IN COLLIDING s-d SHELL NUCLEI Rajeev K.Puri and Raj K. Gupta Physics Department, Panjab University, Chandigarh-160014, India. Some reactions between s-d shell nuclei show /I/ an explicit preference for transfer of alpha-nuclei and the suppression of this effect on adding neutrons to either the target,projectile or bcth . This phenomenon is interpreted /2/ as the collective mass transfer effect,using proximity potential of Blocki et.al. In the- following, we have calculated the fragmentation potentials and the formation yields, using the energy density formalism (EDF)/3/. The fragmentation potential is calculated /3/ as a function > of mass - asymmetry t=( Aj -A2 )/(A, +A2 ) at the touching + : configuration Rt- Ro» Ro2 Vty) = -B,-B2+Vc+ Vp+Vj (1) Ro; are half-density radii of colliding nuclei, B; , the 2 experimental binding energies, Vc = Zf Z2e /R and in EDF the nuclear interaction potential V/v (R) is defined as: VA/(R)= /[H( p,r,J)- H,(f> , c,,^ )-n2(f>2,zz,Jz) ]dr = Vp +Vj (2) Here Vp (R) is calculated in proximity concept and Vj (R) by generalizing spin density J to nuclei with valence particles (, or holes) outside the closed core.For p , we use Fermi density and for c,the Thomas Fermi approximation. The mass fragmentation yields are calculated by solving the stationary Schrodinger equation in ^ at a fixed R = Rt: For mass parameters, we use the classical model /4/. Solving eq. (3) numerically, we get / Vfii)2l^, the probabilty of finding the two-fragments at a fixed R. *The probabilty for the ground state (w=0)yield, scaled to a fraction yield ( dij= 4/A),is then, >/z Pc W - / Y^z ^1Y &m to] i (4) The temperature, 0 , effects are then included by assuming a Boltzmann like occupation of excited states. 215 Fig.l shows the ^ calculated fragmentation potentials for compound systems Ni-56,58,60. We have allowed two particle transfers in each case. Interesting enough, N = Z, Ni*-56 system shows an explicit preference for alpha-cluster structure , supporting the experiments and earlier results of Saroha et.al./2/. Furthermore, addition of 2- and 4- neutrons ( Ni-58 and Ni-60 ) makes the potential energy minima less and less deeper, leading ultimately to minima at non-alpha nuclei. This again confirms the experimental results of Betts/1/. Fig. 2 shows the calculated mass yields for Ni-56 system, along with experimental data /I/ for 0-16 + Ca-40—> Ni-56 at 75 MeV and earlier calculations of Saroha et.al /2/ at 0 =2.75 MeV (which corresponds to centre-of-Mass energy of 44.3MeV). We find that our results, using EDF with Skyrme force SIII( ^=0), are in better agreement with experimentals /I/, as compared to that of Saroha et.al./2/. We have also plotted here the yields (dashed lines)for constant BTJTJ = 1 X 10^ M fm? , which give some what improved results. It 32 It HAS1 HUHBCIt HA1S HUMItS Fig.l Fragmentation potentials. Fig.2 Mass Yields. References: 1. R.R. Betts, Bad Honnef Conference, 1981. 2. D.R. Saroha et.al., J. Phys. G: U_ (1985) L 27. 3. K.K. [\iri, Ph.D. Thesis,1990 (Panjab University, Chandigarh). 4. H. Kroger and W. Scheid, J. Phys. G: 6 (1980) L 80. 216 FUSION LIMITED BY TEMPERATURE D. Bandyopadhyay and S.£. Samaddar Saha Institute of Nuclear Physics 92 A.P.O. Road, Calcutta-700 009 J.N. De Variable Energy Cyclotron Centre 1/AF, Bidhannagar, Calcutta-700 O64 The classical dynamical model for heavy ion fusion predicts1 the cross section to be inversely proportional to Ecn at high incident energies. Experimentally, however» it is indi- cated that the fall-off of the cross section is much faster at energies close to the fermi domain and ultimately it vanishes at E/A ~30 to 40 MeV. In this work we show that this fast fall-off may be related to the temperature ' . effect on the interaction barrier which has so far been neglected in all the dynamical calcu- lations. It has very recently been se?n that in contrast to the fission barrier, the fusion barrier as given by the interaction free energy may increase1 with temperature and ultimately the pocket in the effective potential may vanish, The effective interaction potential between two colliding hot nuclei (assumed at same tempe- rature) in energy density formalism is given by where F ( ?, + ?i ) is the free energy density of the two overlapping nuclei at r where the total dersity is 5J + ft and F (£ ) correspond to those for separated nuclei. The free energy density is evaluated in the Extended-Thomas-Fermi approxi- mation3. The conservative force between the hot V colliding nuclei is given by -(^ F/3R)T . The equations of motion and the dissi.. ative forces ars taken as in ref. 1. The calculations h^ve bs-en performed under forzen density approxima- tion with spherical shapes for the interacting ion s» 217 The calculated results are displayed in the accompanying figure for the system MJa + ^Ca. The solid line is the result with the inclusion of • the temperature effect and the dashed curve rep- resents the result without it. It is seen that the fusion cross-section vanishes at incident en- ergies above 25 MeV/A which appears to be a litt- le low compared to the experimental value. This nc_y be attributed to the neglect of the pre-equi- libriuni particle emission which will lower the effective temperature and this effect has been neglected here. References : 1. J.R. Birkelund et al, Phys. Rep. 56 (1979) 107 2. J.N. De and ¥. Stocker, Phys. Rev.C(in Press) 3. M. Brack et al., Phyc. Rep. 123 (1985) 275 1000 - 1:500 c •M-I 218 A SIHPLE WO-CHANNEL BARRIER PENETRATION MODEL OF HEAVY ION FUSION Zafar Ahmed, NUCLEAR PHYSICS DIVISION, B.A.R.C, 13OM13AY -85 The limitations of the one-dimensional barrier penetration model have been remedied in the theory of many coupled channels [1]. Incorporating the internal degrees of freedom of colliding nuclei, the anomalous fusion rates were successfully interpreted below the Coulomb barrier. The penetration through many coupled channels also contains the earlier prescriptions as special cases. The present work looks through the possibility of simulating the fusion rates (below and above the coulomb threshold) by using aiv amenable two-channel barrier penetration model, where the strength of the coupling is aade energy dependent. These channels do not represent the vibrational or rotational levels of the colliding nuclei; instead it is hoped that this model would simulate the effects of the nuclear structure and the nucleon transfers in a gross but simple way. This modtl constitutes yet another interesting realization of the energy dependence of the fusion interaction much argued [1-3], and demonstrated recently [4]. It needi- to be emphasised that the famous parabolic barrier and the Morse barrier [6] are suitable one-dimensional models. However, owing to the asymptotic behaviour of their wavefunctions the use of these potentials is prohibitive in the frame work of coupled channels . We shall therefore make use of the Eckart barrier (V=sech x) [5] to model another one-dimensional fusion interaction barrier as V, (r) = (V +D )sech x, with D =(n /2m)l(l+1)/r , x=(r-r )/a, a =2V /mm (in tune with hw of Hill-Wheeler). This model admits analytic penetration factor and exclusively realizes the 1-dependent curvature of the top of the barrier: iiiu =W(h /2mrQ ) Ch"u)/4V J1 (1+1). For two channels we use V (r)=(V +D )sech2(x); V (r,E)=V (1-Tanh (aE/V ))sech2(x) ,V (r,E)=V (r,E), V (r)=(V +V,+D )sech2x. V ,u and V, are three more parameters added to the usual one-dimensional models. Using the Gauss hypergeometric functions [5] and the properties of the gamma functions we obtain o",= (Tr/k )X_ (21 + 1) (cos H T_ +sin HT ) where 1 2 T+=1/(1+exp2n(/(V+/A)-/(E//\)), 8-( 1/2)tan" (2Vc+ (E)/Vd), A=(L) /-1Vo , 2 2 2 f (E) = 1-Tanh(«E/VQ), V+ is given liy V =VQ H.)Q + ( 1/2) (Vd + /(Vd +4Vr f )) 219 We hope t.hat. the formula pre>- nted hcie will be helpful in systematization of the fusion data ^oth below and ahove the Coulomb barrier. Regarding its general applicability ami iis predictions of the spin distributions, work is in progress. However, we present four s££Ple£ of our fits viz.- r°Ar, 22Sn), (IS6, Pb), (i8Ni, Ni) and ( Ni, Ni)^ Wherein we have used the values of V , hm and r from the earlier works and varied u,V ,V to accomplish agreement with the experimental data. Finally it may be noted that the search of the parameters(u,V and V^) is essentially to simulate a suitable energy dependence of the Fusion interaction. .£ would like to thank A.K.Nohanty, Suryanarayana(SVSS), Dr.S.K.Kataria and A.Navin for useful information, suggestions and encouragement. [1J-C.H.Dasso et al. Nucl. Phys. A432 (1985) 495 see also the refs. therein. [2]-M.A.Nagara.;an and G.R.Satchler Phys. Lett. 1986) D173 29 [3]-V.S.Rainamurthy et al. Phys. Rev. C41 (1990) 2702. [4]-A.K.Mohanty et al Phys. Rev. Lett. 65 (1990) 1097. [5]-C.Eckart Phys. Rev. 35 (1930) 1303. [6]-Z.Ahmed Phys. Lett. A (submitted) (1990).[7]- W.Reisdorf et al. Nucl. Phys. A438 (1985) 212. [8]-F.Viderbaek et al. Phys. Rev. C15 (1977) 954. [9]~H.Beckerjnan et al. Phys. Rev. C23 (1901) 1581. [10]-M.Deckerman et al. Phys. Rev. C25 (19Ji2) 037. 10' 40 125 Ar+ 3n(7) 16 +20a V =107.83 MeW O Pb (8) R°= 11.29 fm V = 76.3 MeV R°= 12.25 £m hw= 4.0 MeV hw= 4.0 MeV <<= 1.8 <*.= 1.0 Vc=104 V = 10 MeV YJ LpJ 120 140 _1OJ (10) vHi V (9) VQ= 96.0 MeV + 0 /V= 97.9 MeV Ro= 8.20 fm 10 Ro= 8.30 fm hw= 4.0 MeV = 1.0 *= 1.3 Vc'=~14 MeV, VJ = VQ= 13 MeV,V,/=o 100 105 B7.4 95.0 102.5 2^0 DATA AHAUSIS OP ^Za (20.1 MeV/u) + 9Be REACTION 7ECC-RIKEN COLLABORATION Introduction : The projectile fragmentation reaction, and the transfer reaction with medium energy heavy-ions have been proved to be very useful for producing exotic species on both aides of the P -stability line /i/. In this article we will discuss the preliminary analysis of 20.1 MeV/u 64- 2a + 9-Be reaction. Our aim was to look for new isotopes around Z=JO, especially the heavy mirror nuclei like 61-Ga, 63-Ge, 65-As etc.. Experiment : The experiment was carried out in RRC, RIKEN, JAPAN. A 17«2 mg/sq. cm Be foil was used as target. The RIKM Projectile Fragment Separator (RIPS) /2/ was used to filter out undesired reaction products to the extent possible and to separate the projectile from the react •'.on products. The maximum available energy of 64-Zn beam was 20.1 MeV/uo This gave rise to the problem of multiple charge states (including the fully stripped one) of all the species. This did not allow the use of achroma- tic energy degrader in the intermediate focal plane and the RIPS was operated in the dispersive mode with only + 0.5$ rigidity acceptance. A gasAE detector, a position sensitive silicon detector and a parallel plate avalanche counter were used for the determination of AE, E and T.O.F. A wedge shaped target (Al) was used to select the beam in identical condition for calibration of various 2-d and 1-d plots. The identification consists of generating 2-d T.O.F. vs B plots after Z selection from 2-dAE-E plots (Fig.1). For nuclei which are produced in small quantities further 1-d projections of the selected portions in T.O.F. vs E plot were generated to look for possible peak structure in the A spectrum. This way we already confirmed tiie existen- ce of several Cu, Zn, Ga and Ge isotopes. The identifica- tion of 61-Ga, 63-Ge and 65-As which are expected to get produced with very 3mall cross-section are yet to be con- firmed although the preliminary data analysis shows encour- aging trends. A complete analysis will be ready very soon. • P. 2 221 Acknowledgement : We acknowledge Br, Bikash Slnha, Director, VECC, for initiating the collaboration* Wo also sincerely acknowledge ftrpf, I. Tanihata of HIKEW for pro- viding us financial support and for active collaboration*! References s /1/ M. Langevin et al Nad, Phys.; A 455, 149 (66) /2/ T. E*bo et al BIKEU-AF-HP-63 (1989) RUN 0029 START -> 19:31:46 ST0P -» 19:32:19 «] OE-E . 2 _5_ j.4_ J5 79 19L 240- 180,- IPO - •S) —I I—) 240 I PSSf) 222 niSJMTKGRATlQM Of MSAfT HTPEBMUCLEi. I.Oosvami Physics Dipt. ,goalpara Collsg*,0oalpara-7831O1, <* T. D*Gasvaml, Physics Dmpt.,9auhatt CTniver*tty,Gauhatl-781014* Mypernuclei,th9 bound states consisting sf nucleons and hyperoas,constitute a distinct class sf nuclear species. A large fraction of the lastbda hyperona produced during high energy interactions remains tra^fsd tn*td* the excited target nuelsUTns lambda hyperon$ survive long enough inside these sxcitmd nuc.'ri and a large number of then are emitted along vlth *.he heavy fragments in which they art trapped* T,'i<,'3# heaoi, hypernuclet decay predominantly rtQn-mesoni£i...ly releasing a large amount of energy. This causes secondary stars in nuclear emulsion. The presence of 2&moda hyperc,13 tnstce nuclei may cause 4gf to shrink the nuclear core. There nay be certain changes in surface tension /// also, la auch it becomes interest ing to study the disintegrations of hypsrnuelei by eihisaton of heavy fragments. A stack »f phoionucl'sar emulsion exposed t» 1.8 defjc jT"eegor^ (flux - about 2J.lCrl~ per s^.csuj has been uaec t*> study the disintegrations! 9f Ag,ir nuclei (Sh> 7,Sh = Ao. of heavily ionieiny tracKa) under high, magnificat in ( 7875±-oll t&merslcn ojjectioejto detect the presence of the associated heavy hypernu- dear decay stars by eliminating baeh-ground events, some of that experimental results era presented in table J Table J t Experimental Be suits Eotnt Stars events Production classification scrutinised oblained C.S. (P.h ) (mbJ Mil 25,000 238 1. 10 1.33 +0.07 ±0.09 £ M M 45,000 7 15.02 0.02 +0.01 ±0,01 r A i 45,ooo 55 "0.12 0,15 +C.Q2 ±0.02 MUM 60,000 12 0.06 0,07 ±0.02 ±0.02 223 M B ti z*~ The heavy hypernuclei having charge, mass, szoment® and mechanisu of emission similar t© tao&a of spoliation rastdues/2/ are classified as R 3 S. S M 3 g" Tho heavy hypernuclsi having chsrgo, mass, ao&snta and utchanisn &f emission similar £© those of short heavy fragment* /J/ are clo- elaeaifled aa S a 3, FoMvi ;=» Tho avQ&ts iffith e, p&if ©/ fcespy fr®QB*nte chargeaaa8$ moiz&nta sad mechanise &f Qnteston similar io those 9/ fission events 14} except that on« e/ the frej&entt contain* a lanMa hypa^on are classified an r s jr. £1 ti 3 .'- Thess G&onts ar-a similar to those ef MultiJ'regnentatton aoents /$/ in ra&pect of charge,XQSS moaanta and a*cAcntia of eaiesion »/ fragment*. In addition to iHis,on* of th& fragments contains a lambda hypercn* The investigation shows that the existence of lanbda hyperone inside the excited target nucleus d&oo not prevent the nucleus to disintegrate by anu •/ the process (under investigation; •/ eaixeto* of heavy fragments* /f/4.S. Bychkoo £?. Mue2. phye 40 (1984) 259 2S(B) (t965) XO £»9esma*i I T.C.(fo9mami0 Pros (DAE) Symp JneJ. pkj,: JO (B) (1967)106 i S T.D*9ossami, Proc (DAK) *V»P MucJ.Phy 32 (B) (1*89) P*7 /5/ £»9o*vamt 224 •TO-/ .':. ?3MLi SIC r:;!S & ap ysies -9ttyt0*u- 78107 4. Dunn ; •igh snergy interactions all of the highly rutc:. disintegrate £y omitting particles and -{? •:>/ these highly excited nuclei eventually p •orfa<*Lx.g a pair of ieavy fragments each — mostly due fusion /}'32/* Most of such binary Ciitlalo- -us are Ilk* < is occur Iste In the de~excttatlon chain of the high2 «.rcited, thermaliJted target nuclei* It has &lS9 seen ®::- i-Sfc that most of the excitation energy 9f the hlghJ. 'jzeiSed fissioning target nucleus4mmm ts voso&ed ey : .per&tton of particles prior to scission. fftus it bee ;• interesting to study the high energy fission er?o- •,'\i using photonuclear emulsion detector* Because, tk Kotonuclaar emulsion 1$ a three dimension -al visual •*CfcGJ% in afhlch events due to nuclear distntegret s my *e scrutinised in'ivldually* Tito sizclia of photonuclear emulsion exposed to 1*8 s Qsf/c I" •«.•-•;!«a (flux - about 2110 X" per *** CJU> and SO 9*t/§ prcians (flux - about 5X10* proton per sq* cm.) ha*+ keen ua*€ to study the disintegrations •/ Ag,Br nuclei (S-> 70 $h « !•• of heavily Ionising tracks) associated aish a pair of tracks due to heavy fragments mhieh are likely «u« to fission*40,000 disintegration stars from £" stack and 5,000 disintegration stats from stack have bsen scrutinised un*sr high magnification f 1975 I - oil Immersion objective)* After necessary corrections for loss of events, the results are summarised tn table I* Table J i Sxpertmental results. Particulars s.,9 ds7/e t" 20 lief I o p Stars scrutinised 40,000 5,000 Svenfs obtained 1,203 . 177 Freqve*cy(corrected) ?»C. 6,04+0*13 7*0890.54 Cross-secttonlCorrected) mb 7.31+0.22 21.5~§+1.65 Mean value of .Vj. 1}. 27+0.14 15.34+0.31 Av.Sz* energy (M*f)appr. 450 485 " fragment Charge (2) appr. 6 to 17 6 to 17 ?ragr>*nt aass (li appr* 11 to 40 ft to 40 fragment 7elacify( tn cjappr. 0.048 0.050 Tf& ratio of fragments 1.16+0.04 l»19+p*13 Forward velocity of the preflsston nuclei (tn c) appr* 0*004 0*004 The mass of the fission fragments may be lower than half the mass of the target because the profloslon nuclei are formed aftsr evaporation of a number of particles. 225 From Pig 1 it may be observed that vtth the increase of excitation energy to about 500 Met, the frequency of fission events also goes on increasing gradually. O Also,it may be seen that the frequency for fission z of a nickel like prefragment Is about @% a! /2/.Thls is in confor- mity totth the earlier 0.0 observations /J/. For disintegration of a nucleus theruattxed ftgm t : Percentage of after acquiring more preftsston nuclei excitation energy than formed at different Mh higher N. value and also a lighter residue. For lighter residues tne fission berr- ler heights are expected to be loser* But as seen from Fig 1, the frequency of fission decreases at higher 3. values* This may be due to the following : (I) The processes like mulilfragmentatlon and vaporisa- tion may become Increasingly Important, Such processes do not bear signatures of equilibrium decay, (it) Some of the residues nay be lt&ht enough and the pairs of heavy fragn-azts ars not produced, or (itl) a combtnacion of (t) and (it) aoooe. This leads to a belief that even by icjuirlr.g cr. excttatlon energy of about 500 Me? (Carres so,id Ing nuclear temperature of a£o«c 7 Me'/.1, most of the Ag,3r nuclei undergo e^utltbrtma decay ay evaporating particles znd fragments* Some of these evaporation residues ultimately dtstntograte by fission, /// K.Gosuaxl and T,D,Gosaaai Proc (DAS) symp .V':;ci, phys 3<(3)C 1939)P. 7 /«?/ K*Go3wamt and T.D.Goswaal. Gau-'iatt Onto. J.Sci* (to appear) /J/ T.C.jtwes et al Reo.Lett.55 (1985) 1062. 226 ANALYSIS OF PARilCLE PRODUCTION IN THE SPALLATION REACTION Amar Sinha and M. Srinivasan Neutron Physics Division Dhabha Atomic Research Centre Trombay,Bombay-400 085 In connection with our work on the application of spallation neutron sources for the simulation of radiation damage in fusion reactor structural materials we have carried out a detailed analysis of the particle production characteristics and cross- sections at medium energies for production of helium,transmutation products etc in the spallation of lead and some structural elements such as Fe-56,Cr-52 etc.We will discuss in this paper the methods applied and present some of the representative results. We have used Intra Nuclear Cascade Evaporation (INCE) model to treat nuclear interaction beyond 50 MeV.This model treats nonelastic interaction of high energy hadrons with complex nuclei.A key feature of. this model is that at sufficiently high energies,the initial phase of the reaction can be treated in terms of collisions of incident particles with individual nucleons inside the nucleus.The struck nucleon can cause further collisions .giving rise to a "particle" cascade inside the nucleus.After the intranuclear cascade,the nucleus is left in an excited state, and the subsequent deexcitation is determined using evaporation model.A montecarlo approach is adopted to incorporate this model into calculational sci. *o . Results and Discussion: Table 1. gives yields of neutrons,protons,mesons and various other quantities in the spallation of lead at incident proton energies of 50 MeV to 3000 MeV. it also lists interaction cross-section at these energies.lt is to be noted that the inelastic cross-section first decreases and then increases from E=300 MeV onwards.lt is due to the openinig of pion channel around this energy.There are marked differences in the yields of neutrons and protons as well as in the mean energies of emission of neutrons and protons.Fig.1 depicts helium production cross-section for Fe-56 and Cr-52 and fig. 2 depicts transmutation product cross-section for Fe-56 at: 600 MeV.It is to be noted from fig. 1 that helium production cross-section increases by a factor of three when incident particle energy increases from 50 to fiOO MeV. References: 1. Sinha A. :Nucl. Inst. Meth. A274 (1989) 5fi.V>67 227 M/)i f 1 vino /wo HHAH rm.not np FMUIED PARTICIC in in-inr M1GK1 }1VU NtU flIW KESCWJ e 1MB) HELD ENERGY rlELD 0 r HS-3 HB-4 HEV IHELAirtC CAS CAS HfAH CAS £•AT CJ>S WfA« 1 a- SO 1*32 0 33 .01 3T.a 22. a 0 . 7 3. 0 12? 3.7 - - - too 7713 0 43 O.3 49. t 31 0 1. t 4. 3 70 3 (TO - - - .04 .01 300 tsar 0 g 0.7 si *3 .0 t. 9 4.1 J3 - - - .2 .097 — .3 400 1»03 1 1 0.* 11* 71 2 .4 7. f 33 IS 02 .03 .0(4 .32 .ia .Di 0.0 COO 1710 1..37 1.30 13» 73 3 . 1 B. .1 37 18 a. 1 0. I .05 .a .3 .04 .# 1000 172$ 1.a 2. 19 4 s 10. S 0 .2 0.2 0. M 1.2 0.7 0. 13 1.0 taoo 1?30 2. 2.B « 0 If. fl 0 .28 0.3, 0.27 1.3 0.47 0.31 2.4 2000 I7«3 2. 7 3.« 7 4 fj. 4 0 .37 0.42 0.3? 2.8 (.27 0.B3 2.8 2300 17 ta 3. i 4.2 8 s 14. 0 .43 0.52 cm 3.0 J.94 0.77 2.at 3000 1733 3. 4 •» » 5 fl |9 j 0 .34 0.81 0.63 3.6 1.7B O.»5 3 23 H0JE-.1. - 1H01CA1E3 VALUES ME NEGLIGIfllE 2. lie PLANK PLACES IH HE Mflif IHDIC*1£S THAT THESE VALUES NOT evALUAlEO. 3. CAS :CASCAX EVAPfYAPORATIOH 4. ALL EN6RSIE3 ARE IN «£V cen',5 sic I |»H iri ' 400 3UU •ji. INCIUtNl riLUllluri tflkMU* 228 c) NUCLEAR MATTER AND NUCLEAR COSMOHflfSICS APPLICATION OF THOMAS-FERMI THEORY FOR FINITE SYSTEMS V.S.Uma Maheswari, V.S.Ramamiurthy and L.Satpathy Institute of Physics, Bhubaneswar, India The disagreement between the Droplet Model(DM) and Hartree- Fock(HF) predictions for the central compression variable ^- = fc°~^°°) l 3 versus A~ t } where p^, p0 are saturation densities for nuclear mat- ter and finite nuclei respectively, is a longstanding problem1. The DM predicts an monotonic increase in p0 with decrease in A, whereas HF results2 shows a "(down-turn" in •& over low and medium mass regions. The extended Thomas Fermi (ETF) calculations within the leptoder- mous framework overestimates p0 quite similar to DM prediction. As a way out of this discomfeature, Myers3 et.al., have argued that the leptodermous expansion breaks down for medium and low mass regions and there should be an exponential term of non- leptodermous origin in the mass formula, which they have adopted in a very phenomenological manner. In this work, we show that within the leptodermous framework, one can explain the trend of BF results by correct enumeration of quantum states, which is not properly accounted for in the TF theory, when ap- plied to finite systems. It is a universal fact that in a finite system, the single particle states does not start from zero kinectic energy value. There is always a lower bound to the spectrum4. Thus it is imperative to have a lower limit to the momentum Km, of the single particle spec- trum while applying TF theory to finite systems. Consider a nucleus of A Fermions, being described by a finite square well potential, Km is approximately given by ^, where R is the size of the system. We there- fore propose a first order refinement to the TF expressions for density and kinectic energy density as given below. Pi ~ Then TF calculations are done for a symmetric system, using Skm force, neglecting the coulomb effects. This is done by using energy density 229 funcfcional(EDF) formalism, where the total energy is given by = / subject to particle number conservation and parametrising the density as a Fermi-like distribution function. Then p0 is obtained by minimising E with respect to /?, where R and po are connected by Here diffuseness parameter a is taken to be 0.6 consistent with electron scattering measurements. As shown in the Fig, the TF calculations using Km reproduces the average trend of HF results. In the same Fig, the conventional TF and ETF results obtained (without using Km) are also compared with the HF results. The dramatic improvement of the density behaviour for medium and low mass and its near agreement with HF clearly establishes the importance of the correct enumeration of the quantum states. It must be noted that the receipe presented here is of general validity for all finite Fermion systemd. References 1. F.Tondeur et.al., iN'ucl.Phys.A394{ 1983)462-476 2. J.Treiner et.aL,Ann.Phys(NY) 170r 406-453 3. J.Treiner et.al., Nuci.Phys.A452( 1986)93-104 A. S.K.Kataria and V.S.Ramamurthy, DAE Symposium ('980) 230 n ON -EXISTENCE, OF SUPERLUMINGSJTY OP SP£KD OP SOUND IK NUCL£/iR MATTER BcKJ>as and R.K.Satpat^iy Sambalpur university Jyotivihar, Burla-768019 Recently,using zero-range Skyrme interaction Osnes and Strottman1 and Su-et'al have found that the velocity of sound in nuclear matter violates the causal constraints v The relation for the speed of sound for an arbitrary density and temperature in symmetric system is given by where the prime denotes /4f and I is the thermal energy per nucleon.For a non-relativistic Fermi gas, b is defined as Since the potential energy term contains error 231 function,for sack of convenience of differentiation the equn(l) is parametrised in a power series as E.-"rTf + f where Here a1# a2,a3,b1#b2,b3 are constants and«(=o . Observation and Conclusion; Using equations (1) to (6) we calculate the values of the speed of sound in symmetric nuclear matter at thermal energy lOOMev.The results are shown in the following table along with the results of Ref.i with Skyrme force (SK) Set-ill. Velocity of sound in nuclear matter 2 f/ V for nuclear matter SEI MSK SK i 0.197 0.126 0.206 2 0.290 0.233 0.459 3 0.379 0.367 0.770 3.8 — — 1.006 5 0.556 0.6 30 — 7 0.742 0.8 38 9.2 1.0 36 1.0006 — It is found that in nuclear matter v becomes super luminous at fz. *)-2-Po for both SEI and MSK; unlike with (SK) set-ill which is at f«3-8fo as reported in Ref.l.Similar results are also obtained at other thermal energies.From our above observations we conclude that superluminosity does not Occur in nuclear matter in the normal density region with SEI and MSK which have the correct density dependence unlike the Skyrme force (SK) set-ill.Thus these potentials can be safely used for other nuclear calculations without any modifications. 1. £.0snes and D.otrottman,phy,I 232 QllATtK - AtJTIgUARK BOUND STATED ' A.K.Gnutsm Physics Department, R.B.S.Cl >u. inn the past two decades, the colliding boam experim •KI (i) have resulted the production of a number s fv-'Irons and lrptons. The potential models are fou. ^2) to be successful in explaining the haciron 'roctroscopy. It is considered tfv>t, the quarks .rich are the constituents of hndrons aossor.r, tvio important proportii?^, one is of c^nCipprient ivhile, the othe; is of --.symptotic freedom. The forces '.vhich confine • c quarks ore independent on qurirk speci-os. At shor' Nistincos the potential ic of coulo'nbic type while a., lone <; ist.^ncos, the potential is of lino^r type. -m?nic oscillator potential yields tho sim- ilar revi,:ts as provided by the linear potential. on'jidcrinq the qupr' 1. 3ch".-itters R.f. ?n'; i>trauch K. Ann. <'«ev. :'u •ici. ~,h, ^9 (197;J), lieports of UbOV, CUrW, i 2. Is.T.j J.ii. .->no 3chnit.?Rr I-I.J. U12, ?4i (lO'/O) V 'rid !iVl--»sa A I.'-l", ?-167 ) ?ih? JL Lett. ":-'•., 71 2 (1979). 233 .9OX1O"6 .BOxlO"6 .70x10"* 45 G«V 47 G»V .6OX1O"6 49 G«V ..SOxlO"6 .40X10"6 • 3OX1CT6 . 20x10"* . lOxlO"6 n-A Toponiuu mass Stat«(n) ~ FIGURE i 234 HOT NUCLEAR MATfER IN A CHIRALJL.Y INVARI-^T i-SRHIONIC Fli TKiSORY Safayet kariin Chowohury and Sasabindu Sarkar Department of Tneoretical Physics, Indian Association for the Cultivation of Science, Calcutta - 700 032. .ve use a chiral field theory for nuclear snatter purely based on fermionic field to investigate the nucleon-antinucleon plasma at high' tempera- tures. Previously this phenomenon has been investigated using the famous meson field theorie (1 - 2). However in this novel approach, a chir- ally invariant model containing only ferniionic degrees of freedom without any meson fields, is considered. The most simple lagrangian used in this model for saturating nuclear matter is given pjflJ (V Now a non (Jvanishin - g density dependent effectiv- -•e mas(Vs of the nucleon can be obtained from the above lagrangian by applying the Hambu-Jona-Lasinio symmetry breaking mechanism (4). The resulting self-consistency relation for this mass at a finite temperature T is analogous to the gap equation in the B . C. 3. theory and is given W 235 n^ and n_, are Fermi distribution functions for particle and anti-particle. For calculations the model uses a three momentum cutoff parameter /\ . For given cutoff /\ t the coupling constant g is uniquely determined by fitting the free nucleon mass at K_, = 0. Now solving equation (2) for nucleon-antinucleon plasma for which )) = 0/ a phase transition corresponding to a sudden drop in m* is obtained around 125 MeV. References • — 1. J. Iheis et al, Phys. Rev. D 28, 2286(1983) 2. 3. Sarlcar, S. Niyogi and s. K. Chowdhury Phys. Rev. D32, 1323(1986) 3. V. Koch, T.5. Biro, J. Kunz and U. Mosel, Giessen preprint UGI 86-3. 236 d) INTERMEDIATE ENERGY NUCLEAR REACTIONS AND NON-NUCLEONIC DEGREES OF FREEDOM N-N SCATTERING WITH COGEP K.B.Vijayakumar and S.B.Khadkikar Physical Research Laboratory Ahmedabad. We have investigated the effect of exchange of confined gluons (COGEP) among relativistically confined quarks in nucleon-nucleon (N-N) scattering calculations. In RHM 111 the Dirac wave function itp) is expressed in terms of the two-component spinors x an<3 A .A + (1) The COGEP is obtained using confined gluon propagators. The confined gluon propagators are derived in the CCM 121. The central part of COGEP in the static limit is 4 3 a N A .A • D ( r) + 1 t. s 0 (4n I -C r D (?l') ( 1- 2/ 3cr. 0".) (2) 4 (E+M)' 1 j >' / 1 _ re/ 2 where D. ~ D (1 / 7T ) e r In our model a' (15.01 Mevfm ),E (428.65 MeV), M(160,6 MeV) and b (0.86 fm), are chosen in RHM to give reasonable values for the properties of the nucleon. In eq. (2) c( 1.80 fm ') is fitted in CCM to obtain the glueball spectra. The scattering phase-shifcs (PS) are calculated using Kohn-Hulten-Kato variational principle/3/. We obtained good agreemment with the experimental PS for 'S P P with a =2.8 (Figs.1,2 ar.d 3). For S results are in agreement with /4/ without censor forces ( Fig. 4) . We have plotted the diagonal kernels of the adiabatic N-N potential ( V ) in the Born-Oppenhamer approximation for both S and P against relative distance (R) between the nucleons (Figs.5 and 6). For Sn the adiabatic potential has a qualitative similarity to a 'typical' N-N potential, with 237 a short-range repulsion and an intermediate range attraction. For P the potential i:: totally repulsive, as expected the PS arei negative. The significant repulsion in the potential for P at short distance arises from the centrifugal barrier. /I/ S.B.Khadkikar and S.K.Gupta,Phys.Lett.124B (1983) 523. 121 S.B.Khadkikar and P.C.Vinod Kumar,Pramana 29 (1987) 39 /3/ M.Kamimura, Supp.of the Prog.of Theor.Phys.62(1977)236 /4/ K.Brauer et al, Nucl Phys.B253 (1990) 308 I to IIOO •000 tco • I ' •00 \ TOO \ •00 \ 900 I 400 - \ (OO - \ too - \ 100 a0 00 OS 10 1 5 Z£> 2.5 30 55 4.0 4.9 SO °* I* >» 24 10 « R (FERMI) R (FERMI) 238 FERMI- BREIT INTERACTION AMONG CONFINED QUARKS AND GLUONS. P.C.VinodKumar, K.B.Vijayakumar and S.B.Khadkikar. Physical Research Lab. Ahmedabad. In this report we have obtained confined one gluon exchange potential (COGEP) /I/ among relativistically confined quarks 121. For the confinement of the quarks we have made use of the Relativistic harmonic (RHM) /2/ Lorentz scalar+vector potential which explains the properties of light hadrons. To see the effect of the confinement of gluons on the confined quarks we are making use of the confined gluon proagators. The confined gluon propagator are obtained in tha current confinement model (CCM) /3/ which was developed in the spirit of RHM for the confinement of gluons. In RHM we perform a similarity transformation Uip = x so as to completely eliminate the lower component. The quark wave function ( 2> (E+M) E+M :U= 2 (E+M) (1) 'N= 3E+M cr.P 1 + -o-.P E+M (E+M) E+M Any operator (0) acting on 0 is then transformed to 0 acting on x ° ~^ > ° y ^2^ The COGEP is obtained from the relativistic expression for the "scattering" amplitude" for the quarks 2 ab M . (3, fi ab here ip are the wave functions of the quarks, D = 5 D are the CCM gluon propagators in momentum representation. In CCM the coupled non-linear terms in the equation of motion of a gluon are simulated by a self induced colour current j = 9 A (= m A ) or equivalently an effective mass 239 2 4 2 2 term for all the gluons with m =c i -2c 8 . The equations 2 of moton: DA +m A =0 are easily easily solved by using harmonic oscillator modes in the gauge d A =C. The consistency of 3 A =0 and 9 j s 5 (m A ) =0 imposes a secondary gauge condition : ( V A +c r.A)= a.A termed oscillator gauge', where a is the usual harmonic oscillator annihilation operator. The complete propagators D (r) and D (r) are given by D (r)=4nD (r) and 00 0 a a (4) D., (r) 4n i k ik a.a where D and D are given by F -3/2 2 2 T -3/2 2 2 3/4 Cjcr) W (c r ) 1/4 c(cr) W (c r ) ; C 3/2 (47T) (471) (5) where W s are Whittaker functions ( e ). Using eq ^3) M becomes . 4 + + ~ N (6; fl r- X. X. U(P.,P.,q> x. X. A. .A., By taking thi e Fourie] r 13131transform of ; each term potential operator in the coordinate space is obtained. The central part of COGEP in the static limit is a N A .A D 1 4 ? (4n6(r;-c r' D (ri)(l-2/3cr . cr) (7) 4~ (E+M) In addition to the above interaction, the full COGEP has the usual tensor, Darwin and orbit-orbit terms. We have used the above potential to investigate the nucleon-nucleon interaction. Ill A.De Rujula et al Phys.Rev.D12 (1975) 147. Ill S .B. Khadkikar and S.K.Gupta, Phys . l-.-t t . 124B (1 9ri 3 ) V?.! . 13/ S. B. Khadkikar and P.C.Vinod kurnar, .-camana 29 (1937) 39 240 E2-'M1 RATIO FOR A->N + ^ IN A CHI RAL QUARK MODEL B. Ghosh and S. C. Phatak Institute of Ph-/si cs . Bhubaneswar-751 OO5 The ratio V. of E2 to Ml transition amplitudes CR = 'MyjMl|A:O has been observed *o be nonzeroC R = - O. V<, to -1 . 8%[ 1 ] 5 whereas any quark model in which nuc 1-: :>n and delta states are constructed by putting three quarks in S orbitals yields R=0. Attempts such as the D-state admixture induced by tensor component. of colour hyper fine- interaciiori between quaiks[2] and reiativistic recoil corrections!! 1 ] ,;ave yielded nonzero but small values of R. In the present work, we have evaluated R in a chiral quark .'Model including the coupling of the pion to the photon.The transition matrix element for A-^N + v' is given by m I JC ^ IA • ft ••£L-~ .3/2 /=— NN where jCx) is the transition current operator, m and m are the spin projections of delta and nucleon respectively. In the above expression we have assumed that the emitted photon has momentum q along the z-axis and has positive helicity. One can calculate Ml and E2 amplitudes directly. However, it is convenj ent to express the ratio R as R = C A -V3 A 3/CV3~ A +A D C2D 3-'2 1 '2 3/2 i/2 where A CA j is the transition amplitude when m =3-'2'.'1 • 2Z) . The transition current operator is JCXJ = i (.x.i + l C xl> =e v '.>:)<•«/' (x^ Helrf- ! x)V(Kx.i~'W x.Wii Cx)] C 3".> where >/< c :< ) ari'l >p<. :•:?> .-u e quark and pion field operators respectively. The calculation of the quark par* of th'."* •• i "irr". I t l on in^.'• r ' :•; ••'lenient oji -/es 241 /2mVIl - /2 where gCrO and fCrl) "'.re t h^ upper and i 'jw components 1 Z T^=<3/2tAl /2-t..|3/2N 1 CC2S +1DC2T X c c C=N,A o "2C +W k ' C1 L -.k . D C -*£ D C -C 1 C O. 5k 4< 3/2m 1 j 3/21 /21 1 > qC X'VC 1 3/211 /2; S 1}} +<< 3/2m32m. .1 /2m 1 /221 > C k C A N x C 0. 1/2 x+O. 5C 1 - xWC 13/211 /•" -Jl) c where M =fj -M and k ' •-=-(. >," ' A8 A B model calculation with b.= q = -O.3K"<. Further wnrl- : n p,- -.-:jr e". : C1JJ. Bi ^nkowska -?Lal. Piv i .-.-.].' Lv_.y ,rid M. i't'V. Phy-: 242 A LOWER LIMIT OF g^ FROM NRQM R. Nag, S. Sanyal and SM. Mukherjee Department o-f Physics, Banaras Hindu Univ., Varanasi-221 005 The , vasurement of the integrated spin structure f_i. i-rtion of the proton, g^ , by the EMC group /I/ remains an unsolved problem. In the present work we obtain a lower limit of g^ ,in the •framework o-F non-relat ivist ic quark model (NRQM) and using the experimental value of 6^ /Gy as an i np ut . The quantity, g ^ 5 is measured from the asym- metry, A, which is defined as A = (dcrrjr - dtr ) / (dcr1^ + do**1" > (1) This, in turn, can be related to the virtual photon-nucleon asymmetries At and A2 : A = D (A, + ^ A2 ) (E) D and sre kinematical factors. Also, positivity demands that }A,l N< 1 and JA^J v< R where R is R = cL &T and is quite small in the energy range of the EMC experiment. Thus . is defined in terms of A^ alone as ) = F« A. /2 x ( 1 + R ) (3) X and g is : g ^ = l g. In NRQM we write the total wavp+unction (WM of the proton as : •x s sre the unperturbed WF of symmetric, mixed- symmetric etc. types and 6^ « ars the corresponding expansion coefficients. The operators for g^ and GA / Gv do not depend upon the space part of the WF explicitIv. Hence, their expectation values can be expressed in terms of the G L aLo r WWritint g P £ (( G )) etct . 243 g^ = ( 5 F^ +3 P^s - 3 Pfi )/13 (6) The normalization condition gives: + P* (3) Other excited states have been ignored since their contribution is very small. Since P^ etc. are probabilities, they must be greater than or equal to zero. Solving <£• - S) -for these probabilities we get a lower limit -for g .^ , a-fter inserting the experimental value -for 6^ / Gvy we get g * >; 0.1874 <9> This value should be compared to the EMC value o-f g^ =0.114 + 0.033 Our result is surprising and implies that the basic premise o-f NRQM should be re-examined. /1/J. Ashman et al, Phys. Lett. BSOfe, 3fc4 (19SS). 244 DISTORTION EFFECTS IN (p, A,++) REACTION Nee lima G. Kelkar and B.K. Jain Nuclear Physics Division, B.A.R.C., Bombay 400 085 Effect of distortion in the continuum waves has been investigated for the (p, A++) reaction using the factorized form of the T-matrix,1* where * is the appropriately symmetrized T -matrix for the elementary pp —* n A*"*" reaction in nuclei. ^ ( w where W , the measure of imaginary part of the potential is Here j denotes proton or A++. Following the pro- cedure used in ref.(2) the real and imaginary parts of the potentials for the present calculations are given in Table 1. Using relativistic and non-relativistic expre- ssions1' for T , the missing mass spectra, &f/dCA&''} for a lp shell nucleon with the kinematics of mass 16 nucleus are shown in fig.l. Compared to our earlier plane wave results*', we find that the 245 present results are similar in shape. Main effect of the distortion is the reduction in magnitude. >The reduction factors at various energies are listed in Table 1 In'fig.2 we show $(*•*} (- 5@*&*0/Jb')<&*) using plane wave and distorted wave prescriptions. Multi- plication of this factor with the mass distribution the A++ gives da~/dC-XA.*O. Table 1 Incident Wp VA (MeV) (MeV) (MeV) (MeV) 400 -33.05 -38.88 -9.16 -30.04 10.7 500 -27.5 -56.0 -4.64 -37.25 11.7 800 -12.0 -83.32 4.29 -46.27 10.6 1000 6.85 -93.77 5.03 -45.05 8.8 3000 33.15 •110.5 11.57 -38.58 4.9 REKCKE) P W.B.A. NON-REL(O> 10 O.W B* (US Tp(G«) 5 2 ' ^> So« > a r°r 1 I \ 3 • as N £ • 10 ^V ^—A N. X o' 1 fa Vv — 1 / X \ 1 "^id* _ 3 / h \\ K // 2 0.15 1 1 / \ fc>r b \' XI r /'/ \ 01 » \ \ \ -r -n' /V ' \\ 'x\ ^\ 005 'l 1 1 tWO HO DOO BSO 1300 D50 1100 1150 1200 I2S0 1300 1)50 K00 Ho. 2. 1. B.K.Jain, N.G.Kelkar and J.T,Londergan, Phys. RevcC submitted. 2. Hashima liasan and B.K.Jain, Phys.Rev.C33,1020 (1986) 246 MULTIFRAGMENTATION VERSUS LIQUID-GAS PHASE TRANSITION IN NUCLEAR SYSTEMS A. Das, M. Mishra, L. Satpathy Institute of Physics,Bhubaneswar-751005 and M. Satpathy Physics Department,Utkal University,Bhubaneswar-751004 In recent years, the liquid-gas phase transition (LGPT) in nuclear systems and the nuliifragmentation(MF) phenomena associated with disassembly of hot nuclei are subjects of intense interest. It is expected that the data on MF will carry the signature of LGPT. The Purdue- Fermilab1 experiments en p+Kr and p-fXe reactions have aroused the hope of such a sjp.-iture, which has not been fully established yet. Two areas of yfcudies have been carried out in this field. The first area of study questions the possibility of occurence of LGPT in nuclear systems, which has been examined by many authors in the frame work of temperature dependent Eatree-Fock(TDHF) theory employing nucleon- nucleon interaction. These studies seem to suggest that the limiting temperature Tum for finite nuclei is about 6 MeV^. In the second area of study, one tries to describe ilie MF data of different heavy-ion reactions carried out in the laboratories. Using various models, one can explain the mass yield distribution, isotopic yield and kinetic energy spectrum observed in the experiments. The theoretical frame work is mainly based on statistical mechanics in which the excited target decays into various fragments governed by the availability of phase space in various channels. In such studies it has been found that there is a critical temperature 3 Tc of about 7 MeV at which the nucleus favours to decay into various small fragments. This temperature Tc is also called as a phase transition temperature. The unresolved problems in this field is whether the two temperatures are distinctly different or related. Recently we have made some improvements in the MF model4, by taking both the Coulomb and the nuclear interactions amongst the frag- ments. We have shown that by taking nuclear interaction the temper- ature comes down to a realistic value of 6 MeV in p+Kr and p+Xe reactions. We have now applied this new model to study how popu- lation of various fragments vary with temperature. The microscopic studies describe a phase transition from nuclear liquid to nucleonic gas 247 consisting of single nucieons. On the other hand, a phase transition in MF phenomena is described by the decay of a nuclear fluid into various small fragments with mass number A/ < 4. Thus by studying the de- pendence of population of various fragments on temperature, we hope to relate these two temperatures: the Tum from microscopic studies to the Tc from MF phenomena. Using improved MF model, we have done the calculations for 63C7«29 83 and /fr36 systems for temperatures in the range of 5-20 MeV and cal- culated the fraction f of the total yield which constitutes all light frag- ments upto Af < 4. In Table-1, the values of fraction f as a function of temperature T are presented for p+Cu and p+Kr reactions. It is interesting to see for T=5 MeV, about 65% of the fragments are pure nucieons and light fragments with mass Af < 4. With the rise of tem- perature, this percentage rises above 85%, when T reaches 15 MeV. Thus the phase transition seen in MF phenomena is largely a transition to a nucleonic phase like that of the gas phase of the LGPT. It is ac- companied with smaller components of large fragments which decreases very fast with rise of temperature. Thus there is an underlying unity between these two temperatures. Including the clustering effect in the microscopic TDHF studies, one may hopefully achieve a value of Tum, which will be same as Tc of MF phenomena. Table-1 63 T Ctt29 5 66.112 65.228 10 75.353 74.772 15 85.740 85.468 20 91.708 91.604 References: 1 . J. E. Finn etal, Phys. Rev. Lett. 49, (1982) 1321. 2 . H. R. Jaqaman, Phys. Rev. C39, (1989) 169. 3 . L. Satpathy etal, J. Phys. G14, (1988) L245. 4 . L. Satpathy etal, Phys. Lett. B237, (1990) 181. 248 STUD* OP SBCOIfDARY PARTICLES PRODUCED IN HIGH ENERGY FADRONIC INTERACTIONS H.Khushnood and Ansari A.R. Hitfh Energy Physics Lab,Department of Physics, Jamia Millia Islamia,New Delhi-25. To explain various experimental results on multiparticle production in high energy hadronic interaction,many theo reticalmodels have been pro- posed.In one class of models,the final state is envisaged to be reached instantaneously after the £@ Hi si on, whereas in the other class of models,the particle production is visualised to take place in tw© steps.Piratly,some exited intermediate states, •:ire ball,Nova,,Cluster etc. are generated whicBo subsequently decay into the final state particles. In th@ present study an attempt has been made to compare the experimental values of the aver- age number of charged shower particles in high energy hadron -nucleus interact ion, 249 to be slightly energy dependent in both p-A and i\"-k interactions. The mean normalized multiplicity,RA, has been studied in terms of the created charged particles and has been defined as UJ Tfp* of liH L: ' "V ' ^"lPtlMO »» 1 - p- \ p-m,al«. 11 to 5. •0+0.10 6. It O.it l.es+o .07 . 1- * 11. 5 10.« «. 1«+O,ll • It 0.1* 2.01+0 .01 1 , 11. 5 10 .B» 6. 50+0.10 *. 2S 0.3* 3.03+0 .Of i 14 11 .13 4, S7+0.tl 4. is 0.34 1.07+c .ot «»l 1 I 1 .. 11 .C7 6. 6O+0.10 4. CO 0.1« 1.95+0 .04 50 15 .OS a. 70+0.10 • (4 0.11 1.79+0 .0* 1 67 18 4P 9. 57+0.11 9. 54 0.11 l.«l+0 .07 1 300 31 58 1». 50+0.30 11. 5) 0.11 2.06+0 .01 1*1 • 1 100 ie *>> jB 10^0 30 15. 11 0.11 1.89+0 2| Iif '* 400 44 58 16. 40+0.21 16. 76 0.11 3.U5+0 04 1 1000 70 41 »». 30+1.«P 3«. 36 0.11 1.99^0 31 1 •o* • 10 9 01 5. •0+0.10 3. » 0.10 1.66+0 09 50 14 11 e. 17+0.11 «. 14 0.10 1.7S+0 OS 60 15 59 s. 5«+0.37 «. 15 C.lj l.*3+0 07 100 38 46 n. 00+0.10 11. 14 0.11 1.74+0 09 140 17 99 ti. 18+0.!• o.u 1.69+0. 04 References: 1. T.Aziz and K.Zafar; Prenama,13,81(1979). 2. H.Khushnood et al.; Can.J,Physics(1990) 250 N-N interaction in confinement mode! for QCD. K.B.Vijayakumar. Physical Research Laboratory Ahmedabad. The nucleon-nucleon (N-N) interaction is conventionally explained by the exchange of various mesons. With the advent of deep inelastic scattering experiments confirming the existence of quarks and their colour degrees of freedom, attempts were made to explain the N-N interaction from a more fundamental theory, i:e, Quantum chromo Dynamics (QCD). In M.I.T. bag model and in the non-relativistic-quark model (NRQM) IM confinement of quarks has to be incorporated phenomenologically. These models have incorporated the confinement of quarks, but the effect of confinement of gluons has not been taken into account. In these models the color-magnetic part (CMP) of the Fermi-Breit free one-gluon-exchange potential (OGEP) is responsible for the short-range repulsion and a and % mesons have to used to obtain the bulk of N-N attraction /I/. We have investigated the effect of exchange of confined gluons among relativistically confined quarks in N-N scattering calculations. For the confinement of quarks we are making use of the relativistic harmonic oscillator Lorentz scalar+vector confinement model HI. For the confinement of gluons we have made use of iiie Current Confinement Model (CCM) /3/ developed in the spirit of RHM. The confined gluon propagators (CGP) are derived in the CCM. Making use of the CGP we have obtained confined-one-gluon-exchange potential (COGEP) between the quarks. With the COGEP we have investigated the central-pan of the N-N interaction. In RHM HI the Dirac wave function (\|/) is expressed in terms of the two-component spinors % and <|>, the lower component of y is eliminated by a similarity transformation. The equation of motion for % then satisfies the 'harmonic- oscillator' equation. We have an exactly equivalent non-relativistic Hamiltonian which we can use as in NRQM. The parameters in RHM are chosen to give reasonable values for the root mean square charge radius and the magnetic moments of the nucleon. The parameter in CCM is fitted to obtain glue-ball spectra. The size parameter in RHM is of the order of the physical size of the nucleon (0.86fm). This is also required to obtain the strength of tensor interaction. We have employed the formulation of NRQM based on Resonating Group Method and the phase-shifts (PS) are calculated using the Kohn-Hulthen-Kato variational principle /4/. We obtained goog d agreemmenagreemmeng tt with the experimental PS for ' ' i S ,','P ,an,and PP witwith aa =2.8=2.8.. For S results are in orr iis i agreement with 151 without tensor forces. To understand the nature of the potential we have plotted the diagonal kernals of the adiabatic N-N potential in the Born-Openhamer approximation IM against the relative distance (R) between the nucleons for various channels. The results of our calculation for SQ shows that the CMP of COGEP provides short-range repulsion and o intermediate range attraction.. The COGEP has two terms c r" D (r) and 5(r). At short distances the i exchange kernels of 5(r) dominate over the exchange kernels of c r D (r) thus providing the short range repulsion. But in the intermediate and long ranges the exchange kernels of c r D (r) dominate over the exchange kernels of 8(r) thus providing the intermediate and long range attraction. The color electric terms in COGEP and the confinement potential of the quarks do not play any important role in N-N scattering. For P the potential is totally repulsive, as expected the PS are negative. The significant repulsion in the potential for P at short distance arises from the centrifugal barrier. It should be noted that due to dependence on X ...X . , only the exchange term of the matrix elements contribute to N-N interaction. The exchange kernels being non-local contribute significantly to the N-N interaction. !n conclusion, With a single free parameter as we are able to obtain good agreement with the experimental phase-shifts for various channels. In our calculation the term in COGEP arising out of confinement of gluons is responsible for the required attraction in the N-N interaction. This clearly shows that the confinement of gluons plays an important role in deriving N-N interaction starting from »h" quark and the gluon degrees of freedom. Ill K.Shimizu Report Prog.Phys.52 (1989) 1. Ill S.B.Khadkikar and S.K.Gupta,Phys.Lett.l24B (1983) 523. /3/ S.B.Khadkikar and P.C.Vinod Kumar.Pramana 29 (1987) 39 141 M.Kamimura, Supp.of the Prog.of Theor.Phys.62( 1977)236 ISI K.Brauer et al. Nucl Phys.B253 (1990) 308 CHESHIRE CAT SYNDROME IN N-N SCATTERING S.B.Khadkikar and K.B.Vijayakumar, Physical Research Lab. Ahmedabad. We present here the results of calculation of S-wave NN scattering phase shifts. We have made use of the relativistic harmonic oscillator Lorentz scalar+vector confinement model (RHM) /I/ for the confinement of the quarks which explains the properties of light hadrons. The RHM is equivalent to the NRQM through a similarity transformation. We have made use of a similiar confinement scheme for gluc.is the so called current confinement model (CCM) 121 for the confinement of gluons which describes glueballs. We have obtained confined one gluon exchange potential (COGEP) making use of the confined gluon propagators (CCM). With the COGEP we have investigated the central part of the NN interaction. We have performed two calculations: (1) without the exchange of c and n mesons and with the quark core size of the physical nucleon (henceforth referred to as c{i)). (2) With the exchange of i-l The central part of COGEP in the static limit is 4 a N A .A The parameters used in c(i) are b=0.86fm, M=160.6 MeV, E=428.6SMeV, a =3.50, a2=15.01 MeV fm~2 c=1.70fm"1. The s potentials and the parameters with cr and TT in c(ii) are /3/ b=0.55,M=160.6 ,E=641.28, a =0.2, a2= 66.28 c=1.70, m =500, s lit o in I 160 240 320 4OO ELOb BARYON SPECTROSCOPY IN CHIRAL COLOR DIELECTRIC MODEL S.C.Phatak and S.Sahu Institute of physics, Bhubaneswar 751005 Although quantum chroniodynaniics (QCD) is generally accepted as the fundamental theory of strong interaction, there exists no exact so- lutions to the theory in the nonperturbative, low-momentum regime. So some phenomenological models possessing the essential features of QCD has been developed,one of which is the color dielectric model (CDM) introduced by Nielson and Patkos[l] which is successfully applied to the description of static properties of hadrons. The CDM are described by quark fields ^.color dielectric field x which represents the nonperturbative features of the QCD vacuum and an effective gluon field A^. The outstanding feature of the CDM is absolute confinement of the quarks. In the present work we have studied the baryon spectroscopy in the context of chiral CDM. The Lagrangian density of the chiral CDM is [2] C(x) = ^ \ \; - u(x) w^ere mj is the quark mass and the summation is over all flavors, n is the pionic field, Ffju is the color electromagnetic field tensor and /,r=93 Mev is the pion decay constant. Potential 2 3 4 U(X) = B(aX (x) - 2{a - 2)X (x) + (or - 3)X ) For a > 6, U{x) is such that it has a double well structure with an absolute minimum at x=0> which corresponds to physical vacuum and a secondary minimum at x=l corresponds to perturbative vacuum. The energy density difference between the two minima measures the pressure of the physical vacuum; i.e. the bag constant B. The CDM has five parameters : the bag oonstatiUB).a,,.a. . the light quark masses m,t and the .strange q'l.irk mass ms. For cn'cula 255 tional convenience we have defined mGB = (^r) as an independent parameter. The quark and the color dielectric field equations are solved in mean field approximation where as the gluonic and pionic effects are included perturbatively[3]. In the first stage of the numerical calculation the parameters - B,a,mcB and mn are adjusted to fit the N, A masses. The centre of mass correction has been included. The CDM has been extended to the strange baryonic sector. By fixing the observed value of f}~ mass we have calculated the strange quark mass and then all other strange baryon masses are calculated. For the best fitting parameter set the gluonic contribution decreases with increasing baryon masses, where as the pionic contribution de- creases seperately with increasing baryon masses for octet and decuplet. We find that the strange quark mass is about 43 Mev larger than the light quark mass. The numerical results show that the agreement with experimen- tal masses is better for strangeness -2 baryons. The fitted parameters, calculated masses and experimental masses are given in the Table I. TABLE I The parameters used are: m -.16 GeV, B =. 1 GeV, a=2O and m_ =1 . 8 GeV. u GB Particle m CGeVD m, L CGeV) exp theory N 0. 938 0. 938 A 1 . 116 1 . 148 Z 1. 193 1 . 242 ^;° 1 . 318 1.343^ A 1 . 326 1.236* Z* 1 . 385 1 . 476 1 . 531 1 . 549 1 . 672 1 . 672 * * masses iji ed to f i •< the paramet er s 1. H.B.Nielsen and A.Patkos, Nucl. Phys. B 195 (1982) 137 2. H.Kitagawa, Nucl. Phys. A 487 (1988) 544 3. A.W.Thomas, Adv. in Nucl. Phys. 13 ('983) 1 256 MASS SPECTRA OF BARYONS llarikesh Singh* and A.K. Gautam + * Physics Department, Institute of Basic Sciences, Khandari, Agra. + Physics Department, R.B.S. College, Agra. The model of quark confinement developed by Chodos fs of fundaments ' importince as it is the model of quark confinement used to discuss 'he- structure of various nuclei and hadrons. The quarks are considered to be existing in a bag of radius R in such a manner that no quark can come out of the bag. The total energy of the hadrons is given by ' E(R) - IN.irr,2 * x.2/R2) + B(^R3/3) i 1 : 1 •here, W., m. and x. are the total number of quarks, mass of quark and quark n.om 1. Chodos, A., Jaffe, R.L., Thorn, C.B. and Weisskopf, V.F., Phys. Rev. 9D(1974) 3U71. 2. Close, I.E., "An Introduction to Quarks and Partons" (1982) Academic Press. 3. Polls, A. and Guardiola, R. "Quarks, Mesons and Isobars in Nuclei' Proceedings of the Fifth Topical School, Mstril (Granada, Spain), (1982). 257 31 3 0 2 9 U 27 2 -fe 3-M1515) 4. 2 5 5-NO67O) G.N0689) 24 7:H(1700) ,,N(180 K)>N(1990) 2-3 ,1 = N(219O) 12»N(22OO) 22 i3iN(222O) K»N(26OO) 15N(M30 I A (1236) ft (1650) pG0 ^. A (1690) >9 A> h, fl (I960) j - A(2160) 1.7 k • A (2850) 16 is OS 1 2 5 J 35 4 45 55 65 7 »• R (Fermi) FIG. 5 VARIATION OF MASSES WITH BAG RADII FOR THREE QUARKS SYSTEM uuu FOR LASTED DATA. V 258 COULOMB ENERGY AND MASS YIELDS IN NUCLEAR MULTIFRAGMENTATION PROCESS M.Mishra and L.Satpathy Institute of Physics, Bhubaneswar-751005 The general picture of the multifragmentation, observed in proton induced heavy-ion collisions is that the energetic proton imparts energy to the target. The excited target expands allowing for thermal equi- librium and then decays statistically into various fragments. The effect of Coulomb interaction between the various fragments was first realized by Gross et.al.,1 and its effect on mass yield distribution (MYD) curve was studied in the mean field approximation. Recently, Beangelis et.al.,2 iiave calculated the relative yields of various fragments in a model, based on the principle u minimal information. They claim that the Coulomb energy is not necessary to produce a minimum in the MYD curves, which is in contradiction to our earlier work3. In this work, we reexamine the Coulomb effect on MYD curves within the framework of the ou .* grand canonical model. The calculations are performed for symmetric nuclear systems with mass numbers A = 100 and A = 250 and compared with the results of Ref(2). The binding energy of the system includes volume, surface and Coulomb energies. The Coulomb energy consists of self Coulomb energy of the t** fragment Ai and the Coulomb interaction with the rest A—A{. The results for the symmetric nuclear system with mass number A — 100 at temperatures T = 5MeV and T — lOMeV are shown in Fig.l. The solid curves are the mass yields including Coulomb effect, the dashed curves are without Coulomb effect and dashed-dot curves include only the self Coulomb effect. By comparing MYD curves with(solid curve) and without(dash curve) Coulomb effect, the behaviour of the mass yields suggests that the Coulomb energy is not necessary to obtain the minimum in MYD curve at intermediate temperatures. However, any real physical system, like nucleus is highly influenced by Coulomb effect and thus should be considered. If only the self Coulomb effect is included, the minimum of the MYD curve cannot be obtained as shown by the dashed-dot curve compared to the solid curve. Hence the mutual Coulomb interaction between the fragments are to be included to obtain a U-shaped MYD curve at intermediate tempertures. This result is in total agreement 259 with our earlier result3. The study of Coulomb effect on MYD curve for asymmetric systems is in progress. 10 20 30 40 50 60 70 80 90 100 Moss Number A Fig.l References: 1. D.H.E. Gross et.al., Z.Phys.A309 (1981), 41. 2. A.R.Deangelis et.al., Phys.LettB231 (1989), 1. 3. M.Mishra et.al., J.Phys.G14 (1988), 1115. 260 INSTANTON CONTRIBUTION TO ELECTROMAGNETIC MASS DIFFERENCES OF BARYONS C.P. SINGH, 5. SINGH and R.L. SINGH Physics Deptt. V.S.S.D.College Kanpur *APS University Rewa (M.P.) INTRODUCTION; There have been many attempts to explain the hadronic structure using different models and then ultimately to develop a basic theory* The development of QCD in recent years and that of theory of instanton seems to provide a theoretical basis for hadron physics. Instantons are classical euclidean solutions of gauge theories. As such they are exp- ected to play an important role in QCD and to effect the structure and interaction-s of hadrons. In case of mesons a lot have been done using instanton theory but only a little attention has been paid for baryons. Here we wish to present our results on Electromagnetic Mass Differences of baryons calculated considering instanton contribution within the frame work of bag model. ELECTROMAGHETIC MASS DIFFERENCES OF BARYOHS: ":'••* The E.M.M.D. between any two isomultiplet is given by ^M - C*M)elec. • (AM) mag# + CAM) g^ + (AM) ^ ....(1) The bag model allows an explicit evaluation of (AM) and CAM),,^ terras using quark wave function. The term (&ML quark arises due to quark mass difference anJ .jcplicitely evaluated by Bickerstaff and 2 3 Thomas . The last term is instanton contribution and it is (AH). " $'n for h baryons Ins' . (2) =• 0 for 3/2 baxyons where 1- 3 (V^ - V^) - 12 ^ (mu- m^) Cn^ +*O ....(3) with V Contd 2/- 261 ( 2 ) TABLE EMMD OF BARYOHS M (AM) Mass ^ ^c (A M)Total (/iM) total differences withuk inst. without inst. exp. contribution contribution. p-Yi -1.79 +0.50 -1.29 -1.29 -1.2934 + .00004 Ae+-A+ -1.80 +2.03 - +0.23 +0.23 - A+-A& -1.80 +0.42 - -1.38 -1.38 - ££ — A,~ -1.80 -1.06 - -2.86 -2.86 - £*-£" ~2-15 +0.32 -0.099 -1.92 -1.83 -3.10+0.14 £C-ZT -2.15 -1.30 -0.099 -3.54 -3.45 -4.86+0.07 £ -£. -1.83 +0.39 - -1.44 -1.44 - >!*-£*" -1.83 -1.11 - -2.94 -2.94 -5.5+2.5 ^.°-2" -2.52 -1.50 -0.198 -4.21 -4.02 -6.34+0.08 2"°- -"" -1.86 -1.15 - -3.01 -3.01 -3.2+0.6 £^+-i-^ -1.85 •2.67 -0.071 +0.74 +0.82 - Sj" -5:" -1.85 +1.02 -0.071 -0.90 -0.83 - rt £ _--.:*; -2.122 +3.23 -0.142 +0.96 1.11 - - ._ C -2.17 +0.69 -0.071 -1.55 -1.48 ~ C —c - REFERENCES; 1. A. Belavin etal. Phys. lett. 59B. 85 (1975). A. Polyakov etal. Phys. Lett.(59B 82 (1975). 2. N.G. Deshpandey etal. Phys. Rev Dljj, 1885 (1977). R.B. Blckerataff and A.W. Thomas Phys. Kev D?S 1069 (1982). K.P. Tewarl, C.P.Singh and M.P. Khanna Phys. j-ev. D31 642 (1985) 3. G Yang etal. 2 phys.C particle and field 26, 77 (1984) 262 PION CLOUD COHTRJBUTIOIJ TO \U\DROV. MASSES III VAP.IA3L2 3AG PRESSURE MODEL O.P. Singh, S. Singh *« R.L. Singh * Physics Deptt. V.3.3.D. College Kanpur *AP3 University, 3cwa (M.P.) Introduction : The MIT bag -.odel provides a satisfactory dynamical frame work fcr treating hedrons as systems of confined quarks. The quarks are 'jnfined EjKHsfeHj: >'-y a pre^r^re term 0 which is taken as constant parame- ter. One of the '•'••- '.ificatiens over original bag model is due to Joseph 2 and Nair which considered bag pressure as variable in accordance with hadxonic density- Another modi£led bag model la cloudlv toag model in which around and inside the nucleon circulates a cloud of pions moving freely every where except at the bag surface where they can be emitted or absorbed. Here we wish to estimate the pion cloud contribution to the hadron masses in the frame work oJT •••ixiable bag pressure model. Hadron masses : The hadron mass is .jiven by " " **E + E (1) ( where ER = ,/3 [>- > ^ "<» ^ * ^ , is the varinl-'lc b-io pressure r.icdcl LCJT.I .".n;l E =.--'• ;s— >- ( "" n ' ( (3) is Llio pheno : x nolo.;iC'ii V' ;r ri.'_..uiv" jT t:n- jiuii self energy with p a^ CjnstanL. Ucin^ '.;u.':e o::pi-._r. _' c.c v. o !uv. calculated the hiiron masoe which are c,iv .i :n i-ho L.I.J1L>. 263 Tobl* t HaJnn rianacc Particle E Ep Total R liar.3 Ccv. Ctv. 1ZV. Civ. r» Input .940 A 1.198 -.043 1.155 1.116 •£_ 1.229 -.024 1.205 1.193 c 1.397 -.011 1.3fl6 1.318 2^ 2.417 -.024 2.393 2.4J Ac 2.332 -.013 2.269 2.273 A 1.19O -.040 1.150 1.2 36 1.3S6 -.024 1.332 1.38S s* 1.521 -.011 1.510 1.533 2.462 -.024 2.438 2.48 a Input 0.13*7 K .716 -.159 .507 .496 *\s .926 _._ .926 .958 •!><. 1.918 -.159 1.759 1.865 Pt 2.092 2.092 2.03 - *\c 3.244 3.2-14 2.96 Pb 5.165 -,161 5.024 5.271 Pb 5.356 - 5.356 6.502 _ 6.502 9.76 - 9.76 .636 -.284 .302 .776 to .636 -.240 0.396 .782 It" .801 -.160 .611 .892 .966 - .966 1.02 1.9J7 • -.157 1.780 2.007 2.10S 2.105 2.14 3.249 _ J.2«9 3.095 5.190 -.100 5.030 5.321 S.SO4 6.504 Y 9.76 9.76 9.46 U from our estimates wo find that ploo cloud Contribution significantly Improve* the rcsulta. IMs clearly Indicate* tha prwa«nc« of plon cloud around nod inside tin nucleoua. • Rofereacjo i- 1. A. Chodo* *tJU.. rtiy«. R«rv £9, 3471 (1974) T. Da araral «t«l. tTiyi.tUv I)f2 2060 (1975) *^* <^"pH ond H.K. U%Xr I*rciD3nA 16 49 (1981) 3. A.W. »>oo«« «rt4l. Phy». Rov £2_3 3838 (1980); £2^ Zlt (1981), O.A, >dllor «U1. n»y». l.tt. P91. 19? (1900) 264 ROLE OF RHO IN CHARGE EXCHANGE REACTIONS A.B.Santra and B.K.Jain Nuclear Physics Division BARC, Bonbay 400 085 It has been seen in the case of nucleon-nucleon (NN) interaction that one boson exchange potentials (OBEP) are able to give fits to the phase-shifts comparable to the best phenonenological potentials. The fora of OBEP being guided by meson field theory, is dominated by the exchange of single i, r\, ut and Q Mesons. The rho Mesons being heavier (m -770 MeV) than the pions (• =140 MeV) are important in describing the intersediate region To.Sfm < r < 2fm) of the NN interaction. It sisulates «ost of the correlated two pion exchange procsses in T=1 channel. Realizing the importance of rho exchange in NN interaction one would like to know its contribution in charge exchange reactions. The charge .exchange reactions usually include Cp.n) or (n,p), (p,A ), ( He,t) and (Li, He) reactions. In this note, we try to understand the role of rho in (p,A ) and (n,p) reactions on proton. These reactions where one unit of charge is transfered between the projectile and the target can be mediated through the exchange of isovector mesons such as pion and rho. The transition potential for these reactions can be constructed as a sim of one pion and one rho exchange potentials. The rho •esont because of its vector character, appears to be with the same sign as pion in the central part but with opposit sign relative to pion in the non-central part of the transition potential. we have analysed p(p,A )n reaction at 2.23 GeV/c bean momentum in DWBA with the above transition potential. The distorted waves, in eikonal approximation, are written directly in terms of the scattering amplitudes. In this approximation, the distorted waves are completely determined in terms of total cross-section and th? ratio of the real to imaginary component of the scattering amplitude. Same parameters have been taken for entrance as well as the exit channel. Results of this calculation are shown in fig 1. In this figure, four momentum transfer distribution is given for various combination of pion and rho in the transition potential. A and A denote in GeV the cutoff length parameter in wNN and pNfl vertex* form factors respectively. Calculations using only one pion exchange transition potntial with hard form factor agrees well with the experimental points. If we include rho in addition it is found 265 that the results, though show large effects, are not in accordance with the data. It is found2 in p(n,p)n reaction that the normalized four momenta distribution [(do/dt)/(do(0)/dt) vs t] and he quantity [/ do(0)/dt] are independent of incident neutron energy. Thi§ feature is found to be of kinematical origin. The value of the zero degree cross-section lies around 150»b. We have analyzed this reaction for 580 MeV incident neutron energy in DWBA with the transition potential consisting of one pion and one rho exchange. The distorted waves are constructed as before with appropriate parameters The results o thi. calculation are shown in fig.2. Calculations with only Pions in the transition potential underestimate very much the value of the zero degree cross-section with soft as well as hard form factors (less than 90mb for the hardest form factor). The shape of the normalised four momentum distribution is axso seen to be completely away from the experimental points. If the rho is introduced in addition, the results show the desired saturation of normalized four momentum distribution at higher amentum transfers. The value of the zero degree cross-section is found to be 140mb which is near to the experimental value. Thus, the role of rho appears to be puzzling from the analysis of these two simple charge exchange reactions. In one o- them its presence seems to be irrelevant, though in the other one it is found to be absolutely necessary. 10 1 P(n,P)n 1 ' • .. Tn s 580 MeV OB os 2 —• 0.6S - bL- 02 -— 0.65 00 0 i 00 0.05 010 0.15 0.20 t(GeV/c)2 0.1 02 0.3 OA 05 0.6 -l(GeV/c)2 References: 1 A M Eisner et al., Phys.Rev.D_138( 1965)670 2. W.Hurster et al., Phys.Lett.2QB(1980)367 266 e) RELATIVISTTC HEAVY-ION COLLISIONS AND QUARK-GLUON PHASE A STUD* OF COLLECTIVE FLOU OF NUCLEAR HATTER IN La + Aa(Br) REACTION H.S.PALSANIA. BHAGUAN SINGH. A.GILL, V.KUHAR, K.B.BHALLA AND S.LOKANATHAN Deptt. of Physics, Univoraity of Rajasthan, Jaipur. Study of nuclear matter of other than normal density (i.e. fo= 0.15 GeV/fa ) Is i very important problam of the subject of ralativletic nucleus - nucleus collision •*. A systematics of "Bounce-Off i.e. a collective effect ia being studied for the last fivo y§a?e or ao in the energy range few hundreds of tlev/n to fev Gev/n ' . In thio paper we present results of La + Ag(Br) system in collision at lab. energy 1.2 Gev/n. A stack of emulsions was exposed to the above energy at Berkeley Bevatron in the year April, 1983. On collection of over 600 Interactions we select 107 La + Ag(Br) interactions having multiplicity of projectile fragaenta (??'a,Z>2^ 4 or more and target fragments (TF's.ZM) 8 or nore. Angles of PF's are measured following coordinate method and considering lengths of individual tracks > 1 a.a. Fig(l) givou plot of the difference of the azimuthal angles ot unit principal vectors of PF's and TF's i.e. A*=*Tp-4pp. Froa the figure It May be seen that there are 69 out of 107 events showing .Aft >. 90*. The average value of £J =110.04 +. 4.89*. A line corresponding to no correlation has been shown in the figure. The ratio(C) of no. ot eventa with AS 2 '°* and with A* <_ 90' cornea out to be 1.820 which ahowa that there is a reasonably strong back to back correlation between the projectile and target fragments. Flg(2) gives the frequency distribution of the polar angle S between principal vectors of the Projectile/Target fragments and the beaa direction for the above 107 events. The average angles are 9pp=*Z. 66+0.25 for the projectile fragaents and 6jF=»30.06+.1.90 for the target fragaenta. The 6pF being about 2.S* ahowa thai aost of the bulk of projectile get collectively deflected on either aide of the beam direction. Fi«(3) ahowa aslauthal correlation of Individual projectile fragments a.) t£ 'a (2=2) and b) fragaenta (Z^Z) w.r.to th« direction of the principal vector of TF'«. Froa the data, the ratio C i.e. projectile fragaenta having A* >90* to £ 90* is coaputed separately for oC'm ttla 3*) and th« fragaents (fig 3b) In order to atudy the difference of aechanisa of emission. Th« ratio coaa out to be 1.60 for oC's and 1.97 for the fragaenta. Also, the average value of * being A^'ot91 • 21±3 • *5 for o '• and A*F=103.32+5.27 for fragments infers the effect to be stronger in case of fragments than oc'a. 267 _TL_ Oola — N» corrriotloa lk» to- 20 20 £ 12 i» £ 20 10 80 _L _L J_ _L Q0 WO 200 0 1^ (0 60 80 K)0 120 * e,, *0r 20- M - J •« 160 200 Fig.3 Awnothai comlaUans •! a) MMoual alpha - tragmtnls from Pro]*ctil* and b) hwniar that ••prm proj«ta» IragnMoU wy. Is U» alrtctlon of prttxipal «wtor »l TF'l. REFERENCES (1) R.Stock .Natur* Vol. 337 (1989) 319 (2) Kuaftr, V., ot. al.. Z. Phyo. A333. C1989) 373 and Heckman, H.H.. «t. al. , Phyo. Rev. C34. (1986)1333. (3) Guotaffaaon. H.A.. at. al., Phys. Rev. Lett.52.(1984J1590 and V.Kumar, Invited talk, Proc. of the Synposlum on Nuclear Phyelcc A'iarah,India,32A (1989) 144. 74 ef 268 A STOCHASTIC MODEL FOR MULTIPARTICLE PRODUCTION A. K. CHAUDHURI VEC Centre,1/AF, Bidhan Nagar, Calcutta 700 064 In recent years, the negative binomial distribution (NBD), with two parameters Me assume that in the collison, a single hot excited particle producing source (called ancestor) is produced. The excitation energy of the ancestor being directly proportional to the cm collision energy(V £). The ancestor with probability X per unit time gives birth to a new (secondary) particle which are also in a excited state. The secondary particles and their descendants (which are QCD string like exitation) can break up (in to two) independently, with probability ft per unit time. The break up probability ft depends on the excitationenergy of the particle breaking up. Then the generating function (g.f.)for the number of particles produced in the interval 0-t is given by dG(s,t)/dt =X G(s,t) CF(s,t)-1D (1) with the initial condition G(s,t=O) = 1. F is the 269 g.f. for the secondaries, which as defined in the model obeys Furry distribution law. Solving eqn(1> for G we obtain. -X//? G(s,t) = Hs+<1-s> exp(/?t) 3 .(2) Eq(H) is nothing but the generating function for the negative binomial distribution with the parameters, References: C1D For review see A. Giovannini and L. Van Hove, Acta Phys. Pol. B19 (1988) 495. C23 A. Ramakrishan, in Some simple stochastic processes, J. Roy. Sta. Soc. B13 (no.1) 1951. 270 FORWARD-TRANSVERSE ENERGY CORRELATIONS IN ULTRA-RELATIVI3TIC HEAVY ION COLLISIONS S.K.Gupta and Swapan Das Nuclear Physics Division Bhabha Atomic Research Centre Bombay-400 085 The study of the correlation between -forward and transverse energy emissions provides a diagnostic tool to understand the reaction dynamics in relativistics heavy ion interactions. The shape of the correlation curve as a -function of projectile and target masse^ provides constrints on the reaction dynamics of co")issions in nuclei. The energy recorded in a zero-degree-calorimeter corresponds to the number of the projectile spectators and thus determines the number of projectile participants which would be interacting with the target nucleons. Within the framework of the eikonal model /I/ simple algebraic relationship between the number of the projectile spectator nucleuns and the number of collisions or the number of the target participants have been derived /2/. The transverse energy generated in the col I ision may be proportional to e.i.tr1 er the total number of participant nucleons or the number of the collisions. These hypotheses can be tested by comparing with the experimental data. The forward- transverse energy correlation measured by the E802 collaboration /3/ for 14.5 GeV per nucleon Si beam on targets of Al and Au are compared in Fig.l with these relationships. This comparison shows that the transverse energy is proportional to the total number of the participant nucleons in the case of Au while there is a significant departure for Al from this hypothesis when the zero degree energy is less than 150 GeV. This departure may be due to cascading by the secondaries. However the number of collisions hypothesis completely disagrees with the data. Comparison is also made 271 •for the f orward-transverse energy correlation measured by the NA35 collaboration /4/ with 2r->0 BeV/nucleon Sulphur beam incident on S, Cu, Ag and Au targets -for the pseudo-rapidity lying between 2.2 and 3.6 in Fig.2. By using transverse energy per participants as 2 GeV for all the targets, the correction is in good agreement with the participant number hypothesis. In case ot £ target, the transverse energy is underpredicted by about 10% at lower values of the zero degree energy. However the collision number hypothesis departs considerably -from the data. 1. S.K. Gupta, Z. Physik A 351 (1988) 457. 2. S.K. Gupta, Phys.Rev. C 39 (1989) 737. 3. M.J. Tannenbaum, Int.Journal of Mod . Phys .A 4(1989) 3377. 4. J.W. Harris, Nuclear Physics A 498 (1989) 133c 200 300 400 -zoc ENERGY IN ZDC ( GeV ) ENERGY IN ZOC ( GeV ) Fig.l Fig.2 272 ENERGY DISTRIBUTION OF MUON PAIRS AND PHOTON PAIRS IN RELATIVISTIC HEAVY ION COLLISIONS G. Janhavi and P. R. Subramanian Department of Nuclear Physics, University of Madras, Madras 600 025 Among the various signatures suggested for the dete- ction of a quark-gluon plasma (QGP) produced in relativistic heavy ion collisions, the emission of dileptons and diphotons provide an excellent probe since they don't interact strongly with the consti- tuents of the QGP. We consider a baryon-rich QGP attainable at lab energies of the order of 10-15 GeV/N. This QGP undergoes a first order phase transition into a hadron resonance gas (HRG), conserving both entropy and baryon number [1]. Our QGP phase consists of u, d, u, d quarks, and gluons; the HRG phase is made up of all non-strange hadrons and their resonances with mass < 2 GeV. Our calculations include interactions in the QGP phase via the running coupling constant and the Hagedorn's correction for the finite size of the hadrons in the HRG phase. Recently, Yoshida [2] has studied the energy distribution of dimuons and diphotons produced from the central region in relativistic heavy ion collisions using a hydrodynamical model. We have extended his calculations to a baryon-rich plasma. We study the production rates for dimuons and diphotons as a function of their energies (E,, E_) for two equations of state (EOS) of the QGP. We consider the process q q —> pf u" + X in the QGP phase and TT^TT"—> p+ u" + X in the HRG phase. We calculate R, the ratio of the numbers of pairs with energies (E,, E2) = (3 GeV, 3GeV) to those with energies (1 GeV, 5 GeV) for two EOS. The ratio is calculated also for the case when the QGP is not formed. The results are tabulated in Table I. 273 Table I Rpair = DNpair(3'3)/ DNpair(1'5) S/A e Ryy (a) (b) (a) (b) 11 2 .6 3.28 0.968 3.43 3 .25 20 4 .2 3.32 0.962 3.48 3.23 S/A =Entropy per baryon,£= energy density (GeV/fm ) (a) with phase transition; (b) without phase transi- tion and Hagedorn's correction in the HRG phase. It is clear from Table I that if there is no phase transition the ratio Rut/r differs much from that for the case with phase transition. But Ryy does not differ much for the cases with and without phase transition. This shows that the analysis of dimuons will be easier than that of diphotons in order to distinguish the QGP and HRG states. We are grateful to the UGC (COSIST and Special Assistance Programmes) and the DAE for financial support. GJ thanks CSIR for the award of a senior research fellowship. References 1. P. R. Subramanian, H. Stocker, and W. Greiner, Phys. Lett. 173B, 468 (1986); U. Heinz, P. R. Subramanian, H. Stocker, and W. Greiner, J. Phys. £12, 1237 (1986); G. Janhavi and P. R. Subramanian, Phys. Rev. D 38, 2808 (1988). 2. R. Yoshida, Z. Phys. C 45, 485 (1990). 274 PHASE TRANSITION FROM A QGP TO HADRONS IN THE EARLY UNIVERSE K. Sakthi Murugesan and P. R. Subramanian Department of Nuclear Physics, University of Madras, Guindy Campus, Madras 600 025. Using the Standard Cosmological Model one can extrapolate back in time when the Universe was probably in a Quark-Gluon Plasma (QGP) state. Due to the expansion of the plasma, there was an era when the transition from a QGP to Hadrons occurred. Different standard scenarios predict the era of the hadronization phase transition for a Friedmann Universe [1-3j . We consider [4,5] the phase transition of a QGP consisting o •; u, d, u and 3 quarks and gluons into a hadron ;. base made up of all well established hadrons and their resonances with mass < 2 GeV. Our system has a oma.ll chemical potential because of the small baryon - antibaryon asymmetry in the early Universe. We use relativistic quantum statistics for particles in both the phases and include Hagedorn's correction for the finite size of the hadrons in the HRG phase. We also include the interactions between the quarks and gluons in the QGP phase via the running coupling constant. We calculate the energy density for both the phases and also determine the critical pressure and the temperature on the basis of the Gibbs' criteria for different values of the bag constant B and the QCD scale fixing parameter /\. We also find the above parameters by including sufficiently light s quarks in the QGP phase. We use the time - temperature relation for a Friedmann Universe [1,2] to calculate the end of the QGP era (t ) and the beginning of the hadronic era (t, ). In this calculation we conclude that the end of the QGP era is fixed for a given bag constant. The strength of the interactions between the quarks and gluons and the inclusion of hadron resonances in the HRG phase do not alter the QGP era. But these signi- ficantly reduce the time at which the hadronic era starts and hence reduce the phase transition time at a given value of B. If the hadrons are just relati- vistic point particles in the HRG phase, it will also reduce the phase transition time significantly. Our results are presented in Table I for different quark flavours in the QGP phase. They are in good agreement with those of Ref.6. Our model calculation is more realistic and may be useful for the particle physicists and cosmologists to fix the era and hence to choose B and j\. Table I : No. of flavours = Nf; t = 10 s B 3 Nf HRG phase A = 0 MeV A = 200 MeV L MeV/fm v* th/t tg/t th/t 60 2 pions only 8.10 28.60 7.60 17.20 400 2 pions only 3.10 10.10 3.01 7.60 60 2 all* 8.10 26.00 7.50 14.20 400** 2 all 2.97 6o07 2.80 4.35 400 2 all 2.30 2.60 60 3 pions only 8.18 33.70 7.72 18.50 400 3 pions only 3.10 11.96 3.05 8.44 60 3 all 8.16 31.94 7.60 15.50 400 3 all 3.09 8.30 2.90 4.98 * All well established hadrons with mass < 2 GeV. ** Point particles. References: 1. K. A. Olive, Nucl. Phys. B190, 483 (1981). 2. B. Kampfer and H. Schultz, Z. Phys. C 21, 351(1984). 3. E. Suhonen, Phys. Lett. B 119, 81 (1982). 4. U. Heinz, P. R. Subramanian, H. Stbcker, and W. Greiner, J. Phys. G 12, 1237 (1986). 5. K. Sakthi Murugesan, G. Janhavi and P. R. Subramanian, Phys. Rev. D 41, 2384 (1990); Phys. Rev. D 42 (1990), in press. 6. L. Van Hove, Preprint, CERN-TH.5575/90, June 1990 This work is supported by DAE and UGC SAP programme. K. S. M is grateful to DAE for the award of a Senior Research Fellowship. 276 QUARK MATTER IN COLOUR-DiELECTRIC MODEL S. iC. Ghcsh arid S. C. Phatak '. n z 11 t !.:t'.' of Fhvsics, Bhuoaneswar 751 005 iheories of matter at high densities play an important roie in understanding a variety of phenomena in cosmology and astrophysics. There are- speculations about possible existence of quark matter in heavy neutron stars and formation of quark giuon plasma in heavy ion collisions, investigations have been done on this by many authors. On the other hand different quark models have been used to study the properties of baryons. It will be interesting to SLudy the quark matter in such models.Some work have already been done in this di r ectiont 1 -23 . I n the present work we have studied symmetric infinite quark matter at zero and finite temperature in color dielectric model.The Lagrangian,we have used for the present study is given by u x f 5' ' ' s fj2 a 4 * ui> 2 v y u n where >/>, rr and A ^r e quark, pi on and gl uon field; resDecti veiy, f =93Mev is the Dion decay n constant,m is the quark mas x is color dielectric field and Bis the bag pressure, x ~1 corresponds to perturbative vacuum and x ~0 corresponds to physical vacuum.The parametersB,m,a,and strong couolinq constant o< 1=--- I has been obtained by s [ : \ 277 }. =c-ijn where ^. i L empra ture i u ' q E i s •-. e zerot h compcnen '- of' energy momentum tensor an c< n i. s the quark q densi ty. For i nteracti ng cas e we have used diagrammati c: expansion for Ci i n power•s of coupling constant in the usual vvyac 3-4 ] . uon and pi on correcti ons are i nc1uded uo to second order in coupling constant. The dielectric field is obtained from the equilibrium condition C C Tabl e Baryon densityCn. 5 vs. temperature at instability 1 /'•& „ ,-, point for the parameter set B =15.'. 4 Mev',m=12o. 9 Mev,a=36 and a -O. 1O9 TCMe\O 0 as so 75 100 110 n, Cfm~35 . 36 . 32 . 31 . 24 . 17 . OS D 1. M. :<. Glendening NiPA 512 C i 990; '''37 id. BYoniowski ?.-. e^. ai . [-'r.:? -li C I rZ7iC0 i-2S:r2 3. F'ree<;iinan ~'< McLerrari PRD 16 •''. J?7)i 13] ,1147,110-.} 4. f. I. KaousU NPB 148 •'.! L Q7Q' 278 01. TiirJ i-LJiATIFISTIC NUCLEAR REACTION Ai A.P.Sharma Department of Physics, A.M.University, Aligaifc-202002 (India) The Kelativietic nuclear interactions have .o far attracted manyfild attention as this study r>rovide^ us a good information about the space - time evolution of hadronic final states. Due to the production of large-P/p particles in hard processes, the collision characteristics can be •axplained using auark-parton model. Alongwith the high-Po region one can consider the low-P^ region also on the basis of quark-parton .-odel. In the present work the distribution of secondary pions (l\~) in low-P™ region (P^loO Gev/c) produced in 50 G-ev/c -[f ~Em interactions under otrong magnetic field of ~~ 200 KG has been analysed. In each of the six cases of Fig.l a ^ 2 .sharp peal: is clearly indicated for PT £0.l2(Gev/cf p and a shallow peak i^ observed ioi» ?m^^ 0.12 (Gev/cf This can easily be explained on the basis of the -•odel of Dass and Hwa" and other vorkers^? 3,4. The pions ( oea+sea) 'produced?from the sea 2 contribute predominently in the Pn ^ 0,12(G-ey/c) region, while the pions (val^rae and sea) Qcdtri- bute predouenently in the PT % 0.12 (Gev/oL region. •Jhe number of such piona (valence + sea) is^very low, because there are only two valence quarks r>er pion. and contri.biite only slightly for Pfp'>0.12 (Gev/c) region. 1. BaoS rip and Kwa itC,1977,Phys.Lett.E-68, 549 2. Ch^jidra Gu-pt,ohivpxjjri iiK,Verrria ri^ and oharraa AP 1982.Physical review D-26,2202-20. 'i. Chandra G-upt,ohi"\n>uri l:ai,Vercia il:> and ^harma AP 1903,11 liuovo Oinento 75A, 408-15. 4o Sharma AP. Proc.XXI.International Cosmic ray Conference, Adelaide ( Australia),Jan 6-19,1990 (Paper Ho. IIS 1.3-29) . 279 I p1:1111i 1 I ~t" —IITT r it 1 - i o o -f II -a .3 c 'S, i jlltM l-l- > — (lllU II-! -- 31 a: "SI. .ri I'll! I I I L . 11. L ifc-ZluUXl-l-J llULLJ_J I ^ tji " (.l/P/'-'PK/v/l) 280 EQUATIONS OF STATE AND ENTROPY PER BARYON IN A QCD PHASE TRANSITION K. Sakthi Murugesan and P. R. Snbramanxan Department of Nuclear Physics, University of Madras, Guindy Campus, Madras 600 025. It is speculated that in ultrarelativistic heavy ion collisions normal nuclear matter undergoes a phase transition to a quark - gluon plasma (QGP) at very high densities and temperatures. To study the dynamics of the expansion of a QGP into a hadron resonance gas (HRG) phase in the first order phase transition, the total baryon number and entropy must be conserved. The entropy per baryon (= S/A) in the QGP phase has to be higher than that in the HRG phase at the same temperature and chemical potential [1-3J. This depends on the value of bag constant B and the strength of the interactions between quarks and gluons. If B < 200 MeV/fm , one could not obtain a higher S/A in the QGP phase than that in the HRG phase without including interactions ^between the quarks and gluons. When B = 60 MeV/fm ( usually particle physicists and astrophysicists choose this value of B), we find S/A in the HRG phase to be greater than that in the QGP phase upto certain values of the temperature and chemical potential. This is shown in Fig.l. To avoid such a situation, (i) the mesons are treated as relativistic point particles [4]; (ii) Hagedorn's correction is applied to all the other hadrons [2] (baryons and their resonances); (iii) interactions between quarks and gluons are included in the QGP phase [2], Then we obtain a higher S/A value in the QGP phase than in the HRG phase at B = 60 MeV/fm at the phase transition (see Pig. 2). Hence one can study the dynamics of the hadroni- zation phase transition even at lower values of B. Our approach is also useful to study Lhe phase transition for still larger values of the scale fixing parameter of QCD and lower values of B. 281 This work is supported by DAE and UGC SAP programme. K.S.M is grateful to DAE for the award of a Senior Research Fellowship. References: 1. P. R. Subramanian, H. Stocker, and W. Greiner, Phys. Lett. B 173, 468 (1986). 2. U. Heinz, P. R. Subramanian, H. Stocker, and W. Greiner, J. Phys. G 12, 1237 (1986). 3. K. S. Lee, M. J. Rhoades - Brown and U. Heinz, Phys. Rev. C 37, 1452 (1988). 4. H. Kouno and F.Takagi, Z. Phys. C 42, 209 (1989). Fig. 1 Fig. 2 B =60 MeV/fm 40 B = 60MeV/fm^ 100 I A =100 MeV A = 280MeV \\o\k Ml tn 20 o\ 10 10 V 1 i 100 2(10 100 200 282 RELATIVISTIC QCD-MOTTVATED POTENTIAL MODEL OF HEAVY-LIGHT QUARKS CONFIXED NUCLEONS: By R.Swarup, R.N.Singh,Department of Physics,D.S.Col 1 eye,Aligarh ABSTRACT: The constancy of mass spi i 111 rig " tern f or- al 1 quarkonium states in case of NRPM seen to be violated at least for a few systems when light heavy quark pairs art^ involved fr.":r; th.? point of r view of relativistc-QCD however, rerr.i &(Mv - >f») appears to be vanishing. THEORY:The QCD-Relativistic Hani 1 Ionian when treated as a perturbation over the colour-coulomb interaction for the exchange confinement and fine hyperfine interaction yields the mass formula in terns of masses varying as exchange of quark and antiquaik alongwith their spin exchanges. The mass exchange equation for vector and pscudoscalar mesons have beer; derived. One while consider ing the asymptotic freedom <*s (Sq^j as 2 oi*(sr<,i\) = ' ^/i«-2.Lf in CSSVSA^ I (1) where S^1 represents the QCD scale parametric exchange and i\. is the number of fermions.The variation of ^ ' withsfdoei-s introduce variation in in ( M^-MpH aric1 for power law potential lVc 283 Si • NUCl.KUi; COU.ir.fONS AT 4.5 ACcV : f\ IMU:I.;MINAKY KI-::;UI.TIJ l.b. Ojha, U.K. Singh, S.N. Trirathi -.ind S.K. Tuli I'hysics Department Baric-rus Hindu University, Varanasi-2'.il 005 'H We ;J:( .sent a pieiiiuinai.y repor' <>L 1 rseJ.as t.i a 'Si- nacli.".i:; interactions in emulsions irradici tod at tin? Uyrichrophasotrou, Uubna, USSlv' with bi-airi kinetic- energy 4.5 AGeV. The measurements are portormed Jn a stack of NIKFI-BR2 nuclear emulsion. Interactions are obtained by along-tho-track scanning technique v/ith the help of Olympus PH-2 microscopes. In all 457 interactions are registered out of which 200 interactions are selected for detailed studies. The average minimum grain density is observed as -29.5 grains per 100 \i . Charged secondaries arc classified in accordance v»ith their ioaizations into shower, grey, black and projectile fragment. The mean free path is obtained as 8.'; + 0.1 cm. The multiplicity distributions of various particles are mea&uiod. The average multiplicities or shower, grey, black and fragments will bo presented. The i.ei;uits will be systematically compared with the dau- obtained from other experiments [1-4]. Kef.: 1J S.A. A/.imov et al., Nucl. I'hys. AJLT^I' (1987), G'J3. 2) D. Chosh et a.l., Muc! . l-hy:i . \Vj.i, (1-989), 687. 3) R. l-lvanja ct al., Nucl. I'iiya. t\-\] 11 (1983), 507. 4) BCJJI. Collaboration, Phys. Rov. L«-t>, 54, (1985), 771. "*"• 284 EXOTIC BOSON MAPPINGS Y.K. Cambhir Department of Physics, I.I.T., Powai, Bombay 400 076 Nuclear Heavy-Ion (HI) collision experiments has and is still providing a wealth of experimental data. In particular the studies of the decay of the highly excited states above the yrast line, of the compound nucleus formed in HI reactions, yielded a variety of new phenomena like super-deformation, exotic shapes, shape transitions, exotic giant resonances etc. A class of these are being understood phenomenologically, in terms of intrinsic symmetries exploiting powerful Interacting Boson Models (IBM). On the other hand their microscopic interpretation is essentially based on the mean-field theories (MFT), but their complete understanding is still in its infancy. However, some of these have been inter- preted in terms of collective excitations built on the MFT at finite temperature. The most poweful tool emerged from the recent studies on the microscopic foundation of IBM, for the description of the nuclear collective excitations is the Boson Mappings particularly Marumori and Dyson mappings. Therefore, we attempt here to genera- lize these mappings at finite temperatures. Let C+. (C. (-1)jmC. ) denote the fermion (quasiparticle) creatron Annihilation) operators. The corresponding temperature dependent fermion operators t (T) are next introduced through: The temperature dependence appears through the statistical thermodynamic occupation probabilities rij = Pj = [1 + exp((e..-u)/kT)r1 , .. (2) e. boing the energy of the state| jm> , T is the temperat- ure and k the Boltzmann constant. The fermi energy u[for neutrons (u ) and for protons (u )] is fixed through the requirement. E(2j+1)n. = N (neutron) and/Z (proton) number .. (3) The mapping procedure is similar to that followed in the zero temperature case discussed by us earlier . Therefore, due to paucity of space we illustrate the procedure for 285 * the Dyson Boson Mapping (DBM) indicating the various steps involved. Step I : Construct temperature dependent bi-fermion operators using Eq.(1). Step II : Introduce DBM to obtain the boson image of these bi-fermion operators in terms of ideal bosons. Step III : Express the Hamiltonian and other relevant operators in terms of boson operators using the results of Step II. This therefore provides all the required operators and the basis states in the boson representation. This is so far exact and is completely general. At this stage several approximations are introduced, so as to yield certain specific algebras e.g. SU(6) etc. It is also easy to analyse the structure of several specific collective operators. For illustration, the RPA operator at finite temperature is introduced and expressed in terms of ideal bosons. Additional factors involving occupations (Eq.(2)) now appear. The present formulation helps to analyse these and other such problems. Model calculations, specific limits leading to SU(6) algebra and the structure of temperature dependent RPA phonon are currently being investigated. 1. Y.K. Gambhir, J.A. Sheikh, P.Ring and P.Schuck; Phys.Rev. C31 (1985) 1519 286 FORWARD ENERGY FLOW CROSS-SECTION IN ULTRA-RELATIVISTIC HEAVY-ION COLLISIONS Swapan Das and S.K. Gupta Nuclear Physics Division Bhabha Atomic Research Centre Bombay-400 085 The energy recorded in the zero-degree calorimeter is carried by the projectile spectator- nucleons in the nucleus-nucleus collisions. This energy is where E Q is the beam energy per nucleon and nio is the number of the projectile participants. The probability CJ"np (b) at impact parameter b of the n '•> nucleon participated -from the projectile can be calculated according to the formulation based on the eikonal model /I/. The quantity cfn (b) is expressed in terms of che transparency function T(b) which involves nuclear densities and the* nucleon-nucl eon scattering amplitude /I/. Integrating over the impact parameter, we get the interaction cross-section for nr> projectile participants which is given by ' XD C ?O The forward energy flow calculations have been earlier compared with the CERN data using the oxyben beam at 200 A GeV. In this note we extend these calculations on Al and Au targets interacting with the silicon beam at 14.5 A GeV/c. In figs 1 and 2 a comparison has been made between the calculations and the data measured at BNL /3/. The calculations compare reasonably well with the data. 287 1. S.K. Gupta, Z. Phys. A 331 (1988) 457. 2. V. Franco and A.Tekou, Phys.Rev C 16 (1977) 658 3. M.J. Tannenbaum, Int. Journal of Mod. Phys. A4 (1989) 3377. "i s i i r I Beam 5i U. 5 GeV/C per nucleon > 30 CD Target : Au Expt: E802 20 UJ IP 0 0 100 200 300 400 500 EZDC(6eV) Beam Si 1A.5 G( /c TARGET :AI ig. 2 O EXPT:E802 1 3 O LLJ 0 100 200 300 400 500 EZDC(GeV) 288 I-'ISSION IN q-HUCLtUS Aruit Kumar I'alx. rh.C.O. 5th floor,central ruaplex II.A.U.C. Moauay-400 Oli Wo propose the uxistence of a different r.l&sr, of nucleus consists of freely interacting quarks instead of groupod together as neutrons and protons.Here w do'nl prulend lo give a audeJ uf nucleus uaseil on quarks.rathor wo invoke in addition to ordinary nucleus there are soae nucleus cunlajng wily nuarks uf warjuui flavours,which we consider of "up'aud 'down" types are called as q-nucleuslQNI.If ON under gues fissJon procoss how Much onorgy will bo released. Me will be interested in ON of U*5hich is runnier parl of II "fwt/ having /Ob number of quark*.I or %ui:li a syslea having large nuauvr of quarks JI IS difficult to calculate I he •ass of OH using HIT-bag liku audel .ncoause then the radius of the nucleus will be very Mich greater than the .nuclear dimension. To calculate the aass of UN we will set a seau-eaprical aass foray] a jL.lhis is justified by oi.i of tho properties of quarks-whal is known as 'assyaptolic frcedoa" j.c.deep inside the. . nucleus,if probed at very large energy and •oaontuJ1 •* transfer.quarks bevave as if they are free «f interaction and away froa centro the interaction between two quarks increases.This is siailar to sea* extent that in liquid drop nodel where the aoleculos at'" the surface feel aaxiaua tension.He will calculate the aass of ON in usual way He*1-: ((^U t M^I-».E O) and O.I;, is established by Hei/sacker's aasj foraula as is i • whero each ten* has the usual acanjuig.4 is the total nuabvr of quarks with U nuabcr of "up" k Jt nuaber ef "down" quarks.Hero couloab energy is different becaese two typo of charges are distributed uaifonely in a sphere. <) is positive .the reason bring il tries lo koep two kind of chargus in tho splivre and have a tendency lo increase &.£ . Ccfw) is duo to up quarks 4 &-(A) is duo to down quarks including si If interactjons.lhu neyalive sign is put becausu they have a tendency to disrupt thu nucleus 289 = 4-666 The numbers arc phonomenological constants taken from Wuizsacker ' 5 formula with piuuer modifications.(ho example has boon taken is that of counterpart of UXiS i.e. U UN, which may und'.-i go fjssiun JIU 1. idled tiy a high energy neutron where Mo ir* and La*17 »rc (IN 1 uunt erpar ts of Mo a^t Ua'*5 respectively . Now using I mass of U IS mi. r..'? Hoy )mass of la is zan. Mov mass of Mo M 1105. 7/0 Mov where we have used the "running mass* of quarks as Hov. Since the* concept of quark mass is a ilyiiiiinicul uric and is deeply related to the full complexity of intuijclmy guark yluon system. The mass lias a mciiumj as a fu/ii.L.iori of raoroontum transfer i.e. H-Hlq1*). lluwover other values of quark mass also exist as M^s (&•> *• <' S) flev aj*<*. 1*1^— (a-*) A* Mil I K'l MCI S . [t3 • • I • flosf. An I nl 1 oilui.l ion lo Cluarks >• } Ai dduniK. I'ress INew York;19f9l J.Gasser ^ II I outwyloi .I'Mys . Ucpui 1. 1) /. t 1 9U? ) /' 290 f) NUCLEAR INSTRUMENTATION, EXPERIMENTAL TECHNIQUES AND ACCELERATORS FIRST EXPERIMENTAL RESULTS FROM THE HIGH CURRENT ION SOURCE N.M.Thakur and R.C.Sethi Nuclear Physics Division, BARC, Bombay 400085. A high current duoplasmatron ion source, which is designed1 to serve as an injector to the RFQ accelerator, is in operation. This ion source was designed to deliver 20 mA of light ion beams, at an energy of 20 keV. Critical alignment of the ion source, upto 15 microns, was achieved by using specially designed alignment pin3. Diffstack diffusion pumps were used to obtain a clean and oil free vacuum of the order of 2x10"s mbar. The magnetic field in the anode column region was mapped with an axial Hall probe and the variation Is shown in fig.l. The field has a peak of 2.5 kG and a spatial spread of about 2 cms. The large field gradient observed, is a characteristic of strong focussing. The Tantalum filament (10 cms long, 0.6 mm diameter) could give upto 1.5 amps of electron emission at a power of 100 watts. The filament emission characteristics appear in fig.2. Intermediate electrode FJQ. i: Axial Magnetic Field FI<3. 2: Filament Emission Variation. Characteristics So far the ion source has been tested upto an extraction voltage of 15 kV. The source has yielded ~ 12 mA of unanalysed ion current, with Hydrogen gas, at an arc current of 2.5 amps. The yield with Helium is less, and is about 2 mA. The arc current has been found to be emission limited beyond an anode voltage of 140 volts. Saturation of the extracted beam current has not been observed upto 15 kV of extraction voltage, confirming that the extracted beam is space charts limited. For various filament currents, yielding arc currents upto 1.5 amps, the effect of gaa pressure on the arc current is shown in fig.3. Peaks of the arc current occur at a gaa pressure of 0.045 mbar. The effect of the magnetic field and the puller voltage on the ion current is shown in fig.4, The role of the puller electrode in improving the beam intensity is clearly demonstrated in this figure. A puller voltage of 10 kV yields the highest ion currents, with an extraction voltage of 15 kV. The optimum magnetic field, for maximum ion current, is 1.5 kG. Efforts are being made to operate the ion source at an extraction voltage of 20 kV. A magnetic analyser and two beam diagnostic devices have been designed, fabricated and are being coupled to the ion source for the beam analysis, beam distribution and emittance studies. The authors would like to thank Dr.S.S.Kapoor and Dr.M.A.Eswaran for their keen interest in this work. Puller VoLlagd Fi.la.nrton L it O A E < Curren t urron t 0 10. 5 A 1 Io n 0 Ar c C 3 Prusaur* o . 1 > Wagnouc FL6>Li{ 2. O imbar) Via. 3: Arc Ciarr*int va. fid. Ion Curranl vs. a The deuteron RFQ /I/, capable of delivering a max. beam current of 20 mA at an energy of 150 kev, is in the advanced stage of completion and is being made ready for low power R.F.tests. The radial matchers which provide the time dependent focussing have been designed and made with a total length of 4 p/S . About 9 5% matching of the emittance to the acceptance of the accelerator in the radial! plane is expected^as is shown in fig.l. The numerically controlled lathe had^to be used for sticking to the desired profile of 1/ \J sin(kz), where k is the wave vector. The actual profile of the radial matcher and the beam behaviour is also shown in fig.l. Tho shaper portion is confined to a 5 P>}\ length with a max. acceleration A and focussing -RADIAL i 1= 25*0 mA •a ,3-0 ' MATCHER a £ u PROFILE 2-0^ x 10 20 (RA) Fig.l: Studies of the Radial Matcher X as 0.035 and 0.858 respectively. The shaping of the beam to the gentle buncher is more or less 100%, in both the X and Y planes. The acceleration cum gentle buncher portion, comprising of 17(^ cells and trapz. of 0.4,has been fabricated. All the four electrodes, each naving a length of ex 1.2 m^ has been checked for its individual profile and modulation. Barring two high spots of Av=250/l£, the oveiall deviations have been found to be within 30/i The stem structure consisting of three " 0-mode- R.F. cells, has been coupled to the : T(keV) electrodes. . For controlling and studying the deviations from the resonant frequency of 45 Mfla, an B.F.Test assembly has been designed. By varying the length of the stem3, 'an adjustment of-^ 10 MHz is possible. u(nA)Cel.(s- The whole assembly has been fitted into Fig. 2 the copper plated R.F.tank. The bead assembly has been coupled to the system to assess the sycunetricity or the quadrupole field and the variation in the longitudinal field. The high current duoplasmatron ion source has already gone into operation /2/. Using -140 Hydrogen gas, £^.12 mA of unanalysed ion beam has been extracted. The final - 20*00 J expected behaviour of the Fig. 3 accelerator and the variation of its various parameters are shown in fig.2. Eig.3 gives the expected beam characteristics in (AE,A#S) phase space. Studies reveal that about 60% of the beam in the pulse, is confined to a time spread of 4 1 n.sec. and an energy spread of ± 10 keV. The authors thank Dr. M.A.Eswaran for his keen interest in the work. 1. R.C.Sethi et. el., European particle Ace. Conference, Rome, June 1988. 2. N.M.Thakur and R.C.Sethi, in these proceedings. 294 STATUS OP ISOL FACILITY AT VECC A* Chakrabarti, A^ Bandyopadhyay, Arup Bandyopadhyay S.K, Basu, N.C, Bhattacharya, S, Chattopadhyay, M.D. Mazumder', T# Mukhopadhyay, A, Poley and A.X, Mazumdar Dept., Hiillips Olivers ity, Marburg, Germany Introduction : The construction of an indegenous He-jet coupled on~line separator (ISOL) facility was taken up in the begining of 1988* The hardware sissembly is now comple- te. At present tests are being carried out for various subsystems with a view to evaluate the performance of the total system. In this article we would like to discuss the tests that have either been completed or in the process of being completed. Svj8tem_study : The motivation for extending the existing Be-jet facility to achieve mass separation and the basic design consideration for such a system have already been reported /i/. A portion of the ISOL systerj shoeing schema- tically the ion source and th? rest of the beam optical system is shown in fig. 1. The entire system has been tested for vacuum and a. pressure of 4 x 10"' torr has boen obtained in a few hours of pumping. It is expected that the design value of 1 x 16* torr would be achievable in a few days of contiguous pumping* The hollow cathode ion source lias been energized and a fairly stable and strong are (500 mA) could be obtained with He as the are support gas. Studies are now continuing to find the optimum conditions for obtaining a stable and & strong are which in turn ensures a good ionisation effi- ciency. The maximum extractor potential at present is 30 kV. The beam optics har; been designed around a 50 di-pole magnet. Together wit:" a quadrupole magnet this gives a double focussing and a mass resolving power of about 10C0 with a spot size of 2 mm. The present series of off-line tests also includes a measurement of resolving power with beams of Ar and I. A preliminary field mapping of the 295 di-pole magnet has already been done using a hall probe assembly developed at VECC and calibrated with a standard Km magnet.. It is hoped that the off-line tests would be over within a month or so and the system would be ready for on-line testing- and actual physics experiments before the end of the current year. References /1/ A. Chakrabarti, Proceedings Symp. on Hud. Phys.; (MB) 1987t Seminar talk. Fi,.i. 9EAM TRANSPORt Ut*= FOP ISO'-. 296 CURRENT MONITOR AND SCANNING SYSTEM FOR THE RACE-TRACK MICROTRON S.D. Dhole and V.t^ Department of Physics, University of Poona, Pune-7 ABSTRACT Beam current monitor and scanning system are designed and fabricated for the microtron and being used in electron irradiation experiments. IK' ODUCTION : The microtroh, an electron accelerator of the University of Poona is operated in a pulse mode with pulse width 2 usec and pulsating rate 50 PPS to 200 PPS. The electron energy can be set in two ranges 0.5 to 1 MeV and 6 to 8 MeV. For several applications, samples are exposed uniformely with electrons and the fluence level (e/cm^) is required to be known with an accuracy around 1 %. Due to back scattering of electrons and secondary emission from the.surface of the sample it is difficult to estimate fluence level by measuring the charge received by the sample. An induction type current monitor (1/2") ±s therefore made to measure total number of electrons falling per second on a given sample. The beam scanning system moves the electron beam spot on the sample for uniform irradiation. EXPERIMENTAL : The current monitor consists of a ferrite ifing having OD 46 mm, ID 28.6 mm and width 13 mm. Around the ring 2000 turns of 40 SWG enameled copper wire are provided. The two end terminals are connected to an opamp for impedance matching. When electron bunch passes through the ferrite core, pulse voltage is generated across the winding which is proportional to the number of electrons in the bunch. The details of the cystem are shown in the Figure 1. The signal is integrated for ten seconds 297 and the output is fed to an analog to digital convertor. For calibration, a reentrant type graphite Faraday cup was used to collects all the electrons and charge is measured by an current integrator. The signal of the current monitor was fed to an amplifier, gain of which was adjusted in such a way that the number of electrons entering the Faraday cup per second is indicated as average current in terms of voltage on the display system. Figure 2 shows the calibration curve for number of electrons passing through the ferrite core per second versus display voltage. A beam scanning system is employed in which magnetic field is produced perpedicular to electron beam and varies in steps with an interval of five seconds. The electron beam spot on the sample can be moved in X and Y directions covering sample area upto 40 mm x 20 mm. Uniformity of electron irradiation is around 5 %. Copper winding 18 • 1 -Electron I 15 j^X 7/vy^ beam 1 / iyy^\^^ Induetd \*\f J\~T"* ' Voltage * 3 / J/^^J \^f ^-Farrita ring 6 - / 3 0 FIG) BEAM MONITOR Display Voltage ^» FIG 2 CUIBRATION CURVE FOR BEAM CURRENT MONITOR REFERENCES : 1. Manca J.J. '.-t al . ,Nuc 1. Inst. Muth,136 (1976) 249 2. Anderson J-M., Rc-v. Set. Insert. 42 (1971) 915. 298 STUDIES ON NARROWING OF TIME PROFILE OF A CYCLOTRON BEAM BY SHAPING THE SLIT OF THE ION SOURCE P. R. Sanaa Variable Energy Cyclotron Centre, Calcutta - 700064 Ion beams circulating in a cyclotron or extracted from it are pulsed in nature. Though in many experiments this bunching is of no importance, in various expeiements, e.g., study of nuclear isomeric states etc., the bunched nature of the beam is essential. The sm?ller the width of the bunch the better it is. Moreover, the energy resolution of the extracted beam can be reduced by reducing the time width of the beam bunch. When a beam passes through an RF field, the energy of different particles are differently modified and this is the origin of beam bunching in a cyclotron. Since the ions come out of the ion source with practically zero energy, the details of the electric field near the ion source have great influence on the motion of particles. Thus by shaping the ion source slit the amount of bunching can be controlled. Bhandari et al.,[l] showed experimentally that an unbevelled slit gives a narrower time profile than with a bevelled slit (Fig.l). In this work we theoretically explore the possibilities of getting very narrow time profile by taking various shapes and sizes of the source slit. The equations of motion of a particle in a combined electric and magnetic field are: x = (e/m)Ex(x, y)cos(ut-0) + uy y = (e/m)Ey(x, y)cos(wt *) - wx where the symbols have usual meanings. For central region calculations workers take the field Ex to be uniform. But actually the field near the slit depends on its shape and is nonuniform. This has been calculated by the Schwarz- Christoffel technique of conformal mapping for extended slit and puller and by the POISSON code for the actual slit and puller system. Fig.1 shows Ex for various slits. The field near the slit is small for unbevelled slits and this field further decreases as the thickness of the slit increases. The y-component of the field is very small and is neglected for furthewr calculations. 299 With these values ol the field the equations of motion have been integrated. For unbevelled slits, as the field near the slit is low the ions take a long time to cross the initial region and so the particles which are emitted at a later phase do not f'.nd enough tame to gain sufficient energy and so they do not enter the puller at all. Phases have been calculated from 300 K-SHELL VACANCIES AT OXYGEN IONS MOVING INSIDE THIN FERROMAGNETIC FOILS L.C. Tribedi, R.G. Pillay, K.G. Prasad and P.N. Tandon Tata Institute of Fundamental Research, Bombay 400005 Strong magnetic hyperfim fields oriented along the ma- gnetization direction are experienced by swift ions moving inside ferromagnetic solids. These transient fields (TF) are attributed to the polarization of inner bound s-electro- ns of the moving ion arising from spin exchange interactions with the polarized electrons of the ferromagnetic medium. For light ions the TF can be directly correlated to their number of K-shell vacancies inside the ferromagnet. A meas- urement of K-shell vacancies is therefore of interest for a better understanding of the origin of TF. Additionally rec- ent hyperfine interaction studies using the 3" state of 0 shows that recoiling oxygen ions at 7.3vo emerging through a thin Fe foil into vacuum have significantly smaller fraction of H-like Oxygen ions {~ 31%) as compared to that from thick carbon (~ 41%). Substantially larger fraction of H-like ox- ygen ions as compared to Fe are also observed if the ions are allowed to come out through a thin Ni foil. At these high velocities it is expected that there is no substantial difference between the charge fractions inside and outside the solid. We report here measurements of K-shell vacancies at Oxyqen ions moving inside Fe,Co & Ni using the "Probe Layer technioue" in which the K-shell vacancy of the moving ion is directly transferred to the K-shell of the probe fol- lowed by the emission of its characteristic X-ray. Thin targets of Fe,Co and Ni of thicknesses varying between 2 to 20ug/cm were made on lOug/cm thick self-supp- ortinq carbon foils. A~ lyg/cm thick probe layer of SiO was sandwitched between these two layers. Two surface barr- ier detectors were mounted inside the scattering chamber, the first one to detect scattered particles from a thin Au foil for normalization purposes and the second one to detect scattered particles from the target for thickness determina- tion. Oxygen beam, well collimated using two slits of 0.7mm each kept one meter apart, of energy varying from 22 to 56 MeV were obtained from the BARC-TIFR Pelletron accelerator. The X-rays produced were detected in a Si(Li) and a HPGe detector kept o'tside the scattering chamber. In subsequent 301 |6 4 0 36 MeV -8xlO Torgel Fe (2O/ig/cmz'Si(l-8>ig/cm2) 2-5 Si 0 1 -8 Beam *O 36 MeV -6 32 U. co 2-0 a CD Count s I 1-5 . 1 10 100 2OO 3OO 400 4 6 8 Channel no Charge number(q+) measurements these detectors were placed in vacuum inside the scattering chamber. Typical X-ray spectra obtained using the Si (Li) detector is shown in fig. 1. The sensitivity of the Si probe to K-shell vacancies in Oxygen ions wa3 obtained from the yield of Si X-rays for various charge states of Oxygen ions. A typical curve obtained for 36 MeV Oxygen ions is shown in fig. 2. From a detailed analysis of the X-ray yiald and tjie mea- sured sensitivity of the probe the ionization degree I ( °° ) k defined as I ( °° ) = Kx + 2K2, where K^ and K2 are the number -of single and double vacancies respectively in the projectile, obtained are ion velocity Fe Co Ni 7.4vo 69(8) 99(11) 121(16) 9.0vo 95(11) 113(14) 145(19) 9,5vo 80(8) 145(10) 10.3vo 130(17) 109(14) 140(20) The results support the earlier observation of larger number of vacancies in Ni as compared to Fe host. 302 HEAVY ION CHANNELING IN THIN SILICON SINGLE CRYSTAL V.S.Nanal, P.R.Apte, M.B.Kurup and K.G.Prasad Tata Institute Of Fundamental Research, Bombay,400005. Thin silicon single crystal (1.2. jam thick) was prepared by chemical etching of 300 nm thickSilicon single crystal ( (100), N-type, device grade) in the following way. Boron was first diffused in the mother crystal from one side at 975°c for 45 minutes. These crystals were kept at 1100°c for another three hours, so that Boron can diffuse inside the crystal. An oxide mask was formed to demarkate the boundary of individual samples of 5 to 8 mm diameter. The wafer was then etched using the selective etchant Pyracatechol Ethylene Diamine (PED). It etches (100) planes faster than any other planes and the etch rate depends on the concentration of P-type impurity. By varying time and temperature of Boron diffusion, diaphrams as thin as .4 fim in thickness were produced by this process. The crystal quality in terms of strain and defect density vaa examined by studying channeling cf 2 MeV cc-particles in these thin crystals. It was found that very good channeling dips could be observed even for the .4 piu thick crystals. We studied channeling of 12C (at 40,48,55 MeV), 16O (at 50,60,70 MeV) and 28Si (at 64,72,90 MeV), using beams from the Pelletron. Th- crystal is mounted on a double axis goniometer. A heavy ion detector (surface barrier) is mounted at 30° in the forward direction. A thin Germanium detector was kept at 150° for observing the X-rays produced in collision. To align the <100> axis with beam, the crystal is held at a fixed angle •& of 10° with respect to the oeam and is then rotated about the beam axis. As beam becomes parallel to various crystal planes, the yields of elastically scattered heavy ions and X-rays fall giving rise to 'planar dips'. The <100> axis was determined from the positions of these planar dips. The angular variation of be "i X-ray emission and elastic scattering of heavy ions around <100> axis was studied for Carbon, Oxygen and Silicon at different energies. The typical channeling dips are 303 shown in fig.l. The channeling dip is characterised by a minimum yield (x ) and its hal. width EU CIRCLE 1.500 -2 300 -2.100 a CAPSO.s (a). OXYGEN (A). SIUCUW jO) 20 X RAC YlEl 0: FlLI EO S'.UBOI 18 • • PARTICLE YIELD OPEN SiMtjtil 16 « ^ 12 A 11 ~D ' 0 o *' 6 I i 4 1 1 2 1 0 In the fig.2, x . is plotted as a function of energy. From the measureniln d x and 1/2 for the elastically sacttsred particles, it is seen that the present observations in most cases follow the general scaling behaviour with projectile energy and atomic number. The X-ray dips are shallower and narrower than the ones corresponding to the elastically scattered particles (fig.l). This again can be qualitatively understood in terms of the potentials in the problem. However, for silicon beam the difference in the \ between the mln particle and X-ray yields is well beyond expectation. The X-ray x shows verv larcre rain •* -> enhancement. It would be interesting to see if it is the result of any resonance effect due to the symmetric nature of projectile and target combination. 304 PC-HORIZON BASED DATA ACQUISITION SYSTEM WITH ETHERNET LINK A.Chatterjee, Vineet Kumar,A.K.Mohanty B.K.Nayak and Surendra Kumar Nuclear Physics Division, BARC, Bombay 400085 We have previously reported[l] a data acquisition system for the BARC-TIFR Pelletron where CAMAC data is acquired by an IBM PC and transferred to a HORIZCN-III mini-computer over an RS232 serial link. The maximum data rate for this system was limited to 150 parameters/s. We have now upgraded the system, employing a fast Ethernet link between the PC and HORIZON and a DMA crate controller supplied by Electronics Division, BARC[2]. Two independent acquisition programs have been developed on the PC, one is a stand-alone version, while the second transmits data to the HORIZON for processing, display and mass storage. The PC stand-alone system exploits DMA operation to build upto two 2D spectra each with 64x1024 channels in addition to eight ID spectra. For ID spectra the "Area" and '"Integral" functions and for 2D spectra, "Volume" and •'Projection'" functions provide simple analysis for monitoring the data. The "Rate" function indicates the data rate at any time. All operations are supported simultaneously with list-mode where list-data is written to the PC hard disk. At the end of acquisition the ID and 2D spectra can optionally be saved. The system can acquire upto 5K eight parameter events/s, but when a number of spectra and/or list-mode are required, the maximum counting rate comes down. At 2K events/s one can build two 2D and five ID spectra with list-mode on without appreciable data loss. The system with Ethernet link allows a greater amount of processing to be done on the 305 data and uses magnetic tape for storage. We have developed an open networking protocol based on the client-server model of TCP (Transmission Control Protocol). Data from PC memory is transferred to HORIZON memory while it is being acquired under DMA by the PC. This approach is superior to one based on the standard trivial file transfer protocol (TFTF) of Ethernet since it avoids the overheads associated with disk access at both ends and allows the data transmission to proceed concurrently with CAMAC data acquisition. Concurrency is a very important part of an online networked system. In the absence of concurrency, detector signals input to the ADC would be lost during the period of th^ network data transfer'. We have achieved a throughput over Ethernet of 96 Kbytes/s independent of buffer size. With TFTP the transfer rates are much slower, reaching a maximum of 24 Kbytes/s when the file size is as large as 64 Kbytes. The network program at the HORIZON end runs as a background server process. After connection is established, the HORIZON program waits to receive data over Ethernet and makes this data available to other programs running in the multi- tasking environment using shared memory. Other processes are used to (i) write data to tape (ii) build user defined ID and 2D spectra with pre- defined gates/filters (iii) provide an interactive graphic display for monitoring the data. In this way, the added computational power of the HORIZON minicomputer is utilised whil • at the bame time the usual hardware for CAMAC acquisition on the PC is maintained. [1] Surendra Kumar. A.K.Mohanty, A.Chatterjee, Susmita Biswas and V.5.Ramamurthy, Symposium on Nuclear Physios 32£(1989). [2] A,N.Khare, M.D.Ghodgaonk ar. V.Aruna and A.Behre, Proceedings of the National Symposium on Nuclear Electronics and Instrumentation (Bombay, 1989) 496. 306 PDP-U/23 AND STARBURST BASED HULTIPARAMETER DATA ACQUISITION SYSTEM Alok Saxena,Surendra Kumar,A.K.Mohanty,S.K.KaUria Nuclear Physics Division,B.A.R.C,Boinuay-40006 J ihe data acquisition and analysis in an accelerator labaratory plays a vital role, *1ue to increasing complexity of the experimental setup as well as due to limned availability of the accelerator time. The increased demand on data acquisition systems in terms of count rate handling and data processing capability have made pre-processing methods at CAMAC level neces- sary . The pf-esent data acquisition system at Pelletron Accelerator Lab is based on PDP-11/23 computer as « nost computer with a CA.1AC interface and PDP-11/73 based auxilliary crate controller. This system incorporates two processors having access to system crate : a high level multi-user , multi- tasking processor LSI-11/23 for the analysis and the storage of the data and a dedicated acquisition processor ( CES ACC 2180 STARBURST) for real-time event handling and pre-processing . The preprocessing at the CAMAC level avoids the huge time overhead associated with transfer of useless data over PDP-CAMAC interface . In ths present configuration , PDP-11/23 is interfaced to a Kinetic Systems 3920 "CAMAC crate stroller via 2920 DEC card sitting on the Q-bus . Two HLU1/RL02 disk drives and ons 800/1600 b.p.i. 9-track tape drive for the storage of the data and the applications programmes are also connected to the system . Two VT-125 video graphics display terminals with a hardcopy printer ire available for the online monitoring of the data . The STARBURST ,a singlE width CAhAC module ir> manufactured by CES of Geneva and is based on a 16/32 bit 200-ns cycle time DEC J-ll CPU that implements the full PDP- 11/70 instruction set with memory management . It provides a front panel RS- 232 port , a rear auxiliary controller bus (ACB) connector and a Q-bus con- nector . Tha STARBURST is supported by main crate controller via ACB. The STARBURST has 4 Mbytes addressing capability with direct addressing of up to 128 Kbytes RAM. For the present application, the STARBURST is used as a RAM resident front-end processor . One of the utost important feature of this memory structure is the memory mapping of CAMAC 1/0 and control registers into an I/O page beginning at the base address 17764000o. Thus a CAMAC read or write is simple "MOV" instructiu.i using any of the PDP-11 addressing mode.In addition to the standard PDP-11 interrupt vectors ,the STARBURST provides other maskable interrupts . They include two front panel sources for event trigger EXT1 and EXT2 . \ln the present configuration, EXT1, has been utilized for acquiring data front the variuos modules . START-UP con- figuration has been selected as TRAP 24 ,which is convenient to use for a RAM based system . In this configuration , the programs (developed on the host computer PDP-11/23 are dowr.-l ne loaded through CAHAC into STARBURST 307 RAM . The TRAP 24 vector address contains the start address of main program and other interrupt vector addresses contain starting addresb of the ISRo . After the progr ..;. is loaded , the STARBURST CPU is started by issuing CAMAC command F(28).A(0). The acquisition program is stopped by issuing another CAh.AC command F(25).A(0). An external strobe (a TTL pulse ) , when applied to the STAROUUfiT front panel input labelled EXT 1 after auitablt! delay, which takes care of digitizing tiae of CAMAC modules, generate an interupt which triggers the 5TARBURST where the software reacts 10 interrupts by ex- ecuting user written event handler subroutines. These routines read the required data from various modules residing in the crate like TDC ,ADC etc . The acquired data are buffered in the STARBURST memory for later transfer to the POP under DMA. The software element- if the systems have been distributed between the STARBURST ana PDP processors. The software interface between POP and CAMAC is provided by a loadable CAMAC device driver . The multitasking and time- sharing capaolities of the RSX-UM operating system of the PDP has been ex- ploited to run several dedicated tasks concurrently . These tasks share the data with each other through a resident (aeaory block ^rea Df 8Kbytes size . This resident memory common area contains the list buffer data transferred from the STAR9URST as well as one dimensional spectra and setup features .The global event flags have been used for communication hstween various programs runuig on PDP . These tasks can be started and stopped using a con- trol program CACQ . SETUP program defines the e/periffiental configuration .This information is shared by all the prograas . DNLOAD program then downloads the data acquisition program along with the information given by the SETUP prograo to the STARBURST meoiofy . The S7ARACQ program initiates the data acquisition from the PDP and when a buffer is full a flag is set in the mail-box in STARBURST which is read by the PDP . On receiving this flag the data is read from appropriate memory loation in the STARBURST under DMA and then transferred to a tape . This data is available fcr the further processing under resident common . Highest priority is guven to the collec- tion of experimental data and recording them in ev 30G A MD-1OO BASED DATA ACQUISITION FACILITY AT VECC A. Roy, P. K. Dasgupta, A. Bandyopadhyay, S. K. De Variable Energy Cyclotron Centre, Calcutta The data acquisition system so far being used at Variable Energy Cyclotron Centre, Calcutta is based on ND-56O /I/ Computer System and CAMAC interface. We needed a stand-by system based on ND—100 alone so that data acquisition can be done even if ND-500 processor fails.This paper reports a facility built on ND-100 system alone , which has a throughput comparable to that of previous one. The 16-bit experimental data is transferred from CAMAC crate to the main memory through a CAMAC OMA controller (CDMA) module. The transfer rate between the CAMAC crate and main memory via CDMA and JCC-10 is measured to be 2/lu^se/IAbi ts of data . The CDMA is used in LAM synchronised address scan mode to access multiple sub addresses of multiple stations for multiparameter event . The software can be logically divided into four modules :(i) data acquisition (ii) process and histogram generation (iii) one <^nd two dimensional display and (iv) a control program to start and supervise all these operations. The software organisation has six real time programs: (i) CONTROL (ii> CONFIG (iii) PROCESS (iv) ONE-D (v) TWO-D and (vi) SERVICE. User interacts with the system through CONTROL ; which subsequently activates other programs. PROCESS writes DMA filled raw buffers on magnetic tape block by block and also generates histograms . SERVICE inititates CDMA parameters. The raw buffers are switched between SERVICE and PROCESS . The histograms so generated by the PROCESS are displayed as one dimensional plot or two dimensional contour by ONE-D and TWO-D respectively .Experimenter specifies hardware configuration and process setup through CONFIG . The system performance was measured with various configurations and following count rate was observed (i) In siriy"-^ experiment it was possible to generate histograms with negligible dead-time upto input data rate of 10 Kcps. At 12 Kcps it increases 309 to 15% and at 15 Kcps it increases to 50% . (ii) For multiparameter experiments it is possible to store list-data on magnetic tape upto input data rate of 20 Kparameters/sec with negligble dead-time. It increases to 40% at the input rate of 40 Kparameters. (iii) The above experiment was repeated with simultaneous histogram generation for each parameter along with storage on magnetic tape. However histogramming was not allowed on current list buffer when same was requested by acquisition program . It was observed that upto a input rate of lOKparameters/sec there was negligible loss of data for both storage and processing. At 15Kparameters/sJC rate the input data storage is 92% and processing falls to 50% . The respective figures becomes 89% and 1G% at 20Kparameters/sec and 54% and 0.5% at the input rate of 40Kparameters/sec . This system works as a standby to the earlier version H1U based on ND-560 dual processor system. The throughput closely follows the earlier one; the speed reduces appreciably if other tasks &re allowed to run concurrently . A detailed technical description of the system is given in C23 . /I/ A. Bandyopadhyay et al. , Nucl Instr and Meth A257<1987> 309 /2/ A. Roy et. al.,"An On-line Data-Acquisition System Based On ND-100 Computer" - accepted for publication in Nucl Instr and Meth . 310 LOCATION OF MAGNETIC CENTRE IN MULTIPOLE FIELDS BY OPTICAL METHOD M. H. Rashid, G. Rodrigues*, C. Mallilc & N. K. Mukhopadhyay Variable Energy Cyclotron Centre, Calcutta-700064 ** Nuclea" Science Centre, Delhi. To avoid the build-up of serious misalignment, the magnetic centre of multipole magnets should always coincide with the central beam axis. The most accurate method for this purpose uses a colloidal solution of a ferrite CFe3O43 placed inside the multipole magnet. Plane polarised light is passed through the solution. Scattered light emerging through an analyser makes a pattern which determine the magnetic centre with a resolution of the order of 10 /jm. The simplicity of the method is that the pattern is directly observed with naked eyes and neither elaborate equipment nor accurate alignment of the solution are required. Particles with magnetic moments induced in the magnetic field are aligned along the field lines irrespective of the relative directions of the magnetic field H and the moment m. The symmetry relations [1,2] for the multipoles can be written as ft=C n/2D e±n/2 C 1 5 where n=4,6,8 for quadru-, sextu-, octu-poles respectively CFig.l for n=43 . The scattering amplitude of the light after the analyser is given by A ex. P. O, induced dipole moment P=cxE where a is the polarizability and O is the unit vector x the scattered light beam and II the plane of polarisation of the incident light. The intensity of light at the location of the observer is given by I =CK2/4^Co^JL-otlD2sin 311 quadr upol e set-up CFig.4D a tube containi:»o the solution was placed Inside the quadrupole M along the magnetic axis. A white light source S was used. A polariser P and an analyser A were placed properly in exact crossed position. We tried with the solution containing particle size O.5-1.O ^m at a field oi about 2 kG C-6O Amp. D. We got faint cross pattern ol dark lines. The crossing point of the dark lines define the magnetic centre. In the second set-up a rectangular thin container made of two thin optically plane glass plates placed 2mm apart filled with a fresh colloidal solution was used. A higher wattage light source CSOO WD was used at a field of about 4 kG CiaO AmpD. The cross pattern was much more sharp. With the hair-cross of a theodolite, repeatibil i ty of getting the magnetic centre was found to be about 35 Reference: [1] J K.Cobb and J.J.Murray. NIM.46, C1967D 99 C2]J K Cobb et al.IEEE trans.on Nucl.Sci 12.C19653395 [33 R Sugahara et al KEK Report 89-9 CSept. 1989D A. \ A/ A* 0 X ffp. X 312 COMBINED OPERATION OF THE LIGHT AND FiCAVY ION BUNCHSRS OF THE NSC PELLETRON FOR INCREASING THE EFFICIENCY P.N.PRAKASH & A.P.PATRO NUCLEAR SCIENCE CENTRE, NEW DELHI. Production of short burst pulses using the technique of velocity modulation has been-done for a long time with tandem Van de Graaff accelerators ' ' . Various.methods have since been tried to increase the bunching efficiency . In a simple, single frequency double gap buncher a sinusoidal rf voltage is applied as shown in fig la. Particles which reach the first gap earlier are decelerated and those reaching later are accelerated. The length of the drift space is such that the following condition is satisfied w*l/(2*v) = (2*n + l)rr/2 where w = 2*Tf*f, f is the rf frequency, 1 the length of the drift space, v the velocity and n = 0,1,2,.... F:C. la FIG. 1b The 15 UDgPelletron accelerator being installed at Nuclear Science Centre has a beam pulsing system prior to the main acceleration column. The beam pulsing system comprises of a beam chopper which chops the dc beam into pulses approximately 50 nSec wide, spaced 250 nSec apart. The light ion buncher (LIB) consisting of a combination of 4 different tube lengths, one of which can be selected for compressing the 50 nSec wide pulse into 2 nSec pulse at the target. The heavy ion buncher (HIB) has also a combination of 4 tube lengths that can be used to compress the chopped pulse to 3 nSec on the target. The LIB is used for masses upto 80. All higher masses can be bunched by HIB. Table 1 gives the details of LIB &. HIB. ; Tube Lengths (cm) ; Freq. I Distance of PTF* | : LIB ; 77.4, 62. 7, 48.6, 37 . 8 ; 4 MHz 4.5 meter ', : HIB : 13.9, 11.4, 09.5, 07 6 ! 4 MHz : 1.5 meter ,' Point of Time Focus TABLE 1 313 For a double gap, single frequency buncher, the energy modulation is done by means of an rf voltage as shown in Fig la. The theoretical energy modulation is also shown in the same fig. It can be seen that while going through a double gap buncher the beam gets overmodulated. The useful part of a sine wave which can be approximately taken as linear is only 20-25 % of the total period. In a double drift buncher, the two bunchers are seperated by a distance and operate at frequencies f and 2f. The action of the second buncher is shown in Fig lb. The first buncher over modulates the beam and the second buncher compensates for it, resulting in a large bunching fraction, since by the time the beam reaches the second buncher some bunching has already taken place. The seperation between the two bunchers is critical since the bunching efficiency largely depends on this. The ratio of buncher seperation to point of time focus from the first buncher should be between 0.2-0.25 This ratio gives optimum performance for the double drift buncher. In the NSC pulsing system the LIB and HIB are already fixed witn a seperation of about 3 meters. Computer simulation studies were done using a code developed for the purpose to use the HIB a* the second buncher of the double drift buncher with their existing locations. Fig 2. shows the accepetable width by the LIB when optimised. The same figure shows when the HIB is switched on to operate at 2f and voltage optimised. One can see that tha efficiency is almost doubled. At • |«-50 nS Accepted width REFERENCES 1. C D.Moak et al Rov. Gel Instrum, voi 35, no 6. 1964, Page 672 2 H Naylor et al IEEE Vol NS-12, No 3, 1965 Page 305 3 K H.Purser et al IEEE Vol NS-14, No 3, 1967 Page 174 4 W T.Milner IEEE Vol NS-26, No 1, 1979 Page 144.S 5 r, K Mehta & A.P.Patro NIM A26B (19e8) Page 334 314 SPACE CHARGE EFFECTS IN RECIRCULATION INJECTION Arvind Jain Nuclear Physics Division , BARC, Bombay-400085. The MIGMA fusion device. as developed by Maglich and co-workers./I/.involves the injection of a molecular beam of E)^ into a magnet, where the molecule splits into Df + Drdue to the central ion density at the centre of the magnet and gets trapped into a MIGMA orbit. The stripping efficiency is proportional to the central ion >u density nc and is typically 2.6% for n=10 ions/cc. A modified injection concept was proposed wherein the remaining injected beam which passes through the MIGMA chamber without getting stripped or being captured is brought back with the aid of a recirculating channel and reinjected into the MIGMA /2//3/. In the Reoirculation Injection Mlgma("RIGMA") the stripping efficiency can be enhanced from about 2.6% for a single pass to over 60% in 200 recirculations as shown in Table 1. This reduces the average current required from the injector by an order of magnitude, with a corressponding gain in the fuel and power efficiency ^' the MIGMA. Since very high injector currents are involved ,in the present paper we have investigated whether space charge effects permit injection of such high currents duriig recirculation injection. The space charge limit in a synchrotron ring has been derived by Laslett /4/. However, we use the approach of Wilson/5/. We have derived an expression for the space charge limit in the recirculating channel. The maximum injector cur rent Permitt'ed by spa char•ge limits IS gl^/en by; 7 ^ _ i /Z I H . 9x1'0 b u r .B K' < mA i Eq( 1 ) 1/ n I A7, I f we I IS e b- V ...f crosssect'Lon o f the ,;• i rou I at ing b'-am ins V - betatron ftv q u e n • 5. 3 clu •7 P-r !ll i subl shift i n V =0 , n P 315 ,H- 1.the bunching factor B=l,E=injector energy=0.1 MeV,L = path length in orbit=400 cms . .n-charge state of the injected beam=l,A=mass number of the injected beam-4. We obtain, max - 571 mA for the D^beam of Example A in Table 1 and I, = 6384 mA for Example B respectively. We note that the reauired injector currents in both examples A and B in Table i are well within the space charege limits. Table 1 Example A Example B «• 3 t Beam: D, on He Energy (keV): 100 133.3 500 667 Average Current required if there is no recitculation(mA)100 200 1500 3000 With recirculation(mA): 0.5 1.0 125 250 Peak injector current required(mA): 100 200 1500 3000 Space charge limit (mA): 571 659 6384 7371 Number of recirculations: 200 13 12 Central density ncassumed: 1.8 xlO 2.7 xlO Input Beam power(KW): 0.1833 230 Max.output power REFERENCES /I/ For a review,see for example B.C. Maglich.NIM in Phy. Res. A271{1988)13. /2/. Arvind Jain.Proc. Nuc.Phy.Sym.(Dec.1988) Vol. 31B,paper 038. /3/. Arvind Jain and M.Srinivasan . Proc. Nuc. Pny. Sym.(Dec.1989)Vol.32B.paper P66. /4/.L. J. Laslett.BNL-7534.p324. Proc. of 1963 Brookhaven Study on Storage Rings,Accelerators and Experimentation at Super High Energies. /5/.E.J.N.Wilson.CERN 77-07 (1977). 316 OL'ARTER WAVE RESONATOR: DESIGN B. T-.r i ni vasan arici R. -3. F'i 1 i ay NPD. E: ha Li-.a Atomic Research Centre, Bornbay-85 -t- ^ lii.i Ir,i'. . •.:'.;; of funda;iu=ntii Research, Bonibay-5 T;.,-:- ...i.~..;.-ji\ of the QWR, pi armed to be used i n ti"ie Superconducting Booster. is computed in 2 i!iG^rpcri .Gri'Tn. ..>.tr|.'»2. t* i rii. • *_i"ie ui tueriaions arid snape of t he drift tubes are optimized. The charges on the eq;;i potent i ai surfaces of the drift tubes and the ;;;;• rouruii ng cavity, the potentials and fields in the entire region, which is assummed to be cylindericaiiy symmetric, can be solved numerically. The equipotential surfaces are subdivided into a set of charged rings. The potential CV. 2> at any ring is related linearly to i- the set of charges CO.D weighted by the mutual j '_ v_ ~/ '_jr .j«3r_L i '. '<_. , J capaci trances. V. = A. . Q. where A. . = EC. .] - i J J i J i J The terms A_ . ' r. can be computed explicitly. Tha charges and thus, the fields can be solved for a given distribution of voltages on the conducting surface-.. Typically, 20 subdivisions per drift tube pr.v.-ides adequate accuracy. Thr= co-axi ai 1 y resonator section is then dri^iaivrJ ^- .J quartcji- wave transmission line tenniriifird l:.v V. capaci t at i ve load representing the drift ' ;:.:•••- T!lr> diameters of the co-axial line, th^ t .VJ:.- . • •:•. ':•.-=• : i\r..~v :..•;:•„•]:;,:(.,! .wid the length ar« '. i*^ J • ( 317 3 u a u \ ..•' zCmnO 2OO Fig.l Electric Field on Beam axis. the desired resonance frequency C150 R sh 2 [ q J P where, WCoptD is the optimum energy gain for a particle of charge "q" and P is the average power loss in the resonator. The par am&ters, vis. the resonance frequency, "Q" of the cavity, optimum Energy gain, optimum acceptance velocity, peak izur f^.n& Electric field, Drift tube Capacitance, etc. computed for the prototype QWR compares well with tho—e measured experimentjiiy. 318 A POST-ACCELERATOR FOIL STRIPPER FOR THE BARC-TIFR PELLETRON FACILITY S.D. Narvekar, R.R. Hosangadi, L.C. Tribedi, R.G. Pillay, K.G. Prasad and P.N. Tandon Tata Institute of Fundamental Research, Bombay-5 For many atomic collision experiments it is necessary to have a particular ion beam of diffe- rent charge states at the same beam energy. In principle such beams could be obtained by varying the terminal voltage of a tandem van de Graaff acc- elerator and selectina the appropriate charge state at the terminal. However, in practice such combi- nations of voltage and charge states are restricted due to several constraints. These limitations can partly be overcome, relatively easily, by stripping the ion beam after it has attained full energy usi- ng a thin carbon foil. Such a post-accelerator foil stripper can be placed either before or after the analyzing maqnet. We have installed at the BARC-TIFR Pelletron accelerator one such stripper just after the image slit of the analyzing magnet. The switchina mannet is used for the selection of the charge state and also for directing the beam into the target chamber mounted on the 30° beam line. The whole stripper assembly is mounted on a stainless steel flange and inserted in a 4" s s vacuum tee installed permanently on the beam line, at a vacuum of FslO~°Torr and is in operation. The assembly drawing of the stripper is shown in fig.l. Thin carbon foils of thickness 10 to 15yg/cm2 are mounted on eight circular apertures radially seperated by 4 5° on a toothed wheel and are held in position by means of a cover plate. Each one of the foil could-be placed in the path of the beam via suitable movement of the wheel provided by a set of gears. One of the foil posi- tion on the disc is left empty for normal use whe- rein no striopina is required. The position of the foil is obtained from the resistance chain pro vided on the driving aear wheel. The whole gear assembly is cont.mi led from outside by a stepper 319 motor (steo size 7.5° ) whose movement is transmitt ed inside the vacuum via a maqnetic couplinq. The oosition of the foil can be changed by qivinq six pulses to the steppinq motor for each position chanqe. Lonq cabies have been laid from the beam line to the machine control room to remotely con- trol as well as to read the foil position. This system was used in recent experiments usinq 16O beam from the Pelletron accelerator. The beam energy was 36 MeV and charge states of 4+,5*~ ,6*" ,7+ and ff1" were obtained to measure the charqe state dependence of charcteristic K X-rays in thin Si and Ti of thickness 1 to 25ug/cm2 backer on lQpg/cm^ carbon foils.' 320 TRIPLE AXES MULTIPLE TARGET HOLDER ASSEMBLY L.C. Tribedi, S.D. Narvekar, R.G. Pillay and P.N. Tandon. Tata Institute of Fundamental Research Bombay 400005 In several in-beam experiments, which involve measurements on a very large number of targets, it is desirable to have a multiple target holder assembly. In particular, at the Pelletron heavy ion facility, for the study of K-shell vacancy fractions of the Oxygen ions in solid targets, we have designed and made a rotatable target holder which can hold 27 targets. The study involves measurement of the K-shell vacancy fraction in the Oxygen projectile, as a function of target thickness. The vacancy fractions are derived from the X-ray yields of a suitable probe. The ex- tremely thin foils for these measurements are multilayered and comprise of & Carbon backing (10 - 15/zg/cm2}, the probe layer (1 — bfig/cm2) and the target material of interest (1 — 50/zg/cm2). To correct for the background in the probe X-ray intensity due to the backing and the target material, it is essential to have additional foils of the target and backing without the probe layer. These measurements are done on a series of foils, of varying target thicknesses, at different charge states and beam energies. To avoid loading, repeatedly, these fragile foils into the target chamber and to use the machine time efficiently a multiple target holder assembly and a chamber was built. The target foils are mounted on a thin S.S. wheel, 133 mm dia, along two concentric circles. On the outjr (100 mm PCD) and inner (66 mm PCD) circles the foils are positioned apart at every 20" and 40", respectively. A total of 27 foil holders (15 mm OD) can be accom- modated. Three degrees of freedom, 0, $ and z are provided. The $ rotation is used to bring the different targets onto the beam axis. The 0 motion provides a tilt with respect to the beam axis, and is used to generate different thicknesses of the same target. In addition, the tar- get wheel can be raised or lowered to access the two different concentric rings of targets. The wheel is on a shaft supported on two ball bearings which arc mounted on a, bracket. The bracket is carried by a hollow thick walled 321 SiS. tube through a double O-ringscal. A S.S. rod pass- tug through the hollow lube, vacuum sealed independently drives a set ol spur gears which in turn transfer the rotation perpendicularly to the target wheel via a worm gear assembly, to generate the motion. The <£ rota- tion is provided by a step- per motor, situated outside the chamber, coupled to the other end ot the S.S. rod. Outside the vacuum, the sup- port tube is externally threa- ded, and can be raised by a knob mounted on a ball bearing fixed to a surround- ing guide. The knob is grad- uated and a linear scale is engraved on the surface of the tube to read out the ver- tical position. The guide for the support tube is part of a rotating turntable moun- ted on a ball bearing on the top flange of the vac- uum chamber. A HCM'.OIH! Ntcp- per motor drives the rota- tion of this turntable, which provides the O motion. The angle 0 can be read out on a graduated circular scale. Both the stepper motors can be remotely controlled. This entire assembly was tested and has been used in our experiments. 322 AUTOMATION OF DOUBLE AXIS GONIOMETER FOR CHANNELING/BLOCKING MEASUREMENTS V.S.Nanal, W.A.Fernandes, M.B.Kurup and K.G.Prasad Tata Institute of Fundamental Research, Bombay,400005. In charged particle channeling experiments, it is necessary to align a major crystallographic axis with the beam direction. This can be done by looking at the yield of scattered particles or X-rays, as a function of the angle between the crystal axis and the beam direction. Software and hardware, based on microprocessor 8085, are developed for this purpose. Software and Interfacing using microprocessor 8085 We have a double axis goniometer which allows rotational motion about the beam axis ( 323 crystal on a. goniometer BEAM MOTCSS CHARGE DR1VINO DETECTORS INTEGRATOR CIRCUIT TTL CONVERTER 81 35 a R TIMER | s OUTPUT RST 6. B RESET 8065 DAC]—• CRO COUNTER | 825S fr- Microprocessor sends a sequential signal to stepper motor through a driving circuit. When the crystal is positioned and microprocessor is ready for collecting data, it gives a pulse to reset and enable the counter. Timer starts counting the charge integrator output pulses. Meanwhile, microprocessor is free to display the collected data on CRO. When preset charge value is reached, timer gives out a pulse that disables the counter and interrupts the microprocessor (RST6.5). The counter reading is stored in RAM. Microprocessor is now ready for moving the crystal and the process repeats till the final position is reached. ADDITIONAL FEATURES: 1. The motor can be moved either in forward or reverse direction. 2. Either ..of the two detector channels can be displayed and it is possible to toggle the display between them. 3.The data can be scaled for display, if needed. 4. The HEX data in RAM is converted into ASCII and can be sent to a serial device like PC or printer through RS232. 5. The battery back up is provided so as to preserve the data in case of power failures. We have used this system for experiments at pelletron and is found to work satisfactorily. 324 USE OF MULTIDETECTOR TELESCOPE SYSTEM FOR IMPROVING PARTICLE IDENTIFICATION IN HEAVY ION REACTIONS. S.My chi1i,B.J.Roy,5.K.Charagi, N. G .Badiger* , R.V.Srikantiah.M.G.Betigeri and S.K.Gupta.: Nuclear Physics Division Bhabha Atomic Research Centre, Bombay 8!> three element counter telescope consisting of and E surface barrier silicon detectors has be^n set up. For an ion with charge Z and mass M the range is given by R = A Ek /M*"1 Z2 where A is a constant for the stopping material and k = 1.67. From the signals of the three detectors it is possible to obtain two particle identification signals defined as follows: PI1 = [ E+AE1 +AE2J1'67 - [E+/\E2]1 67 =R1/A x M*"1 Z" PI2 = [ E+AE2]1'67 - [E]1-67 =R2/A x M*"1 Z2 Rl and R2 are thicknesses of the El and E2 detectors respectively. From the individual particle identifier signals,it is trivial to identify reaction products with different nuclear charge (Z). However the separation of species with the same Z is non-trivial since the low yield reaction produces are partially obscured by the tails of the neighbouring intense peaks.It has been shown[l] that it is possible to improve the particle identifier resolution by gating PI1 spectrum in coincidence with events identified in PI2 spectrum.o Charged particle beams of B and12 C bombarded a target of Rh-103 [50 microgram thick on a carbon backing of 15 micrograin thickness] at an incident energy of 66 and 79 MeV respectively.Fast coincidence between the two AE detectors provided the master gate.The signals from the LEI, &E2 and E detectors were recorded in "list" mode: in a PC-based multi-parameters system.The events stored were subsequently transferred to magnetic tape via PC-HORIZON link [2] and analysed at the ND system. The particle identifier signals PI1 (as defined 325 above) is shown in Fig.1 for both the B+Rh and C+Rh combinations.The peaks corresponding to different nuclear charges are w^Ll identified and are found to be linear as predicted b" the proportionality S72 The observed width of the peaks in the spectrum are the result of statistical spread in energy loss in the detectors and the extended tails of' the particle identifier peaks are due to anamolously high energy loss due to Landau process.An anamolous energy loss in AE2 has low probability of being' proceeded by an ana::iolous loss in AEl:the two particle signals PI1 and PI2 are independent. Thus although the window in PI2 may contain tails from other groups ,the particles will be correctly identified in the gated PI1 spectrum as shown in fig.l. The resulting improvement in the identifier information is marked. * Department of physics,University of Bangalore References DN.Anyas-Weiss et al.Oxford University Report 66-73 2)A.Chatterjee et al,Proc.Nucl.Phys.(D.A.E),Dec. 1990 • 73 M«V Rh; 'RAW. — RAW -GATGATEE D OM'°C — G.STED ON Be IH PI 3 IM PI 3 V 10 1 3O t>\ 1 (CHANNELS; 326 AT EXPEKiriTlNTAIL TECHNIQUE ?0L THE JTVUI OF HEAVY III THE A.P.uharma Department of Physics, ^. x.. University, Aligarh-202002 "he identification of heavy ions vith charge 3 ^ 1£ car ec-cily be done v.'ith the help of "meteo- ritic cryo-cal detectors'.'A new partial annealing technique hr.L been developed for eliminating the .lover heavy ion charge spectrum of galactic cosmic ra.;, tracks irpto charge Z $• 50 in order to reveal the higher charge spectrum ( 2 > 50) of Uranic-Transur^nic element ueries and superlieavy elements (iillE) of charge, Z-^114. For calibration purposes'the non- relativistic energy ace elerators/cyclotrons have been used for accelerating the heavy ions of charge upto Z=92 (uranium ion) and'the volume tracks so formed due to these ions in raeteoritic detectors have been measured. The detectors were partially annealed under various annealing, conditions causing a track length reduction of volume tracks under these different annealing conditions. This nevj technique of partial annealing and the caliber&tion curves have revealed about 700 uranium -transuranic group tracks alonguith 6-7 ouperheavy element (SHE) tracks in Kature (Cosmos) having charge spectrum in the range Z*^* 110-120. Yhe charge assignment for various cosmic ray tracks ha- been done with the help of known track length Vs charge calibration curve :-.n& using an extrapolation beyond U-±on range tioint. ( 327 .4- 10 Extrapolated i/ curve beyond Under Uion g2 , y annealing conditi: 23S /-i/ r-1 ? •- • r_~ fCurve dueto fresh J accelerated I heavy Ions u 132 V -270 60 8O ICO Heavy Ion charge (Z? — :. l Dependence af etchahle track length on heavy ion charge (Z) in olivine crystals of meteorites 328 SIMPLIFIED RELATIONS FOR THE CALCULATIONS OF ENERGYLOSS RATE & RANGE OF HEAVY IONS IN PHOS- PHATE AND QUARTZ GLASS DETECTORS Shyara Kumar, S.K.Sharma & A.P.Sharma* Department of Physics, K.U.Kurukshetra-132 119 * Department of Physics, A.M.U.,Aligarh-202 001 In recent years, the Solid State Nuclear Track Detectors (SSNTDs) are increasingly being used in different branches of nuclear science & technology. For the calibration of any sclid state nuclear track detector, the knowledge of accurate range-energy and energyloss relations is one of the essential requirements. In the present work, the calculations of energyloss rate, dE/dX and range, R for «°»:?cP' 40 Ar, JJfca, ISTi,5SjPe, \* Kr and 1|? Xe ions with 18 20 B* *° JO 3* energy ranging from 1 to 50 MeV/N in phosphate and quartz glass detectors have been computed theoretically using Hukherjee and Nayak stopping power equations (1). The results obtained from these equations are in close agreement with the experimental results . These calculations are very combersome because of the involvement of many parameters (1). To avoid these combersome calculations, we have tried to develop some simplified empirical relations presented in Table-1 between energy- loss rate dE/dX, the corresponding energy E and the charge Z of the incident particle for phos- phate and quartz glass detectors. A comparison between energyloss rate, dE/dX calculated from Mukherjee & Nayak stopping power equations (1) and those predicted from newly developed empirical relations for various heavy ions with different energies clearly indicates a close agreement (Figures not shown). The values of X*between the values of dE/dX calculated rrc.- chose two ;:?L>.o: .:; .(.•.-; -' .> J v lues ol: *•.".../•>..,. lave ..•.."-•;•! ioun- to \JC l-'l.l and 15.5 for phosphate: anc; 329 quartz glass detector*respectively. These values are even less than X*©.o| (the critical value of X* at 0.99 level of significance). Hence/it is inferred that the agreement between the values of dE/dX determined from the two methods is quite excellent and these newly developed empirical relations can be used nicely for the calculations of energyloss rate dE/dX and range R of heavy ions in Phosphate and Quartz glass detectors. Table-1 Empirical relations for energyloss rate, dE/dX & range calculations for heavy ions in Phosphate and Quartz glass detectors. Energy Phosphate glass Quartz glass detec- Regions detector tor (MeV/N) Energyloss rate, Energyloss rate / dE/dX dE/dX (MeV mg*"^c (MeV mg"1 cm2) dE „ 1.001 z0.99 dE 1.101 z0.995 dX -0. 59*3 E dX E-0 .379 dE „ 0.289 zi-49 dE 0.313 21.496 dX E0 .269 E0.286 21.83 1 829 E2 Where = 0.300 z0*586 MeV/N and 1 336 E2 = 0.060 Z * MeV/N REFERENCE: (1) S.MukS.Mukherjej e & A.K.Nayak NuclNl . InstIt . & MetMthh 159, 421 (1979) 330 RAt,GC-Ct..~RGY RELATION FOK ELECTRONS OF EKERGV LESS THAN 10 KeV SARITA.n.Agraual.P.B.Pal*\/.P.Varshney S.V,College ,Aligarh Introduction— Electrons traversing through matter lose their energy by alastic collision uit.i atomi nuclie and by inelastic collision with atomic elect rons of tha medium .In low energy region ^ICKeVof intarcst tho energy loan is mainly duu to inelastic collisions. Theoretical expressions ha^c been deriv ed for space rate degradation of energy and CSDA • — range values were calculated and tabulated. Range . of electron* iifc matter were also measured experim- entally and range-energy rela-tions were propose?. Zn order to reduce computing tims and the memory space required for calculations,it is convenient and to have an analytical relation between RpSrn energy E.The present papes descxives a. x> .'•-. vei id for electrons in rare gases-. Description - The woxkexS have proposed an A : cal relation between extrapolated range Rex av>d En ergy C fox 20 eV/- lOKeV elactrona in all absoxving Media.Th« calculated results have large descripano/ upto 25%. We propose here an empirical expression^ for CSDA range of" electrons in rare gases in the fox» 2 3 lr»(RCSDA) . AQ + A., lnE + f>2 (lnE ) + AgtlnE) where "rqpft i» *" gm/cm ,E is in HeV , AQ ,A^ fA2 and A3 are parameter*, which mre Z dependent. Zn determining the values of these parameters in proposed expression , least square fit has- been mads to the values of flrcn. tabulated by J.A.La Verne : and A.Dozumder. . ._. Results and Discussion. The parameters obtained a» n listed in Table 1. The calculated values of CsnA in He, f'e, Ar, Kr, and X^usin-j proposed empiricHl relation are listed in Table 2.The calculated resul ts are in- good agreement within a discrepancy less than A%. 331 The proposed relation ia also applicable to deter- mine -the stopping power of the absorber, and thit s*- udy is in progress. Table 1 A A fledium Atomic: No A,] 1 ' 3 He 2 + 1.1334 +2.0855 -0.,0196 -0 .CD 64 Ne 10 \i .4753 +3.5960 +0..2058 +0.0 C24 Ar ie -1 .5565 +0.8063 -0.,1806 -0 .0 333 Kr 36 + 0 .2875 +1.6522 -0..0280 -0.0049 Xe 54 + 1 .7685 + 2.3C1G8 +0..0708 +0.00 00 Table 2 Cncr^y The or •2 Calc. "t^Jev. Th«or. Calc • $Oev Helium I eon 10G 0.410 0.416 + 1 .46 2 .01 ?.C-C >2 .48 200 0.611 0.782 -3 .5? 3.11 3.11 5C0 2.19 ?.2.? + 1 .37 5.8? 5.64 + 0 .34 1 11/1 ii jt 1C0O 5.58 5 .67 .61 • i.H 11. 't 2000 16.2 16.1 -0' .T7.3 --7.3 —— , IUm 5000 75.9 74.4 -1 .97 109 109 __ 10000 257 261 + 1 .17 343 349 •^1 Argon Krvpton 100 3.90 0.89 -e.67 1.42 1.30 -2 .92 200 1 .Qi 1.64 +1 .23 2.69 ?.76 + 2.60 500 4.-59 4 .60 + 0..22 7.97 7.93 -G .50 1000 11 .8 11 .6 -1,.63 19.6 19.3 -1 .53 2000 31.B 31.8 — 50.5 5G.6 +o .20 5000 131 133 + 1,.52 197 199 +0 .51 10000 4 \2 408 -0,.97 590 5B0 -C.34 Xenon 100 1 .45 1 .44 -0..69 2CO 3.06 ~> rj Q -i. ,20 50G 6.56 C.73 + 1..87 1000 20.7 '1 .2 + 2.,41 20CU 56.0 55.1 -1 ,£.-„. ' 5u0ii 220 216 -1 ..00 10OUG 64B 656 + 1.,23 jt- Authors ar: thanU "ul to Dr. D .K . r.upti, Principal, S . V .Colle_}•». .Mirjarh for contribw utoi-y di^cutitii ons on the present work. flefcronces- TT~jTn 7C.A~Vi.-rno and II Jlozumdirr, J .Phys . r.lvm . 2.J.H.Your»g. J.Appl. Phys () 4 .11 . J .Ki1.ti.iiij, I'liyu. #,t..iL. '.ull. .l.( VJ/4) 'ji"J> 'j.ll . lakuf, J.U.CumiiinjI.cuii Jrcl fl.f" .Wjtt, I'liya .Pl.;«l .Hinl Li— Oept. oF Phys , Canjdunduara Colley a, f-tah(2U724'.') 332 TOTAL STOPPING POWER IN LOW ENERGY ELECTIONS MANORANJAN AGRAWAL, P.Q. Pal*, D.K. Gupta, & V.P.Varshney Department of Physics, S.V. College, ALIGARH-202 001 INDIA. The sum of the mean energy loss per unit path length due to ionization (1,2) and radiation (3) is called total stopping power. Total stopping power of electrons in different absorbers are commonly required for many applications in nuclear Physics. An extensive study of stopping power for electrons in high energy region has been done by many workers (4-9), but in the low energy region it.is still comparatively less studied. Berger and seltzer (10) tabulated the energy losses and ranges of electrons in several elements and compounds. Kim et al«(ll) have given an approximate scaling law for the ratio of positron to electron brems strahlung loss which reveals that the difference between the radiative energy loss of positrons and electrons is considerable for energy region from 10 KeV to 500 KeV in heavy element.;. Batra (12), reported empirical formulae for stopping power of electrons in energy 1 KeV to 500 KeV. We have derived simple empirical expression for rapid estimation of the total stopping power of electrons in energy region from 1 KeV to 800 KeV for elements and compounds upto Z=92. This expression is based on the fact that the total stopping power is the product of energy and atomic number dependent terms. Relation is defined as where E • (T+m.C ) is the total energy of electron-, T is 2 the K.B. of electron in KeV, rooc is rest mass energy of electron, is the total energy of electrons in rest mass energy unit and Z is the atomic number of target. All the constants n,c, and D are obtained by least squares fitting methods and are listed in table . kinetic energy Atomic Number n c D T (KeV) (Z) -19.4169 7.4982 1.1766 - 3.2627 4.2928 0.5151 - 3.6600 5.1792 0.7551 - 0.2893 2.2126 0.2198 This relation is applicable in both elements and compounds if Z (element) is replaced by Ze^ (compound) and gives satisfactory results. •Present Addressi Physics Deptt. Ganjdundwara College, Ganjdundwara (Etah). 333 The comparison between theoretical values (10) cn.il calculated values by our equation is shown in graph for only elements C, Al, Cu, Ag and u in the energy reaion upto 800 KcV. The deviation between theoretical and calculated values is less than 5% for Al (3 XeV to 600 KeV) Cu (60 KcV to 600 KeV), f% for Silver (10 KCV to 700 KeV) and 1% for Carbon (<10 to 700 KeV). Berger and Seltzer (10) have mentioned 3topping power values from 2=1 to 10 absorbers only in the energy region below 10 KeV, while we have calculated these values upto 2=92 absorbers in the same energy region. The application of X-rays curing transmission through human bodies, plants, solutions and compounds produces polres of electrons and positrons. The electrons thus formed may have energies less than 1000 KeV, which on collision with tissues and cells of our body may cause significant changes. This work is helpful in the study of these biological h REFERENCES t«i >» i-'or <•>«»>-, (11 F. Rohrlich, B.C. Carlson Phys Rev. 93. (1953) 38 (21 H.A. Bethe. Ann Phys 5 (1930) 326 (31 H.W. Koch, J.M. Motz Rev. Mod.Phys. 31 (1959) 920 (!) R.K. Batra, M.L.Sehgal Mucl Phys A-liTS* (1970) 319 (5) R.K. Batra, M.L.Sehgal Nucl Inst.& method 109(1973)565 (6) ft.K. Batra, M.L.Schgal Nucl Phys A-196 (19757 638 (7) S.K. Gupta & D.K.Gupta Jap. J.App.Phys. _19 (1980) 1 (S) P.B.Pal, V.P.Varshney,D.K.Gupta Nucl.Inst. & method B-16 (1986)1 (9) P.B.Pal, V.P.Varshney,D.K. Gupta Ind.J.pure & ApD.phys 2± (1986) 300. (10) M.J. Berger & S.M.seltzer Nat.Bur.Stand, report Mo. NBSIR 82-2550A (1983) (11) L.Kim,R.H.Pratt et al Phys.Rev. 33A (1986) 3002. (12) R.K. Batra Nuci.lnst. h methods D~^2"8 (1907) 195. 334 STOPPING POWER RELATION FOR LOW ENERGY POSITRONS MANORANJAN AGRAWAL, P.B. Pal*, D.K. Gupta & V. P. Varshney Physics Department, S.V. College ALIGARH - 202001 - INDIA. A new relation for the total stopping power of positrons of kinetic energy (T) less than 900 KeV has been found. Using this formula, the values of the total stopping power of positrons have been calculated for all absorbers of atomic number from Z * 1 to 92. These values are in good agreement with the theoretical (1) and approximate values (2). Total stopping power is defind as the sum of the mean energy losses per unit path length due to ionization (3,4) and radiation (5) losses. The simple relations for the stopping power of positrons in different absorbers are commonly required for many applications in surface layer analysis, semi-conductor detectors, radiation technology, nuclear spectroscopy etc. Many workers (6-11) have done a detailed study of stopping power for positrons in high energy region but low energy is still less studied. Bremsstrahlung losses in heavy elements for low energy region have been reported by kim et al. (12)« Batra (2) has xoportod empirical formulae for stopping power of less than 500 KeV positrons. We have used the fact that the total stopping power is the product of energy and atomic number dependent terms. Sirailer expressions have also been derived for stopping power of electrons (13) in the energy region 1 Kev to 800 KeV ID both elements and compounds. The present relation is expressed asi With Q - y is the total energy of electrons in rest mass energy unit, E • (T+moc ) is the total energy of electrons. mQC i8 the rest mass energy of electron, Z is the atomic-number of absorber. All constant n, c and D are obtained by least squares fitting methods for -Z^92 and are listed in table . K. E.T. (KeV) n c D 10-^T^70 - 4.71543 5. 4682 0. 77693 70=^T^400 - 0.76864 3. 0898 0. 39358 400^T^900 - 0.11555 2. 3 288 0. 30994 •Present adress t Physics Deptt., Ganjdundwara College Ganjdundwara. ETAH (U. P.) INDIA. 335 our expression is applicable in compounds also if Z(element) is replaced by Z f, (Compounds), while Batra (2) has mentioned two separate equations for elements and compounds respectively. The comparison between theoretical (1/, approximate (2) and calculated values by our equation is shown in graph for only some elements like C, Cu and Al in the energy region from 10 KeV to 900 KeV. It is noticed from fig. that calculated results are more closer to theoretical results (1), compared with approximate values (2). The deviation betu-een theoretical and calculated values is lass than 5% foe Carbon (20 to 400 KeV), Cooper {20 to 900 KeV) and Silver (80 to 700 Kev). These stopping power values may be used to estimate the ranges of positrons in matter and the effect? of multiple scattering on the total path length of the positrons in different absorbers. The present study is also helpful in medical research by observing the effect of radiation on tissues of body. e L L 3- SH*«r i o a. a a o Energy (KeV) Referenceqt (1) M.J. Berger, S.M. Seltzer, hot. Bur. stand. Report no. NB5IR 82-2550 A (1983) (2) R.K. Batra Nucl. Inst. & Meth. B. 26. (1987) 195. (3)P. Rohrlich, B.C. Carlson Phys. Rev. 9J, (1953) 38. (4) H.A. Bet he Ann. Phys. ,5. (1930) 3 26. (5) G.W. Koch, J.M. Motz Rev. Mod. Phys. 31 (1959) 9 20. (6) R.K. Batra, M.L. Sehgal, Nucl. Phys. A-156 (1970) 319. (7) R.K. Batra, M.L. Sehgal, Nucl. Phy3. A-196 (1972) 63 8. (8) R.K. Batra, M.L. Sehgal, Nucl. Inst. & Meth. 109(1973) 565. (9) S.K. Gupta, D.K. Gupta, Ind. J. Pure Appl. Phys. 12 (1979)775. (10) P.B. Pal et al. Nucl. Inst. & Meth. B-16 (1986) 1. (11) P.B. Pal et al. J. App. Phys. (U.S.A.) 60 (1986) 461. (12) .L.Kim, et al. Phys. Rev. 33_A, (1986) 3002. (13) M. Agrawal, P.B. Pal et al. Ind. J. Pure Appl. Phys. (in press). 336 CONTRIBUTION OF PAIR PRODUCTION PROCESS TO THE EFFICIENCY OF Ge DETECTORS M.Sudarshan and R.Singh Physics Department, NEHU , Shi 1long-793003 For a precise determination of the intensities of ^-rays an accurate measurement of the full energy peak efficiency (FEPE) of the gamma detector is required. Since the FEPE is measured at discrete and, to some extent, arbitrary energies the basic data points atre fitted to seme appropriate analytical function or semi—empirical formula and the required FEPE values are read from the fitted curve. Many such functions and formulae exist in literature Cl-33. As 3a result of such an investigation for a 38cm coaxial Ge 337 (1) and (2) for representing the FEPE of the 38cm Be(Li) detector reported by Singh E2D and of the 68cm coaxial HPGe detector reported by Owens C3H. The best fit curves for the 38cm tee(Li) detector are are shown in Fig.l. The degree of improvement in the FEPE representation above 1360.25 kev, where pair production plays an important role, by the two formulae after incorporating the pair production term is indeed striking. The agreement (using eqn.i) turns out to be within^/5—10% ebove 1360.25 kev y~ energy. The quality of fits was the same when the FEPE data for the 68cm HPGe detector from 223.430 to 3253.610 kev [3D were employed. Thus by incorporating a term like ex in the semi-empirical formulae of refs. 4 and 5, it is possible to adequately account for the contribution of y—absorption by pair proovction to the FEPE of the Ge detectors. f: FEPE of o 38 cm' Ge (Li) Derec'or r *? cf e^n. U) * ixta at eca ill *•(» » o i ;oo :;co uco Ref er enc es 1. L.A.Macnelles and J.L Campbell, Nucl. Instr. Meth.109 (1973) 241. 2. R.Singh , Nucl.Instr. Meth.136 (1976) 543 3. A.Owens , Nucl.Instr. Meth.A274 (1989) 297 4. J.M.Freeman and J.G Jenkin, Nucl.Instr.Meth.43 (1966) 269. 5. T.Paradellis and S.Hontzeas, Nucl.Instr. Meth. 73 (1969) 210. 338 DATA-ACQUISITION SYSTEM WITH SERIAL LINK TO PC(XT) A.L.KHANDWE AND V.M.MISRA COMPUTER DIVISION,B.A.R.C. BOMBAY 400035. The system consists of data acquision memory* control block and programmed serial data transfer unit. The present system is designed to interfac-:- an ADC module of Nuclear Data,Inc,U.S.A.(/I/).Any other ADC module including in-house developed ADCs (50MHs & 100MHz)with known inputs and outputs can also be interfaced.This is a self contained system with serial RS232C link to PC(XTJ.Many a times an off-line serial data transfer is adequate and cost effective. The system interface to PC(XT) requires software cotrol at transmitting and receiving ends.As data acquisition has an organisation of 8K*24bits,ADCs upto 13bits are compatible and per channel count- capacity is (2~24-l)counts.Acquired data display for programmable region on seven segment LEDs and EPROM programmer are part of the system (/2/). Application software in BASICA to receive data in PC(XT),using its serial communication adapter,has been developed and summerised into three group,vis, a)creation and storage in random access/sequential files,b)display on PC-monitor and Hardcopy in decimal notation and c)display ofa plot(counts vs ch.no.)on PC-monitor from data files. It is to be noted that the data transfer is byte- wise whereas PC(XT) serial adapter converts received byte into decimal equivalent and tem- -porarily stores in screen buffer'. As data word length is 3bytes,three decimal equivalent/byte are recorded in a file and later converted into a single equivalent decimal number which corresponds to a particular memory location.Parameters like data transfer rate,file-sise(upto 8K),counts in decimal/hex notation etc. are programmable. 339 The plot between counts vs ck.no. is displayed on PC-i:icnitor with suitably reduced scales both on x and y -axesCriig:! resolution: 640*200) .Any portion of the plot, can be viewed on expanded scale on any one or both axes as desired and is programme selectable. Ref erences •" /I/ Hardware Instruction Manual for ND560 ADC, Nuclear Data ,Inc. /2/ Interfacing an ADC to PDP 11/23 Computer by A. L. JIhandwe and V.M.Misra at National Symposium on Nuclear Electroics and Instrumentation held on Fet.15-17,1989,Eombay. 340 DEVELOPMENT OF INDIGENOUS WILKINSON TYPE ADCs(50/100MHz) V. M. Misra, A. A. Nadane, V. Geetha, M. D. Mahajan, L. S. Rajput Computer Division, B.A.R.0. Varying analog outputs from different sensors and transducers are processed very commonly in digital computers. Analog to digital converter (ADC) and interface to couple it to IBM PC are important links between analog variables and digital computers. Wilkinson type of ADCs are still very accurate and a must for Nuclear Spectrometry. Many designs of these ADCs are available and as the speed and resolution of these ADCs increase, complexity of the design, development, proper layouts and testing procedures also become very important and complex. The authors have earlier experience of designing many models of Wilkinson type ADCs. A 50 MHz,11 bit ADC, in single bit NIM module has already been designed, developed and prototype engineered(Ref l)and six such units have been delivered for use in the experimental set up for the position sensitive detector system at Solid State Physics Division. All the units have been subjected to detailed testing including DNL and stability measurements. DNL of +/- 1% or better and stability of +/- 1 channel has been achieved. After the feedback from the user, it was found that the performative of these ADCs at the experimental set up has been quite satisfactory. More units are being now fabricated for testing and installation at users site. Encouraged by the above results Emci as a second phase, trie development of a 100MHz ADC was undertaken. First prototype model h-:is been tested vid the performance is found satisra-f'.ory in the laboratory. Now three such units ttr? fabricated and wilJ b-.- tested in detail for a.~:~-rtaining the repea cab i 1 i ty ~.t' the resu 1 t v . 341 The completed unit is undergoing detailed testing. The test results will be reported shortly. Presently the work for upgrading the present models by reducing the discrete components and incorporating the recent and the state-of-art components in the design is also in progress. References: 1. Misra V. M. et.al. "Our Experiences in the Design of Wilkinson type ADCs", National Symposium on Nuc.Elec. & Instrumentation,Bombay Feb. 15-17, 1989. 342 ANALYSIS OF Fe AND Ti BASED ALLOYS FOR ZIRCONIUM CONTENT BY 14 MeV NAA G. R. Pansare P.M. Dighe, and V.N.Bhoraskar Department of Physics, University of Poona, Pune-7 ABSTRACT 14 MeV neutrons were bombarded on natural zirconium and formation cross section of Zr-90m was measured. The result is used in estimation of concentration of zirconium in iron and titanium based alloys. Estimated values of zirconium in standard samples are in excellant agreement with the expected values. INTRODUCTION : The low value of thermal neutron absorption cross section (0.18b) has made zirconium most attractive from point of view of reactor applications. In addition zirconium has good corrosion resistance which has made it useful in industrial applications. For several applications it becomes necessary to know the exact concentration of zirconium in a given sample. Keeping this in mind we have analysed a few samples of Fe and Ti based alloys and estimated the zirconium concentration using the measured value of formation cross section of 9vmZz. EXPERIMENTAL : The nuclear reactions used in this analysis are 90Zr (n,n)90mZr and 90Zr(n,2n)90mZr. The formation cross section of 90mZr was measured in this laboratory using 99.99% pure zirconium oxide powder. Samples were prepared by packing (400 mg) fine powder of alloy along with pure (99.99%) aluminium foil in polyethylene bag. Each sample was irradiated seperately with 14 MeV neutrons of flux - 2 X 108n cm"2.sec"1. Since the half life of product nuclei, 90mZr, is small (0.8 sec) cyclic activation method was employed for analysis. For neutron flux measurement the reaction used was 27A1 (n,oC)24 Na 343 The induced gamma activities due to zr produced through the reactions 90Zr (n,n)90mZr and 51Zr(n,2n)90mZr, and 24Na produced through the nuclear reaction ^hl (n,»C) ^Na, were measured by a HPGe detector coupled to a 4096 channel analyser. For each sample the number of activation cycles were 100. Activation cycle was as follows irradiation time - 5 sec, cooling time - 1 sec, counting time - 5 sec, waiting time - 10 sec. The measured value of the formation cross section of 90mzr is 480+30 mb. Concentration-'- of zirconium in different alloy samples are given in tables I & II. n Table : I Concentration of Zr(%) in Fe based alloys Sample No. F-10 F-11 F-12 F-13 F-14 F-15 STD 0,.01 0,.15 0..05 0,.11 0.25 0.03 NA 0.,02 0..13 0..10 0,.12 C.26 0.05 Table : II Concentration of Zr(%) in Ti based alloys Sample No. T-10 T-ll T-12 T-13 T-14 T-15 • STD 3,,00 2.,00 6..50 5.,00 4.00 1.00 NA 2. 43 2. 03 6.33 4. 64 3.97 1.04 STD : Standard values NA : Neutron Analysis The results indicate that our method of analysis is accurate, quick and does not need much sample handling. There is also no need to change the physical form of the sample. ACKNOWLEDGEMENT : Thanks are due to the DRDO Ministry of Defence, New Delhi for the financial support. REFERENCES : 1. S. Amemiya, V. N. Bhoraskar, K. KATOH and T. Katoh, J. Nucl. Sci. and Technology, 18 (1981) 323 344 AUTHORS. .NAME Page No. ABONDANNO. U. 203 AGARWAL, Y.K. 1,97,105,107 AGRAWAL, BIJAY 11 AGRAWAL, H.M. 151 AGRAWAL, M. SARITA 331 AGRAWAL, MANORANJAN 333,335 AHMED, ZAFAR 143,219 AMBEKAR, V.S. 117,119 ANAND, R.P. 113,129,131,155 ANSARI, M.A. 123 ANSARI, A.R. 249 A?TE, P.R. 303 ARORA, B.K. 77 ASHOK KUMAR 135,185,187,189, 191,193,197 BABA, C.V.K. 97,105,107 BADIGER, N.G. 325 BANIK, D. 3 BANERJEE, A. 93 BANERJEE, S.R. 125,127 BANDYOPADHYAY, A. 295,309 BANDYOPADHYAY, ARUP 295 BANDYOPADHYAY, D. 137 BASU SOMAPRIYA 3 BASU, M.K. 91 BASU, P. 117 BASO, D.N. 173 BASU, S.K. 295 BERA. P.K. 177 BETIGERI, M.G. 325 BHATTACHARYA, R. 75 BHATTACHARYA, P. 117 BHATTACHARYA, S. 117 BHAGWAT. K.V. 141 BHARDWAJ, H.D. 165 BHARDWAJ, M.K. 121,163 BHATNAGAR, V.K. 185 BHATNAGAR, P.K. 189,191 BHALLA, K.B. 267 BHATTACHARYA, N.C. 295 BHORASKAR, V.N. 131,297,343 BISWAS, D.C. 117, 119 RONSIGNORI, G. 31 34-5 BURTE, P.P. 115 CALEB CHANTHI RAJ, D. 13,85 CHATTOPADHYAY, S. 1,97,295 CHATTERJEE, J.M. 3 CHATTOPADHYAY, R.K. 3 CHAND, B. 73,79 CHATTERJEE, A. 99,101,109,30b CHAKRABARTY, D.R. 103,105,107 CHATTERJEE, M.L. 117 CHAUBEY, A.K. 121,163 CHATTERJI, J. 127 CHATURVEDI, L. 153 CHAUDHURI, A.K. 269 CHAKRABARTI, A. 295 CHARAGI, S.K. 325 CHEEMA, T.S. 77 CHINTALAtJDI, S.N. 5,83,127 CHIKARA, B.K. 57 CHITRA, A. 63 CHOUDHURY, R.K. 105,109,117,119,129, 131,155 CHOWDHURY, S.K. 235 CINDRO, N. 203 DANGE, S.P. 211 DASGUPTA, S.S. 161,171 DAS, A. 247 DAS, B.K. 231 DAS, U. 177 DAS, SWAPAN 271,287 DASGUPTA, P.K. 309 DASGUPTA, M. 1,97 DATAR, V.M. 103,105,107 DATTA, S.K. 127 DATTA, S.S. 159 DATTA, S. 203 DATTA, T. 211 DE, J.N. 137,217 DE, S.K. 309 DEVI, Y.D. 17 DEVARE, H.G. 41 DEY, C.C. 75 DHOLZ, S.D. 297 DTGHE, P.M. 34.3 DTNKSH, B.V. 119 ESWARAN, M.A. 103 2,46 ESWARAIAH, K. 187,189,191,193 FERNANDES, W.A. 323 GAMBHIR. Y.K. 31,285 GAUTAM, R.P. 163 GAUTAM, A.K. 233,257 GEETHA, V. 341 GHOSH, S. 125 GHOSH, B. 241 GHOSH, S.K. 277 GILL, A. 267 GODIYAL, RAVI DATT 135,187,189,191,193,197 GOEL, ALPANA 45 GOVIL, I.M. 159 GOSWAMI, ASHOK 115 GOSWAMY, J. 73,79 GOSWAMI, K. 223,225 GOSWAMI, T.D. 223,225 GUPTA, J.B. 15,35,51,53 GUPTA, D.K. 37,39,333,335 GUPTA, K.K. 37,39 GUPTA, RAJ K. 145,213,215 GUPTA, S.K. 271,287,325 HOFF, R.W. 7 HOSANGADI, R.R. 319 IYER, R.H. 111 IYENGAR, K.N. 113 JAIN, B.K. 245,265 JAIN, H.C. 1,97,105 JAIN KIRAN 9,43 JAIN, ASHOK K. 7,9,43,45 JAIN, ARUN K. 169 JAIN, ARVIND 315 JANA, A.K. 179,181 JANHAVI, G. 273 JHINGAN, M.L. 1,97 JOHN, B. 99,101,115 JYRWA, B.M. 195 KAILAS, S. 99,101,109 KALPANA 3ANKAR 65 KALSI, P.C. 111 KAMALAHARAN, B. 61 KAPOOR, S.S. 101,109,113,115.117 129,131,155,293 KAR, K. 3 KARMAKAR. S. 161 4-7 KATAKIA, S.K. lul, lib. 139,141.199,30 KELKAR, NEEL.1MA G. 245 KKREKATTE. S.S. ^9 KHAMDWE. A.L. 3 3 y KHAN . Z . A . 20 7 KHAliKIKAR, & . B . '<-: 3 2397, , 253 KH .1 •' MMKHKR. Jp'Ii] S M 7 ', • ,'.'.t • • '•iUKHOpADHYAY, T. ::•.)!; MUKHuH HYAY, M.K :•]! MURTHY, G.S. KRISHNA 5 MURTY, G.S.K. 83 MURUGESAN, K. SAKTHI 275,281 MYTHILI, S. 325 NADANE, A.A. 341 NADKARNI, D.M. 109,113,117,119,129,131 NAG, R. 243 NAIK, H. 211 NANAL, V.S. 303,323 NARVEKAR, S.D. 319,321 NAVIN, A. 97,99,109 NAYAK, B.K. 105,109,119,305 NAYAK, R.C. 87 NTJASURE, A. 99,101,115 NIMJE, V.T. 293 OJHA, I.D., 284 OZA, H.H. 103 PADMINI, M.D. 201 PAI, V.N. 183 PAL, U.K. 103 PALSANIA, H.S. 267 PAL, P.B. 331,333,335 PANDEY, A.K. 111 PANT, L.M. 119 PANDYA, S.P. 21 PANDA, P.K. 27 PANSARE, G.R. 343 PARDHASARADHI, S.K. 3 PARIKH, J.C. 19 PATRA, C.N. 211 PATI, A.K. 289 PATRA, S.K. 27 PATRO, A.P. 313 PHATAK, S.C. 241,255.277 PHILOMIN RAJ, S.I.A. 59 PILLAY, R.G. 301,317,319,321 POLEY, A. 295 FOTBHARE, V. 25 PRASAD, R. 37.39,123.165 PRASAD, K.G. 301.303.319.323 PRAHARAJ, C.R. 11,33,55 PRAKASH, P.M. 31 3 PtlKT, RA.TKEV K. 213.215 RilTTASWAiMY. N. (J. 175 RADHA KRISHNA, K. 33 RAGOOWANSI. N.L. 103 RAJASEKARAN, M. 13,85,209 RAJASEKARAN, T. R. 209 RAJPUT, L.S. 341 RAMAMURTHI, K. 65 RAMAMURTHY. V.S. 109,139,199,229 RAO, M.V.S.C. 5,83 RAO, BHASKARA K. 81 RAO, SESHAGIRI V. 81 RAO, Y.S.T. 93 RAO, MOHAN A.V. 153 RAO, RAMA J. 153 RASHID, M.H. 311 RATH, A.K. 33 RAVI KUMAR, G. 5 RAY, S. 125 REDDY, BHULOKA S. 83 REDDY, A.V.R. 115 RIZVI, I.A. 121 RODRIGUE8, G. 311 ROY, B.J. 325 ROY, A. 1,97,105 ROY, A. 309 ROY, SUBINIT 127,167 RUDRA, P. 67 RUDRA, N. 137 SAHA, M. 23 SAHA, ASOK 89 SAHOTA, G.P.S. 159 SAHOTA, H.S. 159 SAHCJ, B. 195 SAHU, K. 205 SAHU, S. 255 SAHU, R. 21 SAHU, PRADIP.K. 205 SAMADDAR, S.K. 137,217 SAMANTA, C. 125,167 SAMANT, M.S. 129,131,155 SANTRA, A.B. 265 SANYAL, S. 243 SARANGI, P. 205 SARANGI, SUBRATA 19 SARKAR, SASABINDU 235 SARMA. P.R. 299 SASTRY, S.V.S. 109, 119, 141, 19.9 SASTRY, D.L. 5,83 SATHYAVATHIAMMA, M.P. 175 SATPATHY, L. 205,229,247,259 SATPATHY, R.K. 231 SATPATHY, M. 247 SATYA PRAKASH 115,211 SATYANARAYA, G. 5,83 SAVOIA, M. 31 SAXENA, A. 101,109,117,307 SEN, S. 23 SETH, MADHUP 135,187,197,193 SETHI, R.C. 291,293 SHANMUGAM, G. 59,61,63,65,201 SHARMA, A.P. 279,327,329 SHARMA, S.K. 329 SHARAN, M.K. 105 SHARMA, R.C. 111 SHARMA, O.D. 149 SHARMA, S.D. 49,159 SHARMA, R.P. 3 SHARMA, D. 49 SHARMA, ARAVIND 49 SHARMA, PRAVSEN 49 SHARMA, SATENDRA 51 SHARMA, V.K. 57 SHASTRY, C.S. 195 SHEIKH, J.A. 55 SHELINE, R.K. 7 SHIROMANI, A.K. 233 SHYAM KUMAR, 329 SINGH, R- 337 SINGH, HARIKESH 25? SINGH, C.P. 261,263 SINGH, S. 261,263 SINGH, R.L. J61.263 SINGH, BHAGWAN 267 SINGH, R.N. 283 SINGH, B.K. 284 SINGH, H. 121,163 SINGH, H.M. 149 SINGH, N.L. 153 SINGH, C. 157 SINGH, G. 3 INCH, B.P. 159 SINGH, PRAGYA 165 41 351 iUNGH, N. 73,79 SINGH, F. 99,101,109 SSINHA. AMAK 227 L'.INHA. PIYUSH 69 SINHA. B.K. 75 LvOOL), p . 0 . 7 tiKI KANT I AH. K.V. 325 SR1NIVASAN, B. 317 SRINIVASAN, M. 227 SRIVASTAVA, B.B. 69,149,189,193 SUBKAMANIAN, P.R. 273,275,281 SODARSHAN, M. 337 SUDHEENDRA, H.S. 175 SURESH KUMAR 103 SWARUP, R. 283 TALUKPAR, B. 181 TANDON, P.N. 301,319,321 TAYAL, D.C. 157 THAKUR, N.M. 291,293 THIAGASUNDARAM, M. 63 TOMAR, B.S. 115 TREHAN, P.N. 73,79 TRESSLER, N. 25 TRIBEDI, L.C. 301,319,321 TRIPATHI, S.N. 284 TULI, S.K. 284 TYAGI, R.K. 37,39 UMA MAHESWARI, V.S. 229 USMANI, Q.N. 29 VARMA, R. 105 VARSHNEY, A.K. 37,39 VARSHNEY, V.P. 39,331,333,335 VERMA, S.R. 185 VIJAYAKUMAR. K.B. 237,239.251,253 VIMEET KUMAR 305 VINODKUMAR. P.O. 239 352.