Fifth International Conference on High-Energy Physics and Nuclear Structure

Fifth international Conference on High-Energy Physics and Nuclear Structure

Uppsala, Sweden, 18-22 June 1973

CONTRIBUTED PAPERS

Editors: S Dahlgren 0 Sundberg G Tibell Ten years ago the first international conference on High Energy Physics and Nuclear Structure was organized atCERN, jointly by CERN and the Weizmann Institute. After meetings in Rehovot (1967), New York (1969) and Dubna (1971) the turn has come to Uppsala for conference number five in the series. The interest in the field covered by this type of conferences, on the borderline between high-energy physics and nuclear structure physics, seems to persist and we present in this volume a large number of papers submitted to the Uppsala conference. By and large the division into chapters follows the evolution of the conference program. The conference was organized by an International Advisory Committee in con- junction with a Swedish Organizing Committee, the latter with headquarters at the Gustaf Werner Institute, University of Uppsala. Financial support for the organization has been obtained from the following IUPAP, the International Union of Pure and Applied Physics The Royal Swedish Ministry of Education and Cultural Affairs The Swedish Atomic Research Council The University of Uppsala The City of Uppsala The conference is also sponsored by the European Physical Society and the Swedish Physical Society. The organizers gratefully acknowledge the full support of the Rectors of the University of Uppsala, Professor T Segerstedt and of the Agricultural College of Sweden, Professor L Hjelm, for the local arrangements.

Gunnar Tibell Conference Secretary G Backenstoss Karlsruhe L Bertocchi Tri este G E Brown K0benhavn K M Crowe Berkeley T E 0 Ericson CERN K Gottfied CERN P Radvanyi Orsay F Scheck Ziiri ch Yu Shcherbakov Dubna V G Solovyev Dubna J D Walecka Stanford D H Wilkinson Oxford

ORGANIZING COMMITTEE S Dahlgren Uppsala A Johansson Uppsala S Kullander Uppsala 0 Sundberg Uppsala G Tibell Uppsala Conference Secretary H Tyren Uppsala Committee Chairman K E Bergkvist Stockholm I Bergstrbm Stockholm J Blomqvist Stockholm S Hultberg Stockholm T Berggren Lund G Jonsson Lund C-J Herriander CERN

-ii- TABLE OF CONTENTS

I ELEMENTARY PARTICLES Their properties and elementary interactions i 1.1 - A nucleon-nucleon potential that includes the effect of the A (1236) -AM Green and P Haapakoski 3

1.2 A field theoretical approach to nucleon-nucleon dynamics - G Turehetti . . 4

1.3 - Elastic 7r p differential cross-section at 49 MeV -EG Avid, •

D A Axens J Beveridge, G Duesdieker, L Fstauka, C H Q Ingram,

R R Johnson, G Jones, D LePatourel* R Ortha M Salomon, W Westlund and L P Robertson 5

1.4 - Inelastic 230 MeV it p-interactions - Yu A Batusov, S A Bunyatov, G R Gulkanian and V M Sidorov 6

1.5 - Determination of irN scattering amplitudes and necessary measurements to reduce uncertainty of amplitudes - A Yokosawa 1

1.6 - Diftractive dissociation and hadron structure r H J Lubatti and K Moriyasu . „ 8

1.7 - Dif tractive dissociation of pions and neutrons at 15 GeV/c in •n d interactions -PL Bastien, L A Dunn, R Harris, H J Lubatti, K Moriyasu, W J Podolsky, H H Bingham, W B Fretter, W R Graves, L Stutte and G Yost 9

1.8 - da /dfi, oel tOt* and Re A (0) for elastic pp-scattering at pp PP 1-1000 MeV -IF Amirkhanov, 0 V Dunibrais, R Ya Zul 'karneev and

Kh Murtazaev 10

1.9 - Excitation of unitary analog states - A Deloff and J Piekarz 11

1.10 - Some features of the A-N interaction deduced from hypernuclear y-transitions - A Bairiberger, M A Faessler, U Lynen, H Piekarz, J. Piekarz, J Pniewski, B Povh, H G Bitter and V Soergel 12

—ill- 1.11 - On the enhancement in Ap invariant mass spectrum near EN threshold in K-nucleus interactions at 3.5 GeV/c - B Badeiek, J Ste- paniak and P Zielvnski 13

1.12 - A measurement of the E magnetic moment - J D Fox, W C Lam, P D Barnes, R A Eisenstein, J Miller, R B Sutton, D A Jenkins, M Eakkause. J R Kane, B L Roberts, R E Welsh and A R Kvnselman 14

1.13 - A search for parity non conserving effects in the C(a,y) 0 reaction - E Bellotti, E Fiorini and P Negri 15

1.14 - Search for a parity-violating contribution to nucleon-nucleon scattering - D Nagle, C Hwang, N Jamie, P Lovoi, J MoKibhen, R Mischks, G Ohlsen, J Potter, R Stevens, P Debrunner, D Fritz, H Frauenfelder and L Sorensen 16

1.15 - Parity non conserving nuclear interaction and the second class axial current - M Chemtob and B Desplanques 17

1.16 - Parity violation in atoms in a renormalizabie theory of weak and electromagnetic interactions without neutral currents - C A Piketty 18

1.17 - Time-reversal violation via second-class current? - K Kubodera and M Rho 19

1.18 - Determination of the axial vector form factor in the radiative decay of the pion - G J Igo, N Chirapatpimol, M Dixit, M Nasser, J B Carroll, D Ortendahl, V Perez-Mendez and A Stetz 20

1.19 - Polarizability contributions to the neutron-electron amplitude at threshold - J Bernabeu and C Jarlskog 21

1.20 - Least squares adjustment of the coupling constants in nuclear beta decay - H Paul and A Kropf 22

1.21 - Determination of the A-hyperon-proton elastic scattering cross- section using the experimental results on the interactions of fast particles with carbon nuclei - B A Shahbazian, A A Timonina and N A Kalinina 23

-iv- I I 13 COHERENT PRODUCTION

II. 1 - Naive view of high energy hadron-nucleus collisions - 14 A S Goldhaber 27

11.2 - Partial wave analysis of 3ir states coherently produced on nuclei - 15 Collaboration CERN-ETR-Imperial College-Milano 28 11.3 - Energy dependence of coherent production of three pions on nuclei between 9 and 15 GeV and comparison with diffractive three-pion

production on hydrogen - P MHklemann3 K Freudenreiah3 F X Gentit,

16 G Bellini, M di Corato3 G Vegni3 C Bemporad, W Beusch* E Polgar3

D Websdalej P Astbuxy3 J G Lee and M Letheren 29 -12 — — + 12* 17 II. 4 - Measurement of 3ir mass spectrum in the reaction ir C —>IT IT IT C

(4.44 MeV) - G Asaoli3 H R Barton* L £' Eolloway, L J Koester, 18 U E Rruse, L J Noduimanj J H Smith and R Wojslaw 30 11.5 - Coherent non-diftractive nuclear production processes - G FSldt 31 19 11.6 - Non-diagonal contributions to incoherent nuclear production processes - G Faldt 32 11.7 - Scattering, excitation and dissociation - A Malecki 33

20 j. .). -• II. 8 - Coherent production of K TT IT on nuclei and determination of the + + K ir ir~ -nucleon cross section - C Bemporad3 ft' Beusch, J P Dufeyt 21 E Polgav, D Websdale3 0 Zaimidorogat K Freudenreiah, F X Gentit, P Mtthlemann, P Astbury* J

A J Hers, E Hagberg3 S Kullandev, P C Bvuton3 C S Onrran, J K Davies3

S M Fisher3 F F Heymann3 D C Imrie and G J Lush 35 11.10 - P- He coherent scattering at 24 GeV observation of elastic scat- 23 tering and production processes by a missing mass method - Colla- boration Clermont-Fd-Lyon-Strasbqurg-CERN , 36 11.11 - Study of nuclear interactions of 200 GeV protons in emulsion -

M Juric3 0 Adampvia, E M FxiedlSnder3 I Otterlund3 G Bamann3 37

R Devienne3 J Hebert, J Lory, CMeton3 D Sohune3 B Willot3B Charquet3

T$ai-CM3 G Baroni3 P Ctier, J P Massus3 R Kaiser3 J Pelliaer and G Rey

-v-

it. II. 12 - One pion coherent production in D-P interaction - R Batdini-Celio3 F L Fabbri and P Piaozza 38 11.13 - High-energy coherent interaction of deuteron.s on protons -

J Banaigs, J Berger., L Goldzhal*L Vu Hai3 M Cotteveau, C Le Brun, F L Fdbbri and P Pioozza 59 11.14 - Unfolded phase shift analysis - G Albert and P Poropat 40 11.15 - ir Production on deuterium - G Albert and L Rosa 41 11.16 - High momentum tail in spectator distribution - G Albevi, M Gregorio and Z Thome 42 11.17 - Coherent particle production in nuclei and the diffraction excitation model - A Gw?tu and A Subramanian 43 11.18 - Incoherent particle production in nuclei and models for multiparticle production - A Subramanian, S Lai and P Vyas 44

Ilia NUCLEAR SCATTERING Pion interactions

III.l - The interaction of 50 MeV ir with deuterons - D Axen3 G Duesdieker,

L Felaaka, C B Q Ingvams R R Johnson, G Jonest D LePatoia?ela M Salomon, W Westlimd and L P Robertson 47 2 3 III. 2 - Model-independent determination of the coupling constants s He dp e 3 3 and B He He ir - S Dubnieka, 0 V Dwribvais and F Nichitiu 48 111.3 - On the possibility of determination of the coupling constant 3 3 ir He H - 0 V Dunibrais, F NioHtiu and Yu A Soherbakov 49 111.4 - Pion coupling constant and the He pion radius - V Z Kopeliovich 50 * 3 111.5 - Elastic scattering of ir mesons on He at 154 MeV - M Albuj

T Besliu, I V Falomkin, R Garfagnini, M Kulyukinf V J Lyashenko, A Mihul, F Niahitiuj G Piraginoj G Ponteaorvo and Yu A Scherbakov 51

-vi- 111.6 - Application of accelerated convergence expansion for the phase shift analysis of the elastic ir-He scattering - 0 V Dumbvais, F Nichitiu and Yu A Saherbakov 52

111.7 - On the electromagnetic pion radius coming from ir~He scattering - F Nichitiu and lit A Schevbakov • 53

111.8 - Elastic scattering of ir mesons on He at 70 and 154 MeV -

M AVbu3 T Besliu, I V Falomkin, R Gavfagnini, M M Kulyukin,

V J Lyashenko, A Mihul, F Nichitiua G Piragino, G Pontecorvo and Yu A Soherbdkov • 54

111.9 - Total cross section for the double charge exchange reaction + 4 - ir + He ~> IT + 4 p at 100 MeV -IV Falamkin, C Georgesau,

M M Kulyiikinj V J LyashenkOj A Hfhui, F Niahitiuj G Pivagino3 G Ponteaowoj A Sarapu and Yu A Saherbakov 55

III. 10 - Ambiguities in ir He phase shift analysis - F Nichitiu 56

III. 11 - Small angle iT He elastic scattering at 3.48 and 6.13 GeV/c - A A NomofiloVj rJ M Sitnic, L A Slepetz and L N Strunov 57

, III. 12 - Study of the reaction 12C(Tr,ir)12C* at 4.5 GeV/c - J L Groves,

L E Holloway3 L J Koester, W K Liu, L J Nodulman, D G Bavenhall and J E Smith , .4} 58 i "

v sonance - H Le§niak and L LeSniak 59

III. 14 - ir"*- 0 elastic scattering in the region of the (3,3 ) resonance - S Lesniak and L Lesniqk . _ , 60

111.15 - TT + Ca elastic scattering near the resonance region - R C Bercawt J S Vincent, M Bleaker, K Gwtow, R C Mmeharp, RE Landau and . , . • •. • . .-.•.,-...- - - . R R.Johnson ;•..-_-. .• . . , . . 61

111.16 - An approach to pion-nucleus scattering near the (3,3) resonance with a dynamically modified optical potential - S Barshay, V Ro8tokin and G Vagradov _ . . -•-„•• 62 111.17 - Theory of pion-nucleus optical potential - J B Camczeata and . M K Banerjee ,,,.... . 63 III. 18 - Exclusion principle effects in pion-nucleus scattering near the 3,3 resonance - J M Bisenberg and E J Weber 64

-Vii- 111.19 - Coulomb effects in IT -C and n -C total cross-sections - A S Clough, G K Turner, B W Allardyae, C J Batty, D J Bough, W J McDonald, RAJ Riddle, L H Watson, M E Cage, G J Pyle and G T A Squier 65 111.20 - Optical model analysis of pion nucleus total cross section data - A S dough, G K Turner, B W Allardyae, C J Batty, D J Bough, W J McDonald, RAJ Riddle, L H Watson, M E Cage, G J Pyle and G T A Squier 66 7 9 111.21 - Pion-nucleus coupling constants for Li and Be - G T A Squier, M E Cage, G J Pyle, A S Clough, G K Turner, B W Allardyae, C J Batty, D J Bough, W J McDonald, RAJ Riddle and L H Watson 6 7 111.22 - The forward ir-C elastic scattering amplitude - B W Allardyae, C J Batty, D J Bough, W J McDonald, RAJ Riddle, L H Watson, M E Cage, G J Pyle, G T A Squier, A S Clough and G K Turner 68 111.23 - The role of the 3~3 resonance in the ir-nucleus elastic scattering - R Seki 69 111.24 - Some problems with the pion-nucleus potential -AS Goldhdber 70 111.25 - Low energy pion-nucleus optical potentials - G Fdldt 71 111.26 - Off-shell effects in the pion optical potential - J T Londergon and E J Moniz 72 111.27 - Off-shell TTN amplitudes for the pion-nucleus optical potential - K W MoVoy 73

111.28 - Comparative analysis of pion-nucleus elastic and inelastic scattering - J F Germond and J P Amiet 74 111.29 - Measurement of the II~ total cross-section for He, Li, Li, 9Be, 12C, 32S for Eir from 80 to 260 MeV - E Pedroni , C Cox, J Domingo, K Gabathuler, J Rohlin, P Sahwaller, N Tanner and C Wilkin 75

111.30 - Pion charge exchange reactions - J Alster, D Ashery, N Auerbaah, S Cochavi, M A Moinester, J Warszawski, A I Yavin and M Zaider 76 111.31 - Ericson fluctuations in high-energy hadron physics - P J Carlson 77

-viii- 1Mb NUCLEAR SCATTERING Non-pionic interactions

111.32 - Momentum components of the deuteron: 200-400 McV/c - G J Igo and M Nasser 78

111.33 - Polarization measurements in high energy proton-deuteron scattering - 0 E Overseth 79

111.34 - Measurement of deuteron-proton backward elastic scattering at incident deuteron momenta of 3.43, 4.5, 5.75 and 6.6 GeV/c - C K Hargrove, L Dubai, R J MoKee, H Mes, L Bird, C Halliwell, E P Hincks, R Morrison, A C Thompson, J Walters, J McCaslin and A Smith 80 111.35 - Scattering contributions of intrinsically relativistic pieces of the deuteron wave function - J Hornstein, F Gross, R A Miller and E A Remler 81 111.36 - Fermi motion and deuteron recoil in the relativistic, covariant, eikonal formalism - J M Namystowski 82 111.37 - Covariant recoil-corrections in the generalised Glauber formula - J M Namysiowski 83

111.38 - pd —> ppn rescattering effects - B M Golovin, G I Lykasov and F Sh Khamraev 84

111.39 - Four-momentum distribution in dp —> ppn reaction at 3.3 GeV/c in hydrogen bubble chamber - B C Alladashvili, V V Glagolev, R M lebedev, J Nassalski, M S Nioradze, I S Saitov, A Sandaaz, T Siemiarozuk, J Stepaniak and V N Streltsov 85 111.40 - Ambiguities in the treatment of center-of-mass correlations in high energy proton and pion scattering by the alpha particle - C Qiofi degli Atti and R Guardiola 86

111.41 - P- Li elastic scattering at 600 MeV - J Gardes, F Le Meilleur, L Meritet, J F Pauty, G Peynet, M Querrou and F Vazeills 87

111.42 - Good resolution pp' scattering on C and Ca at 155 MeV ana their analysis in finite range DWIA - V Comparat, R Frasaaria, N Marty, M Morlet and A Willis 88

-ix- 12 58 111.43 - Elastic and inelastic scattering by 1 GeV protons on C, Ni, 208Pb - I Alexander and A S Rinat 89

111.44 - Hadronic shadowing effects and sum rule constraints in high-energy photon-nucleus interactions -^ Weiae 90

111.45 - Heavy-ion collision in the: eikonal formalism - L J B Goldforb end J M NomysZowski 91

111.46 - Nucleus-nucleus collisions at relativistic energies - G Mldt3 H Pilkuhn and H G Sahlaile 92

111.47 - The energy dependence of the real central optical potential for proton-nucleus scattering - W T H van Oevs and Huang Hah) 93

111.48 - A three-parameter nucleon-nucleus optical potential on the energy shell - B Sinha and F Duggan 94

111.49 - High energy elastic scattering of protons by nuclei - J Ullo and H Feshbaah 95

111.50 - Effect of nuclear deformation on high energy elastic hadron nucleus scattering - A Wu Chao and A S Goldhaber 96

111.51 - High-energy approximations to nuclear scattering -WE Fvahn and B Sahiimann 97

111.52 - Fresnel diffraction in high-energy multiple scattering - B SahUr- mann and W B Frahn 98

IH-53 - Cancellations in Watson's multiple scattering series and additivity of phase shifts - D Agassi arid A Gal 99

HI'54 - Kinematics in nuclear multiple scattering - E Kujawski and E Lambert VQQ

III.55 - Off-energy-shell effects in multiple scattering - E Lambert and E Kvjaaski 101

-x- IV PRODUCTION PROCESSES

IV. 1 - Cross sections-for TTfe'froin He on complex nuclei -.N, S*Wdll,r J W-Craig^RE Berg^D Ezrow and H D Holmgren.^^-{'rLlZ^L _-^-\ f 1051

IV. 2 - The (pf'ir. ) reaction and nuclear structure - JM Eisenberg, J V Noble and H J Weber -•»,.-,--. - 106

IV. 3 - Microscopic description of pion induced nuclear reactions •- M Dillig and M G Huber "'" - => 107

IV. 4 - Complete differential cross sections for the reaction p+p->d+ir from 3 to 5 GeV/c -DA Larson, H L Anderson, L Myrianthopoidos, L Dubai, C t Hargrove, R J Makee, E P flincks, D KesslerJ" fl Mes and A C Thompson 108

IV.5 - The reaction pd-> tiT+ - C F Perdrisat, W Dollhopf, C Lunke, W K Roberts, P KitahCng, W C Olsen and R J Priest 109

IV.6 - Mechanism of the reaction p+d—> t+ir and pt backward scattering at high energies - V Z Kopeliovich and I K Potashnikova 110

IV. 7 Pion production from nuclei -MM Sternheim and R R SiTbar 111 IV.8 Effective irM interaction - Il~T Cheon and J Cugnon 112 IV.9 A study of the reaction d+p—>He +ir°, d+p—>H +ir and d+p—>He +n

J Banaigs, J Bergers L Goldzahl, T Risser, L Vu-Hdi, M Cottereau and C Le Brun 113 IV. 10 - Observation of the "ABC" effect in n+p->d+(mm)° - G Bizard, F Bontnonneau, M Cottereau, J L Laville, C Le Brun, F Lefebvres, J C Malherbe, R Regimbart, J Berger, J Duflo, L Goldzdhl, F Plouin and L Vu-Hai u4 IV. 11 - On the nature of the ABC effect - M D Shuster, T Risser and I Bar-Nir 115 IV.12 - "ABC" and "DEF" effects position, width, isospin, angular and energy distributions - J Banaigs, J Berger, L Goldzahl, T Risser, L Vu-Hai* M Cottereau and C Le Brun 116 IV.13 - A study of the reaction d+d->He +(mm)° - J Banaigs, J Berger, L Goldzahl, T Risser, L Vu-Hai, M Cottereau, C Le Brun, F L Fabbri 117 and P Piaozza

-Xi- IV. 14 - Analysis of p+d-> He +X° experiments - H Brody 118

IV. 15 - Nucleus excitation model for ABC effect - M Bleszynski3 F L Fdbbri, P Haahi and P Picozza 119

IV. 16 - Dynamical model for the ABC effect - J C AnQOS, D Levy and A Santoro 120

IV. 17 - Polarization in production reactions on deuterons - K Bongardt and H Pilkuhn 121 12 — IV. 18 - A counter experiment on the production of A C by K in flight -

G C Bonazzola3 T Bressani3 R Cester3 E Chiavassa3 G Dellaoasa3

A Fainberg3 D Fresahi3 N Mirfdhkrai3 A Musso and G Rinaudo 122 A — — A IV. 19 - Spectroscopy of hypernuclei via the Z (K ,ir )A Z-reaction -

MA Faesslev9 G Heinzelmann* K Kilian, U Lynen3 H Piekarz3

J Piekarz3 B Pietrzyk, B Povh3 H G Bitter3 B Sohuerlein3H W Siebert3

V Soevgel3 A Wagner and A B Walenta 123

IV.20 - Pion photoproduction and T vs. T< analog states in N>Z nuclei - A Nagl and H Uberall 124

IV.21 - Pion photoproduction and spin flip states in self-conjugate nuclei -

B A Lamers3 G B Lmers3 C W Lucas3 A Nagl3 H Uberall and C Werntz 125

IV.22 - Coherent photoproduction of IT on He - D Bachelier3 M Bernas3

J L Boyard3 J C Jourdain3 C Lazavd3 P Radvanyi and Z Maria 126

IV. 23 - Pion photoproduction on %e - G Goggi3 G C Mantovani3 A Piazzoli and D Scannicchio 127 V CAPTURE AND ABSORPTION

V.I - Gross theory of muon capture - Y Kohyama and A Fujii 131

V.2 - Dynamics in total muon capture matrix elements - R Leonardi 132

V.3 - Total muon capture rates and the average neutrino energy - J Bernabeu and F Cannata 133

V.4 - Atomic collision quenching of the metastable 2s state of muonic

hydrogen and muonic helium - V W Hughes3 R 0 Mueller3 H Rosenthal and C S Wu

-xii- V.5 - Formation and hyperfine structure of muonic helium (au~e~) - M Camani, K N Huang, V W Hughes and M L Lewis 135

V.6 - Formation of pionic and muonic atoms in liquid helium and hydrogen - G Backenstoss, J Egger, T von Egidy, R Hagelberg, C J Herrlander, H Koch, H P Povel, A Schwitter and L Tauscher 136 14 V.7 - Muon capture by N nuclei - H R Kissener, A Aswad, R A Eramzhian and. H U Jager 137

V.8 - Capture rates of negative muons in 0 leading to bound states in 16N - M Eakhause* F R Kane, G H Miller, B L Roberts and R E Welsh 138

V.9 - Muonic X-rays in lead isotopes - D Kessler, H Ues, A C Thompson, H L Anderson, M S Dixit, C K Hargrove and R J McKee 139

V.10 - Nuclear excitation and isomer shifts in muonic atoms - H K Walter, H Baeke, R Engfer, E Kankeleit, R Miohaelsen, H SahnevBUly, W U SchrO- der and A Zehnder 140

V.ll - Of the structure of K dependence of mesic X-ray spectra upon negative muon depolarization - R Arlt, V S Evseev, G H Orthlepp, V S Roganov, B M Sabirov and H Haupt 141

V.12 - Neutron spectra from the negative muon absorption by heavy nuclei and the resonance model of nuclear reactions - V S Evsee and T N Mamedov J; 142

V.13 - Neutron spectra following muonuclear absorption - J Joseph and B Goulard 143

V.14 - Investigation of Mu~ meson capture by light nuclei - Yu A Batusov, S A Bunyatov, L Vizireva, G R Gulkanian, F Mirsalikova, V M Sidorov and Ch Chernev V.15 3 9 - Pion-nucleus total cross-sections on He and Be , and pionic X-rays in He3 - C S Hsieh, J R Kane, B Sapp, C B Spence, R J Wetmore and J B Carroll 145 V.16 - Anomalies in the strong interaction shifts and width of the Is level in pionic 6Li, 7Li, and 9Be - G Backenstoss, I BergstrOm, J Egger, R Hagelberg, C J Rerrlander, H Koch, H P Povel, R H- Price, A Schwitter and L Tausoher 146

V.17 - On the origin of the 126 keV transition previously observed when K~ mesons stop in 55Mn -RAJ Riddle, G T A Squier, R E Welsh, 134 N Berovic and G J Pyle 147

-xm- V.18 - Study of E-hyperonic atoms - G Backenstossa A Bamberger, I Berg- strdm, T Bunaciu, J Egger, S Hultberg, H Koch, U Lynen, H G Ritter, A Schwitter and L Tausaher 148 V.19 - Atomic capture of negative mesons - M Leon and R Seki 149

V.20 - The K-mesic atom - F Myhrer 150 V.21 - Optical potential for kaonic atoms - M Alberg, E M Henley and L Wilets 151 V.22 - About possible anisotropy of X-ray radiation of mesic atoms - G la Korenman 152 V.23 - Finite size effects in pionic atoms - F Iachello and A Lande 153 V.24 - Transitions to discrete levels in radiative pion capture by light nuclei - V V Kavapetyan, G la Korenman and V P Popov 154 V.25 - De-excitation gamma rays following negative pion reactions and absorption on light and intermediate nuclei - H S Plendl^ H 0 Fun-

stent W J Kossler, V G hind and C E Stronach 155 V.26 - Nuclear gamma rays following ir absorption in light nuclei - H Ullrich, E T Boschitz, D Engelhardt and C W Lewis 156 V.27 - Cluster effects in nuclear pion capture - K 0 H Zioak 157 V.28 - Pion absorption in He -AC Phillips and F Roig 158 44 V.29 - Some photonuclear reactions leading to Sc at intermediate energies - G G Jonsson and M Eriksson 159

Via NUCLEAR STRUCTURE Gross features

VI.1 - Nucleon distribution dependence of p-nucleus scattering - R J Lombard and J P Auger 153

VI.2 - Resolution of the apparent discrepancy in the magnetic form factor of the deuteron -RE Rand, M R Xearian and C D Buchanan 164

VI. 3 - Meson-exchange corrections to n+d *• t+y and to the magnetic form factors of the three-body system - E Hadjimtchael and A Barroso 165

-xiv- VI.4 - Eikonal approximation for magnetic electron scattering - J D Murphy and H Vberall 166 VI.5 - Threshold dependence of moment of inertia on nuclear quadrupole moment -AS Goldhdber 167

VI.6 - Exchange contributions to inelastic scattering from collective

nuclei - V R W Edwards3 B C Sinha and P W Tedder 168 VI. 7 - Anisotropic momentum distributions in deformed nuclei - V R W Edwards 169

Vlb NUCLEAR STRUCTURE Microscopic features

VI.8 - (e,e'p) reactions at 500 MeV with improved energy and momentum re-

solutions - A Bussiere3 A Gillebert, J Mongey3 P X Ho3 M Priou3 D Royer and I Sick 170

VI.9 - (e,e'x) coincidence experiments on Li, Be and Mg - J Julien3

C Samour3 G Bianchi3 P Duval3 J P Genin3 R Letourneau3 A Mougeot3

M Rambaut3 A Palmeri and D Vindguerra 171

VI. 10 - The reactions 12C(Tr+,pn)10G and 12C(Tr~,TrN)11C from 30 to 90 MeV -

J Alster3 D Ashery3 S Coehaoi3 M A Moinester3 I Shamai3 A I Yavin and M Zaider , 172 VI.11 - Off-shell p-p cross sections appropriate to (p,2p) reactions - E F Redish and G J Stephenson Jr 173

VI. 12 - DWIA analysis of quasi-free scattering in Ca - R Bengts8on3 T Berggren and C Gustafsson 174 12 VI.13 - Multiple scattering effects in (p,2p) collisions on G - R Gnardiola and P Pascual 175 2 3 4 VI. 14 - Momentum distributions for neutrons in H, He and He from Quasx-

elastic scattering of 1.3 GeV/c protons - P Kirkby3J M Daniels,

T Gajdicar3 S Fviedlander3 G F Krebs3 H Coombes3 E Dennig and K Kairies 176

VI. 15 - The Li(p,pd) He, .reaction at high recoil momenta - P Kitching3

' W C Olsen3 W Dollhopf3 C Lunke3 C F Perdrisat3 J R Priest and W K Roberts 177

-XV- VI.16 - Quasi-free scattering on clustering particles and Q values - P Cilev and Y Sakamoto 178

VI. 17 - Energy dependence of the cross section of fast deuteron knock out

from Li, ,Be,rC by 380-670 MeV protons .:-fV: I Kqmarov3 G:_E:Ko8arev3 G P ReshetnikoVj 0 Savctienkb and/S:Tesoh 179

VI. 18 - On quasi-elastic reactions with knock-out of a nucleon group .-. I Rotter 180

VI. 19 - Asymmetry in quasi-elastic scattering of polarized 635 MeV ^protons by 6Li nuclei - V S Nadejdin^ N I Petrov and V I Satavov 181

VI. 20 - A microscopic calculation of rearrangement energies in 0 - R Padjen, B Reuben and F C Khanna 182

VI.21 - A self-consistent calculation of the optical model potential for nuclear matter - F C Khanna and Q Ho-Kim 183

VI. 22 - Microscopic description of the spreading and decay of hole states - W Fritsehj R Lipperheide and U Wille 184

VI.23 - Slater determinants, Jastrow wave functions and high,momentum components in electron form factors - C Oiofi degii Atti 185

VI.24 - The best-energy criterion for the nuclear independent particle model - S Boffi and F D Pacati 186

VI. 25 - Density fluctuations and nuclear structure - F Calogero, F Palumbo and 0 Ragnisao 187 VI I MISCELLANEOUS TOPICS

VII. 1 - The geyser, a new detector for nuclear recoils - B Hdhn and H W Reist 191

VII.2 - High resolution apparatus for 600 MeV electron scattering - Ph. Lecdnte and J BelHaavd 192

VII.3 - Total decay of Ag and Br nuclei induced by 10 and 70 GeV/c protons - R A Khoshmukhamedov and K D Tolstov 193

VII.4 - A theory of inelastic interactions between relativistic ions and

nuclei - V S Bavashenkov,. K K Gudimat F G Gereghiy A S Iljinov and V D Toneev 194

-xv i- VII.5 - Fission of heavy nuclei by high-energy particles - V S Barashenkov, 178 F G Gereghi, A S Iljinov and V D Toneev 195 VII.6 - Pion double charge exchange on Bi nuclei - Iu A Batusov, G Ganzerig, I V Dudova, B P Osipenkc, V M SidoroVj V A Xhalkin 179 and D Chultem 196 VII.7 - Total mixing of rotational bands in the transitional region - 180 B S Nielsen and C Sffridergaard 197 VII.8 - Interaction of accelerated high energy heavy ions (0 at 2.1 181 GeV/nucleon) with nuclear emulsion nuclei - R Pfohl* R Kaiser,

J P Mas8uea D Karamanoukianj M Jung, J N Surena R Sahmitta P CtteVj F Fernandez* J Medina, A Dura, J Sequeirosj V Gandiq, 182 J M Bolta and J L Ramon 198

183 VII.9 - A study of nucleus-nucleus interactions produced by heavy nuclei (12gZ«26) at energies > 1 GeV/nucleon - B Jakobsson% R Kullbevg and I Otterlxmd 199 184

185

186

187

191

192

194

-xvi/K I ELEMENTARY PARTICLES

Thei r properti es and elementary interactions I.I

A nucleon-nucleon potential that includes the effect of the AC1236)

A. M. Green and P. Haapakoski Research Institute for Theoretical Physics University of Helsinki

As outlined in ref. 1 the two nucleon interaction in the state is assumedd to bbe off thhe forf m MeV M £?> -Or' - 44 1MeV where A and B are treated as free parameters. This leads to a pair of coupled differential equations, which are solved and fitted to the experimental $(*S ) up to 3 50 MeV. Three sets of values for A and B are given in the table, along with the singlet scattering length, effective range and S('S ) at 25 and 3 50 MeV.

a in rads. Potential A B s rs %< •v (MeV) fm-7. fm fm 25 MeV 350 MeV

1 2,500 1.h -7.7 2.5 0.777 -0. 055 2. 5,000 1.8 -8.2 2.2 0.783 -0. 118 d . 10 ,000 2. 6 -7.1 2.2 0,756 -0. 13 9

The possible effect of the inelastic NA channel on electromagnetic charge form factors is compared with the corresponding nucleon-nucleon T=0 D-state contribution. The effect of this type of interaction in neutron matter is also considered.

1) H. Sugawara and F. von Hippel, Phys. Rev. 17_2 (1S68) 1764-, 185 (1969) 2046

-3- 1.2 A FIELD THEORETICAL APPROACH TO NUCLEON-NUCLEON DYNAMICS by G. Turchetti - Bologna University

The usual approach to nucleon-nucleon dynamics is based on the potentials derived from the one boson exchange approximation. Our aim is to investigate the dynamical content of simple lagrangians, depending at most on one free parameter, and where the pi on is the only source of nuclear forces. Due to the pseudoscalar nature of the pi on it is essential to use a fully relativistic formalism : indeed the negative energy states, which are taken into account, appear to play a fundamental role even at zero energy. The inadequacy of the Born series is overcome applying to the Green function an approximation (Pade) derived from variational principles; this approximation enjoys unitarity, analyticity and bound-antibound state poles. The results obtai ned for the standard Yukawa lagrangian and the non linear 8* model, which fulfills the current algebra constraints, prove that the one and two pi on forces are sufficient to reproduce more than qualitatively all the phase shifts when the negati ve energy states are taken i nto account. The i nversi on in the S waves (the 3PO changes sign) is still lacking but the inclusion of a I I possible couplings between physical and unphysical states (some of them were neglected) could still provide it.

-4- 1.3 Elastic ir+p Differential Cross-section at 49 MeV. E.G. Auld, D.A. Axen, J. Beveridge, G. Duesdieker, L. Felawka, C.H.Q. Ingram, R.R. Johnson, G.Jones, D. LePatourel, R. Orth, M. Salomon.and W. Westlund, University of British Columbia and L.P. Robertson, University of Victoria. — The elastic ir+p differential cross-section at 49 MeV has been measured from 30 to 150 deg using pions produced in the external proton beam of the 184 in. synchrocyclotron at the Lawrence Berkeley Laboratory. Incident pions were selected by time of flight while their momentum was measured to an accuracy of ]% dp/p. The mean pion energy as determined by a range measurement. Particles scattered from a 2 cm thick liquid hydrogen target were stopped in a 12.5 cm diam 30 cm long NE 110 plastic scinti1lator. The resulting pulse amplitude was used to measure the pion energy. The efficiency of this scinti1lator to detect elas- tically-scattered positive pions was measured as a function of energy at the zero degree position. The trigger scintillators, spark chambers and stopping counter were all mounted on a movable arm. Scattered pions were identified by dE/dx measurement as well as by observation of the decay muon in the plastic scinti1lator. Rejection of events due to muons from pion decay in front of the target as well as pions scattered from the target holder was accomplished by reconstruction of the trajectories. The energy-loss resolution of the system was typically 2 MeV.

Results of a preliminary analysis are shown below where the sol id curve 1 is a calculation using existing phase shifts S3=-4.85° P3i =-0.81° P33= 5-13° radians. The error bars represent the statistical error only. The data points follow a flatter distribution of large angles than predicted by these phase shifts and are similar to those of a previous measurement at 60 MeV.2 The effect of including D-waves in the phase shift, analysis is currently being investigated. 1. S. Almehed and C. Lovelace, Nucl. Phys. B40, 157 (1972) I 2. K. Crowe et al. , Phys. Rev. ]8p_, 1349 (1959)

1.6 -—

- \/ y 0.8 •• J/ /

TT+p Elastic Scattering at 49 MeV

* 45 90 135 Lab Angle

-5- 1.4 INELASTIC 230 MeV JC+p -INTERACTIONS Yu.A.Batusov,S.A.Bunyatov,G.R.Gulkanian,V.M.Sidorov Joint Institute for Nuclear Research,Dubna,USSR

ABSTRACT

The cross section of the 7C++p—?• w\ TC+ * n reaction at

TT = 230 MeV has been measured. This allows the elimination of one of the two most probable values of the £ parameter des-

cribing the Langrangian interaction for the TCTC-J»KTC and Kflf-*- ff/V processes near threshold in the "soft" pion theory. Two possible values of the ratio of isotopically invariant amplitudes of the TM-^-KKN reactions have been found at the threshold in the states P..* and P,^ which allows to find out the possibility of the low energy theory of the TCM-^KKA/ reactions

(Gribov,AnselmfAnisovich) in the determination of pion-pion scattering lengths. The cross sections of the x++p-*-7i"+ TC"+ P andw + D-^ + 7r +^+p reactions (Ey St 50 MeV) at TT = 230 MeV have been estimated. Radiation scattering with the emission of hard gamma quanta has been shown to be the main inelastic channel at this energy. 0.5

0.4 -

0.3 - / 0.2 - / A"1

0.1 -/ 0

i i TitMsi 200 240 280 320 360

-6- 1.5

DETERMINATION OF TTN SCATTERING AMPLITUDES AND NECESSARY MEASUREMENTS TO REDUCE UNCERTAINTY OF AMPLITUDES A. Yokosawa Argonne National Laboratory, Argonhe, Illinois 60439

Since preliminary results of the measurements of R and A parameters and of irp charge-exchange polarization became available, a long-waiting crucial task to deduce irN scattering amplitudes has been attempted by several authors. So far, such attempts were made only in irN scattering at one particular momentum and not in other reactions. We report results of 3 4 5 the latest analyses using the new data ' and discuss measurements needed to reduce scattering-amplitude uncertainty. It is well known that in principle one can determine seven amplitudes algebraically from seven measurements. However, in reality, we cannot determine amplitudes uniquely without making proper assumptions. The reliability of such assumptions naturally depends upon the accuracy of the experimental data. We discuss individual t-by-t analysis, and then t- | dependent analysis at 6 GeV/c ir incident momentum. These two different analyses compensate each other, and their advantages and disadvantages are 1 pointed out. Uncertainty of each amplitude is carefully determined. We study the effect of amplitude determination with respect to experimental errors by using the latter analysis. Measurements needed to reduce the uncertainty are pointed out. Methods presented here should be applicable to other reactions at various momentum range.

1. For the final version of the preliminary data, see de Lesquen et al., Phys. Lett. 40B, 277 (1972). 2. For the final version of the preliminary data, see P. Bonamy et al., Nucl. Phys. 52B, 392 (1973). 3. Updated version of the paper by P. Johnson, K. Lassila, P. Koehler, R. C. Miller and A. Yokosawa, Phys. Rev. Lett. 3_0, 242 (1973). 4. D. Hill, P. Koehler, T. Novey, P. Rynes, B. Sandier, H. Spinka and A. Yokosawa, Phys. Rev. Lett. 30, 239 (1973) . 5. LAmbats et al., Phys. Rev. Lett. _29, 1415 (1972).

-7- 1.6

DIFFRACTIVE DISSOCIATION AND HADRON STRUCTURE

H. J. Lubatti and K. Moriyasu, visual Techniques Laboratory, Department of Physics, University of Washington, Seattle, Washington 98195. A new model of hadronic interactions is proposed which explains many of the puzzling features of diffractive dissociation. The model is based on an extension of the familiar Harari-Rosner dual quark diagrams. By introducing self-energy corrections to the bare hadron, new classes of dual diagrams are obtained. These diagrams can be identified as contributions to elastic, inelastic and diffractive scattering processes. Multiparticle production is interpreted in a novel way as arising from radiative interactions of self-energy diagrams.

The new diagrams which are associated with diffractive dissociation provide simple intuitive explanations for many of the experimental features of diffractive reactions. In particular, the nonresonant behavior of the well-known diffractive enhancements (e.g. the A- and A,) is seen to be a direct consequence of the new diffractive diagrams. These diagrams also explain why the Deck model has been so successful in describing the properties of diffractive dissociation.

* Work supported in part by NSF Science Development Grant GU-2655. t A. P. Sloan Foundation Research Fellow.

-8- 1.7 ill DIFFRACTIVE DISSOCIATION OF PIONS AND NEUTRONS AT 15 GeV/c IN ir~d INTERACTIONS

P. L. Bastien, L. A. Dunn, R. Harris, H. 3. Lubatti , K. Moriyasu, W. J. Podolsky, Visual Techniques Laboratory, Department of Physics, University 31 ss of Washington, Seattle, Washington 98195? H. H. Bingham, W. B. Fretter, |j W. R. Graves, L. Stutte, G. Yost, Department of Physics, University of California-Berkeley, Berkeley, California 94720= Preliminary results are presented on the diffractive dissociation of pions and neutrons into multiparticle final states. The data are obtained from ir d interactions at 15 GeV/c in the SLAC 82-inch bubble chamber and are measured on the University of Washington's PEPR system. Pion dissociation is studied in the reaction ir d •*• ir ir ir d

Coherent production events are selected by identifying the recoil deuteron from range measurements and kinematic fits. The well-known A (pir) and A. (fir) diffractive enhancements are clearly observed in the 3ir mass spectrum. In addition, there is an indication of a mass peak at appiox- sMt imately 1.9 GeV. This new enhancement, tentatively called the A. (gir), is the first experimental observation of pion dissociation into a gjj_ threshold state. Diffractive dissociation of neutrons is observed in the reaction

IT d •+• TT IT pp

where the slowest proton is assumed to be the spectator. Evidence for two different production mechanisms is seen in the momentum transfer distribution of the diffracted ir~p system. The low mass pir~ events are extremely peripheral (exp (14t')) while the higher masses are associated with more normal exp (8f) distributions. The low mass behavior is consistent with neutron diffractive dissociation. This conclusion is also supported by p! the pir" angular distributions. There is some evidence for production of r > n | the known N* resonances but only for t1 > 0.1 (GeV/c) .

* Work supported in part by NSF Science Development Grant GU-2655. t A. P. Sloan Foundation Research Fellow.

-9- 1.8

A.Delof J.Pieks

Strange G^ AND He A (0) FOR ELASTIC pp-SCATTERING in the target AT 1-1000 MeV /p,n,A / torn I.V.AmirkhanoVjO.V.Dumbrais.E.Ya.Zul'kameeVjKh.Murtazaov The transform Joint Institute for Nuclear Research,Dubna,TJSSR ted hypernuc: ABSTRACT plet as the i Since KE seal The cross sections of elastic pp-scattering in the re- the forces JJ gion of Coulomb-nuclear interference at 100,500,600,630,and to be divergi largely over* 670 MeV have been measured. On the basis of these experimental ces. In this results and those obtained by other scientists the values of tential has 1 Re A__(0) and of (5*pp have been determined in the energy meters have tial lies bee region from ^ to 1000 MeV. The energy dependence Re A (0) K~ - nucleus has been discussed from the point of view of dispersion rela- able to calp tions. The position of zeros of this amplitude are searched •+ /Z,N/ •» JT sections exh for. ctive excita the peak val vious calcul big: er but t approximatio validity of ^tot for K symmetry. Q?t s&me what sv.

1. A.K.Eeriac 738 2. L.S.Kiss] Argonn'e,

-10- 1.9

Excitation of unitary analog; states A.Deloff Institute for Nuclear Research, Warsaw J.Piekarz Institute of Experimental Physics, University of Warsaw ' .

Strangeness exchange reactions K~n •>3|V\- on neutrons "bound in the target nucleus have been considered. It is assumed that /p,n,A/ form a basic triplet of SU/3/ - Saktita symmetry. The transformation n ->A changes the target nucleus into excited hypernuclear sttte which "belongs to the seme SU/3/ multi- plet as the target and is Colled unit&ry analog stste /1/. Since KN scattering lengths are of the order of the range of the forces it is claimed that /i/ multiple expansion is likely to be divergent, /ii/ Born approximation gives wrong sign and largely overestimated magnitude ox the strength oi' the KIT forces, In this work two channel /ETn, 3t~A/ SU/3/ invariant potential has been used with range - 0.25 fin whose strength parameters have been adjused to fit KH reactions. IText, this potential has been folded into nuclear density to obtain two channel K~ - nucleus optical potential. Using this potential we were able to calculate the cross section CT1, for the process K~+

•+ /Z,B/ •» JT" + /Z,IT-1^.* Around pK ^ 200-300 MeV/c the cross sections exhibit giant resonance like peaks typical for collective excitations. The magnitude of <51 decreases with A-number the peak values being -^25 yib for Ca and «>8 ub for Pb. Pre- vious calculations /2/ gave for £T values roughly 10 times big: er but this was a consequence; of an unjustified use of Born approximation for the K~n -*• jfA process. In order to check the validity of the Saksta symiaetry we calculated also ©^^ and T-i-Q-f. J-or E-nucleus scattering both with and without SU/3/ symmetry. The resulting cross sections were to within 10% the s&me what supports the SU/3/ assumption.,

1. A.K.Kerraan and H.J.Lipkin, Annals of Physics /1T.Y./ 65/1971/ 738 . , ' 2. L.S.Kisslinger, Proc. Int. Conf. on'Bypernuclear Physics, Argonn'e, 1969, p.885.

-11- 1.10

Some features of the A-N interaction deduced On the Enhancer r-oo. hvoernuclear ^ - transitions ITear 5TM threshold

;..itm'ber£er, li.A.I'aessler, U.I/ynen, H.Piekarz B.Badelek J.Pielcars, J.Priieivski, 3.Povh, H.G.Ritter aad V.Soergel * Institute of 1 Institute of I CER1T - Heidelberg - Warsaw

The •binding energies of s-shell hypernuclei: ^H, H, He, A A A 3.5 GeV/c K' the low-energy A -p cross-sections and recently determind exci- CEBN bubble chai tation energy 1.09 HeV of mass number 4 hypernuclei /1/ were with the hyperoi analysed in te~-ias of phenoia.enologice.1 A -N potential. Invariant masi is shown in the The A -IT potential V.^ was assumed to be of exponential of the "best fit shape outside a hard core: formula for i the spectrum in the existence o J experiments con< \ with lighter 1 In this exper aa<3 where P^ denotes the spin-eschange operator, & n - 3 sample of inters more than two p: are spin and isospin operators, respectively, rc, are hard It seems that core redius and range Tjerameter. The quantities. V , W in explaining t and oC are the potential depths. The CSB pert ox the potential contains in addition to the spin-dependent term adopted by Herndon and Tang /2/ elso the spin-independent part. The poten tial strengths were adjusted to fit the above mentioned experi mental date. The resulting f\S intersection is spin-dependent and two terms of CSB potential are equally important. The scat

tering lengths ag and a^ for A -p interaction are round to be ^•-2 F and~-1 P, respectively.

References /V A.Bamberger et al. Phys. Lett. ^6B, /1971/412, and Eucl. Plrys. to be published /2/ R.C.Heradon and Y.C.Tang, Phys. Rev. T?j5 /1967/1091; ibid. 159 /1967/853

205^

-12- 1.11

On the Enhancement in Kp Invariant Mass Spectrum NearTAi Threshold in K -Nucleus Interactions at 3.5 GeV/c

B.Badelek*, J.Stepaniak**, P.Zielinski ** * Institute of Experimental Physics of the Warsaw University *•# Institute of Nuclear Research ,Warsaw

A 3*5 GeV/c K~ exposure of the heavy freon CFxBr CEBN bubble chamber has been used for search of events with tfc.e hyperon. A and protons in the final state. Invariant mass distribution for all A-P combinations is shown in the figure.!The curve represents the sum of the best fit to the background and Breit-Wigner formula for mjip'v/ 2130 MeV/cc region. OJhe shape of the spectrum in this mass region is consistent with the existence of an enhancement observed in several experiments concerning interactions of particles with lighter nuclei. , In this experiment the enhancement is seen in the total sample of interactions and in the sample containing more than two protons per interaction as well. It seems that Butler-Pearson mechanism may be useful in explaining this effect.

-13- 1.12 A Measurement of the £ Magnetic Moment A. search for parrt J. D. Fox+, W. C. Lam+t Brookhaven National Laboratory, Upton, New York 11973 and Tg.Bellotti . E.Fi( P. D. Barnes, R. A. Eisenstein, J. Miller, R. B. Sutton Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 Istituto di Fisics and D. A. Jenkins We have studiec Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 and leading to parity M. Eckhause, J. R. Kane, B. L. Roberts, R. E. Welsh chosen , which are College of William and Mary, Williamsburg, Virginia 23185 states of the same and a) the JP=O",T=O 3 A. R, Kunselman University of Wyoming, Laramie, Wyoming 82070 TJ =2.5 MeV at b) the 3+ O level We have observed x rays produced in atoms formed by Z hyperons with both f lead and uranium nuclei. The fine-structure splitting of the x rays can be r =O.8J MeV a1 used to determine the magnetic moment of the Z particle by a method similar The experiment to that used in a measurement of the p magnetic moment. Although the fine- nali di Legnaro structure splitting for the Z atom was not distinctly resolved, our measure- 12

(+) M.Finlc et al

-14- 1.13 A search for parity non conserving effects in the 12C(o<,y)160 reaction E.Bellotti , E.Fiorini and P.Negri Istituto di Fisica dell'Universita and I.N.P.N.- Milano

19 1 f\ 1 £% We have studied the reaction c< + C -> 1WO —» "0 leading to parity forbidden 0 states. Two levels have been chosen , which are much favoured by the presence of near allowed states of the same angular momentum and opposite parity : a) the J =0~,T=0 level at 10.952 MeV (there is a 0+,0 level with IJ =2.5 MeV at 11.26 MeV); b) the 3+,0 level at 11.080 MeV (+) (there is a 3~,0 level with ^ =0.83 MeV at 11.44 MeV); The experiment has been carried out at the laboratori Nazio_ nali di Legnaro by exposing 20jb\gr/cm targets enriched to 99«9 fo C to beams of o( particles with currents of about 7 MA. The t rays are detected by a 75 cm Ge(Li) detector connected through an amplifying and stabilizing chain to a 4096 analyser. The energy of the c£. particles and the eff iaiency of the detector are routinely tested on the threshold of the reaction 13 i6 •••m C(o(,n) 0*(6.131 MeV) and on the 10.422 resonance of the same reaction. No peaks corresponding to Y"-rays from the parity forbidden states appear in the spectra obtained up to now (runs totalling one coulomb of incoming single charged c* particles). In order to obtain limits on parity non conservation we have subtracted to the spectra obtained at the energy of each resonance the spectra obtained at nearby energies. —4 Upper limits on the parity violating l^ widths of 7 x 10 eV and 8 x 10~4eV for the 10.952 MeV and 11.080 MeV , respectively, have been obtained in this preliminary analysis.

(+) M.Fink et al : Ehys.lett. 38B , 189 (1972)

-15- 1.14

Search for a Parity-Violating Contribution to Nucleon-Nucleon Scattering PARITY NON COt| by Service

D. Nagle, C. Hwang, N. Jarmie, P. Lovoi, J. McKibben, Institut de Physiq R. Mischke, G. Ohlsen, J. Potter, and R. Stevens University of California The study of parity Los Alamos Scientific Laboratory tenuous problem of the n tative understanding, we Los Alamos, New Mexico rlty non conserving (p. n the scalar forced 1J. and In the plausible fr for nueleons on their ma P. Debrunner, D. Fritz, H. Frauenfelder, and L. Sorensen, more, if we accept the p University of Illinois effects may be cla^sifie Urbana, Illinois ducsd by the TON interac The second corresponds state in a p-wave and gl Recent calculations extended these calculati One manifestation of a weak interaction between nucleons would be a TO rescattering effects p-meson. The second meet parity-violating effect in nucleon-nucleon scattering. It is expected that quantitative understand] model for the p-wave ami such effects exist, at the level of 10 or greater, of the normal cross to the cabibbo Hamiltonj given as the product of section, in low energy pp and pd scattering. An experiment has been under- former is fixed by cvc. taken at 15 MeV to detect a small dependence of the pp scattering cross noting that the pseudosc aATr 1 interaction whi< section on the longitudinal polarization of the beam. So far no effect has choice for the sign and -4 of the energy-dependeno been seen, and an upper limit of 5 x 10 is indicated. Efforts are being -4/ra= -0.56/m^.. This i made in ref.[4 ] made to reduce this limit. W<» have made a call potentials. Here,in ordi single-particle potenti; approximation. Fixing t) the isovector and isosc; Work performed under the auspices of the U. S. Atomic Energy Commission. Vv =

•m where the various contr being taken of the inde In comparison to t 30% and 10% effects in larger and,because of 1 by the nuclear correlat one expects from the fc predominantly.A siniilai small here too,even in effect found for the si contributes a AT=1 inti one order of magnitude the structure of the m exchange may also prov: 1.M.Chemtob.J.W.Purso i 2.E.H.Henley,PhyS.rev. 3.B. Desplanques.Phys. 4.R.J. Blin-Stoyle and 5.R.J.Blin-Stoyle,Phys 6;E, Fischbach and D.I 7.R. Delorme and M. Rh

-16- 1.15 ; 1 PARITY NON CONSERVING NUCLEAR INTERACTION AND THE SECOND CLASS AXIAL CURRENT -sft Marc CHEMTOB Service de Physique Theorique, CEN Saclay HP n°2 91,Gif-sur-Yvette Bertrand DESPIANQUES Institut de Physique Nuclcaire, Division de Physique Theorique,BP 1 91406 Orsay,France

The study of parity non conservation in nuclear physics may hopefully help us to clarify the tenuous problem of the nature of the hadronic weak interactions. With the view to reach a quantitative understanding, we have undertaken a study of the two-pion exchange contributions to the parity non conserving (p.n.c.) NH force in the covariant theory already applied with fair success to the scalar forceUj. In the plausible framework where one assumes CP conservation and neglects effects which vanish for nucleons on their mass-shell, the calculation involves a limited number of unknowns. Further- more, if we accept the predicted smallness of the p.n.c. interaction TCNA L2J (A = 33-isobar), the effects may be classified in two mechanisms^. _^The first corresponds to box diagrams with p.n.c. induced by the TON interaction, « = f/v/SF if(TxKJ

noting that the pseudoscalar coupling (p'-p)^ Y cancels out. The Sp coupling gives rise to aATr 1 interaction which is entirely determined once we know its coupling -.onstant g . A sensible choice for the sign and magnitude of the ratio (gp /6A> .suggested !_ '_! from recenT analyses of the energy-dependence of asymmetry between p^and (3= decays of mirror nuclei,is (gL/g,)= -4/nc -O.SS/m^ . This is of opposite sign to,and somewhat larger than,the tentative choice made in ref.[4 ] W«J have made a calculation of all these effects in terms of non relativistic two-body potentials. Here,in order to gain a more intuitive insight , we present results forthe effective single-particle potentials obtained by taking their nuclear matter average in the Fermi gas approximation. Fixing the input parameters at their currently accepted values, gives us for the isovector and isoscalar potentials: „-* vY . = (ff.p)-c(ff.P)-r.,3 (f -_ 0.30.A92 , -o.it-Q.ti i •„ ± i.JO i 3.1 /(ir) -fciO f + s.3«, ± 9.S8

where the various contributions are identified by the couplings from which they arise,account_& being taken of the indeterminacy in relative signs.We use the Cabibbo theory value, f =5.2 10 In comparison to the single-particle^ and p exchanges,the 2% exchanges give rather modest 30% and 10% effects in V. and V respectively. The effects in the two-body potentials are however larger and,because of their longir range relative to the n in V , they are apt to become amplified by the nuclear correlations. The role of nucleon isobars is notsfound to be very significant, as one expects from the forbidenness(due to CP) of s-wave 2K exchange to which they contribute predominantly.A similar argument for the p.n.c. vertex suggests that rescattering effects should be small here too, even in the instance of a sizeable^ N ^coupling. Of physical interest is the large effect found for the second class pseudotensor term.If we accept the above choice of(g_/gA),it contributes a AT=1 interaction with a known sign relative to the ATiO interaction which is almost one order of magnitude larger than the other 2n exchange mechanism. Thus,besides information on the structure of the non leptonic weak interactions,it seems that the consideration of 2% exchange may also provide us with useful tests of conservation laws. 1,U.Chemtob,J.W.Durso and D.O.Riska, Nucl.Phys. 633(1973)141. 2.E.M.Henley,Phys.rev.letters,27(1971 )542;B.H.J.IfcKellar and P. Pick.Phys. Rev.D7(1973)260. 3.B. Desplanques.Phys.lett-Ts (1972); H.Pirner and D.O.Riska.Stony Brook preprint(1973). 4.R.J. Blin-Stoyle and P.Herczeg,Nucl.Phys.B5(1968)29l;B.H.J.McKellar,Phys.Rcv.Dl(1970)2183. 5. R.J.Blin-Stoyle.Phys. Rev. 118(1960)1605 jR.Lacaze, Nucl.Phys. §4.(1968)657. B'.B. Fischbach and D.Tadic,Phys.Reports C6(1973)125. 7.R. Delorme and U. Rho,Nucl.Phys. B34(1971)317;R.Delorme.K.Kubodera and M.Rho.Saclay preprint.

-17- 1.16 PARITY VIOLATION IN ATOMS IN A RENORMALIZABLE THEORY OF WEAK AND ELECTROMAGNETIC INTERACTIONS WITHOUT NEUTRAL CURRENTS Til, C.A. PIKETTT Laboratoire de Physique Theorique et Hautes Energies, 91405 ORSAY, France.

We have evaluated the parity violation (PV) contribution in atoms using a renormalizable model of weak and electromagnetic interactions without neutral currents (: the S0(3) gauge theory of Georgi-Glashow). The calculations have been performed in the unitary gauge. I For simplicity we use first the version with five fundamental hadrons (quarks) {: (p;n,n' ,X; O with charges: (1;OOO;-1)} of the Georgi-Glashow ; model, unacceptable though it may be as it leads to too great a rate for measures time-revei 1^ -» nix . While the available limit on the T-vio] PV contributions to e p and e n interactions are evaluated up to order violation), no suet G a (: G is the weak coupling, a the fine structure constant). class currents. We violation be lookec Three types of graphs contribute (X is the heavy neutral lepton, v the o sitions where the n neutrino) J can be exemplified - squared ones such as to be proportional tor. If this factoj n. experiments seem tc a non-vanishing In - triangular ones such as it has to be a mesc depend upon energy (i.e. single-partic - and finally graphs of the wave function renormalization for charged 1 where Wo is the t such as . _ class current recer be applied direct Im GT a He GT whe is found to be gre or of vertex renormalization for neutral n such as Tt measurable. Failui sort will definite semi-leptonic weah We have studied the divergence cancellation mechanism by using the T'Hooft- Veltman regularization which is compatible with Ward's idendity. We have evaluated the dominant finite PV contribution neglecting pp'/Myj^ (p, P1 are quadrir momenta of the problem, Mjy the W mass) and e/M (e is a nonrelativistic energy of the atomic problem). can be expected the final result is propor- [l] - C.W. KIM 2 2 2 tional to Ga[(M' -M )/Mv^]x|A+BLog(M /Mv^)] where M" and M are the masses [2] - K. KUBODEE of either charged or neutral quarks, or neutral leptons. A slight difference should be noted between e p and e n contributions (due to the absence of 1 Ynn coupling): terms proportional to MXo /My^ and (M -M )/M^ (°r (M^ -M )/M^J contribute both to e p or en when parity^violation takes 2 2 place ifi the hadronic part, whereas the MXQ / M ^ terms do not contribute to t - n when parity violation takes place in the leptonic part.

Similar results are obtained when more realistic hadronic models are used, involving the 9 Han Nambu quarks (we use Fayet's models analogous to the Georgi-Glashow one but much simpler). Finally we discuss some experimental implications in the atomic spectra of heavy atoms and compare them to those obtained when neutral currents are present.

-18- 1.17 DPh-T/73-25 TIME-REVERSAL VIOLATION VIA SECOND-CLASS CURRENT ?

Kuniharu KUBODERA and Mannque RHO

Service de Physique Theorique Centre d'Etudes Nucleaires de Saclay I HP n ° 2 - 91190 Gif-sur-Yvette

s x The \ a)«fPe Pv) asymmetry coefficient D in nuclear beta decay measures time-reversal violation in semi-leptonic As r O weak interaction. While the available data on isodoublet decays (n-*p, 19N -+ 19F) set a stringent limit on the T-violation in the first-class current (i.e. no evidence of T- violation), no such limit has yet been placed on the T-violation in the second- class currents. We revive the suggestion of Kim and Primakoff LIJ that the T- violation be looked for in non-isomultiplet transitions, particularly in transitions where the main Gamow-Teller matrix element is highly suppressed. This can be exemplified by the decays *4C -» 14N and 32P -+ ^2S . Here D turns out to be proportional to 2 Im GA/IGAI where G. is the nuclear axial form factor. If this factor is of order unity, then fi can be measurable. Since the experiments seem to rule out the first-class current contribution to Im GA , a non-vanishing Im GA must arise from the second-class current. Furthermore it has to be a meson-exchange current, in particular, the piece which does not depend upon energy release because the energy-dependent second-class currents (i.e. single-particle current) are known to be suppressed by the factor WQ/ZM where Wo is the energy release. The energy-independent meson-exchange seeond- class current recently studied in connection with the mirror asymmetries'-2J can be applied directly to this problem. If we assume a maximal T-violation (i*e. Im Grp a Re G- where T stands for the second-class current), then 2Im GA/|GA1 is found to be greater than unity and hence D in the range which should be measurable. Failure to detect a significant asymmetry in transitions of this % sort will definitely rid of our suspicion on the goodness of T-invariance in IT semi-leptonic weak processes.

[l ] - C.W. KIM and H. PRIMAKOFF ; Phys. Rev. 180, 1502 (1969) [2] - K. KUBODERA, J. DELORME and M. RHO ; To be published.

i -19- 1.18 DETEBMINATION OF THE AXIAL VECTOR FORM FACTOR IN THE RADIATIVE DECAY OF THE PIONf TO TH: G. J. Igo, N. Chirapatpimol, M. Mxit, M. Nasser University of California, Los Angeles C. Jarl J. B. Carroll, D. Ortendahl, V. Perez-Mendez, A. Stetz Lawrence Berkeley Laboratory, Berkeley, California The neutron April, 1973 at threshold is mea In second order in slope of the electr We are currently running an experiment at the 184-inch cyclotron in The two-pho Berkeley to measure the axial vector form factor in the-radiative decay of the to the functions T sition of the tenso pion, IT -»• evy- We use a 24-element, leadglass Cerenkov hodoscope to detect neutrons ( >/ is t performing a Wick r the photon and a magnet-spark chamber spectrometer system to measure the mo- tegration of the re imaginary energy, mentum of the positron. We are able in this way to completely determine the at q2 fixed, and neutron structure f kinematics of the decay, which occurs with the pion at rest. Our system is ever, T-| ( »> ,1 ) n accessible to exper sensitive to events with large opening angle and maximum positron energy. reasonable or popul This makes the experiment as sensitive as possible to the structure-dependent Using these drawn. With presen component of the decay and avoids the background due to positrons from ordi- is negligible for e percent for muons, nary muon decay. but it becomes larg electrons, whereas We assume that the weak vector form factor for TT -»• evy can be calculated the correction is region the correspc exactly from the lifetime of the IT by using the conserved vector current hy- the transition betn The effective cut-c pothesis. Our experiment then determines the axial vector form factor by meas- photons and its TO] the r~4 potential uring the branching ratio into the kinematic region of interest. On the basis static fields, an of 110 events (approximately half of our final data) we have determined that the ratio of the axial vector to vector form factors, y = 0.1 ± 0.075. This is to be compared with the quark model prediction y = 0, as well as various current algebra calculations which require y ^ 0.5. On the basis of the branching ratio alone we are unable to rule out the complementary value of Y = "2.1; however, we expect to be able to resolve this ambiguity eventually by studying correlations in the momentum and angle distributions.

t This work is supported in part by the U. S. Atomic Energy Commission.

-20- 1.19 POLARIZABILITY CONTRIBUTIONS TO THE NEUTRON-ELECTRON AMPLITUDE AT THRESHOLD J. Bernabeu, CERN-Geneva C. Jarlskog, Department of Theoretical Physics, Lund and CERN-Geneva

The neutron-electron spin averaged forward scattering amplitude at threshold is measured from scattering of thermal neutrons on atoms. In second order in quantum electrodynamics this amplitude is given by the slope of the electric form factor of the neutron at zero momentum transfer.

The two-photon exchange contribution to this amplitude is related to the functions T-j 2( *> >1^) appearing in the gauge invariant decompo- sition of the tensor describing forward virtual Gompton scattering on 2 neutrons ( »/ is the photon energy and q -f^g Square Of its mass). By performing a Wick rotation in the >» plane, with |"q| fixed, the in- tegration of the relevant diagrams only involves space-like photons with imaginary energy. We write dispersion relations for the Compton amplitudes at q2 fixed, and the absorptive parts %( *»,q2) are the so-called neutron structure functions measured in electron neutron scattering. How- ever, T-]( if ,q2) needs a subtraction, and then T-j(o,q2) is not directly accessible to experiments. Its value can be determined relying on reasonable or popular assumptions.

Using these methods, the following results and conclusions can be drawn. With present experimental accuracies the polarizability correction is negligible for electrons, .whereas it can be of the order of several percent for muons. The zone-.of low -q2 gives the dominant contribution, but it becomes larger as the lepton mass increases [~ (10 MeV)2 for electrons, whereas -m2* for muons]. In the extreme relativistic limit the correction is proportional to m in (A/m), whereas in the classical ,«. region the corresponding quantity is linear in A and independent of m; "*ff| the transition between both;cases is governed by the value of A/2m- The effective cut-off A .is given by the inelastic excitations for virtual photons and its value turns out to be A2 =0.14 GeV2. This means that in the r~4 potential, which describes polarizability contributions for static fields, an effective cut-off is appearing at Reff~1 fm«

<* -21- 1.20

Determinat Cross-Sect act

B.A. LEAST SQUARES ADJUSTMENT QF THE Joint COUPLING CONSTANTS IN NUCLEAR BETA DECAY

The effective H. Paul and A. Kropf^ Johannes Keplep-Hoahsahule hyperons on proton A-4o45 Linzs Austria from the results c fast pions and net The weak interaction is characterized by one basic coupling constant. In beta decay, it leads to two types of transitions, Fermi-type and Gamov-Teller- type, whose strengths are given by the coupling: constants H.. and Gfl. We attempt to derive best values for these two constants from all pertinent experiments. The absolute value of G.. is determined from ft-values + + of 0 -0 transitions within an isomultinlet. Pecent remeasurements of the half-lives of the two best known beta emitters of this type, llf0 and 26 Al, have removed a long-standinp discrepancy between the two ft-values. Also, use of the 1971 mass table permits a somewhat better evaluation of decay energies than before. The final value of G.. remains, however, uncertain because of the uncertainty of the radiative correction.

The ratio G./Gv/ can be determined by usin

-22- 1.21

Determination of the A-Hyperon-Proton Elastic Scattering Cross-Section using the Experimental Results on the Inter- actions of Fast Particles with Carbon Nuclei

B.A. Shahbazian, A.A. Timonina and N.A. Kalinina Joint Institute for Nuclear Research, Dubna, USSR

The effective cross-sections for the elastic scattering of slow A- hyperons on protons are determined. The necessary information is extracted from the results of experiments on A-hyperon production in collisions of fast pions and neutrons with protons and carbon nuclei.

-23- 11 COHERENT PRODUCTION II.1

Naive View of High Energy Hadron-Nucleus Collisions*

Alfred S. Goldhaber^ University of California Los Alamos Scientific Laboratory Los Alamos, New Mexico 87544^

As data on high energy collisions with nuclei have begun to appear, speculations have followed about exotic behavior that might occur in these reactions. Such speculations are quite interesting and may turn out to be right, but meanwhile it is important to differentiate between those remarkable features which are already confirmed, and even more remarkable ones which are not. In the present paper such a differentiation is made, along lines recently 2 indicated. The results may be summarized by saying that all available evidence is consistent with the hypothesis that a fast hadron colliding with a nucleus remains a unit during the nuclear interaction. That is, the hadron is absorbed by the nuclear medium exactly as would be inferred from the free incident hadron-nucleon total cross section. Any fast secondary particles observed after passage through the nucleus did not interact separately with the nuclear medium, but rather remained part of the single unit referred to above. This hypothesis is a natural consequence of any "atomic" picture of internal hadron structure, but it is also suggested by other models, e.g., quantum electro- 3 2 dynamics. ' Th[he conclusions drawn here are in agreement with a recent review 4 by Subramanian.

* / Work supported by the U. S. Atomic Energy Commission: address after September 1, 1973: I.T.P., SUNY, Stony Brook, NY 11790. 1. C. Rogers and C. Wilkin, Nucl. Phys. B45_, 47 (1972); L. Van Hove, Nucl. Phys. B46, 75 (1972). 2. A. S. Goldhaber, Phys. Rev. D7_, 765 (1973). 3. E. L. Feinberg, J. Expl. Theoret. Phys. 50_, 202 (1966) [Translation: Soviet Physics JETP 23, 132 (1966)], and P. N. Lebedev Institute Preprint N166 (1972). 4. A. Subramanian, "Collisions of Hadrons with Nuclei at High Energies and the Fragmentation Models," Tata Institute Preprint T1FR-BC-72-12.

-27- II.2 Partial wave analysis of 3TC states coherently produced on nuclei.

Cern-ETH-Imperial College-Milano Collaboration OF (Send by G. Bellini) COMPARISON About 3.10 coherent events T? +Avjr +jr +* +A produced on nine different targets(Be,C,Al,Si,Ti,Cu,Ag,Ta,Pb) have been analysed to obtain the partial wave contributions to the 3*" systems (incidents momentum: 15.1 and 8.9 GeV/c). In order to depress the incoherent background,especially for the light nuclei, only events with t'<0.01(GeV/c) have been selected. Under these conditions the incoherent background is fairly constant for all the nuclear targets and I of the order ofll$ at 8.9 GeV/c incoming momentum. For this analysis the angular distributions e* the normal to the decay plane C. i of the 3it system have been used. The analysed 3>c mass regions range from 0.8flto l.WGeV/c2 at 8.9 GeV/c and from 0.95 to 1.40GeV/c2 at 15.1 GeV/c. Outside these regions the geometrical acceptance is so small that its correction becomes unreliable and the available bubble chamber statistics does not allow to check the different hypotheses assumed in order to correct the data for the efficiency. First of all our analysis suggests that any contribution from the natural spin -parity series is negligible. From the unnatural series only 0" and 1 waves contribute.The 1 dominates A total of : with percentages ranging from~ 70% to~80% at 8.9 GeV/c and from*75 tov80? at 0 nuclei and at inc 15.1 GeV/c. Finally an analysis performed separately for events on light (Be,C,A1 plus discuss the enerc Si at 15.1 GeV/c),media(Ti,Cu) and heavy(Ag,Ta,Pb) nuclei seems to suggest a the three-pion ma selective nuclear absorption,according9to the partial wave of the 3K system. In the 3irmass region 0.95-1.25 GeV/c ,the relative ratio 1 /0~ increases satisfactory. Thj of about a factor 2 from light to heavy nuclei at 8.9 GeV/c and of about a of the unstable | factor 3 at 15.1lGeV/c. THIs systematic effect,on the other side of the same about 25 mb. The order of magnitude of the errors,is still under analysis. nucleons obtaine to increase with found for the fof on hydrogen; the than the cross-sl spectrum on nucl| with that produc abundant coherec resonances seem

*) Work support t) Permanent ad

-28- I II.3 I ENERGY DEPENDENCE OF COHERENT PRODUCTION a? I OF THREE PIONS ON NUCLEI BETWEEN 9 AND 15 GeV AND I COMPARISON WITH DIFFRACTIVE THREE-PION PRODUCTION ON HYDROGEN *^ S ~ :—; : • P. Miihlemann, K. Freudenreich and F.X. Gentit, ETH, Zurich, Switzerland. G. Bellini, M. di Corato and G. Vegni, ' Istituto di Fisica - Sezione INFN, Milano, Italy. C. Bemporad , W. Beusch, E. Polgar and D. Websdale, CERN, Geneva, Switzerland. j§ P. Astbury, J.G. Lee and M. Letheren, Imperial College, London, England.

ABSTRACT

A total of 34,000 coherent events, produced on different target nuclei and at incident pion momenta from 9 to 15 GeV/c, allows us to discuss the energy dependence of ?the;differential cross-section and of the three-pion mass spectrum.tVTlie comparison with the optical model is satisfactory. This model is thenjused to determine the total cross-section of the unstable three-pion system on nucleons; the result is a value of about 25 mb. The value of the forward differential cross-section on nucleons obtained by application of the optical model shows a tendency to increase with incident energy. A similar increase with energy is found for the forward diffractive cross-section qt three-pion production on hydrogen; the absolute value of this cross-section is somewhat higher than the cross-section determined from nuclear"'targets. Also the mass 3 5 spectrum on nucleons derived from the present experiment is compatible with that produced on hydrogen. Furthermore, there is no evidence for

abundant coherent production of A and A3> On the other hand, these two resonances seem to be present in the incoherent background.

*) Work supported in part by the Swiss National Science Foundation, t) Permanent address: Istituto di Fisica dell'Universita, Pisa, Italy. II.4 12 + (4.44 MeV) MEASUREMENT OF 3trMASS SPECTRUM IN THE REACTION IT C •*• TT~ir~ir C G. Ascoli, H.R. Barton, L.E. Holloway, L.J. Koester, U.E. Kruse, L.J. Nodulman, Cone J.H. Smith, and R. Wojslaw, University of Illinois at Urbana-Champaign The Argonne Effective Mass Spectrometer was used in a 6 GeV/c beam (Fig.l) to measure the 3ir5mass spectrum in coincidence with the 4.44 MeV C* y-ray from 2 the reaction ifc^ •*• TT~TT ir~C^ *. Over 2000 good events were obtained. The preliminary mass distribution (Fig.2) peaks around the A^ meson. For these We have studie events, the Y flight time distribution excludes neutrons, and the missing mass 2 where the unde: is that of C± ± 70 MeV. The t distribution (Fig.3) shows a dip in the forward in the forward direction and falls exponentially at large |t| values. On-line analysis yielded an integrated cross section of 0.2 mb for this 3irC* production, i.e. portant but on. 10% of the irC* single scattering. following impn (i ) Since the i nucleus as oppi substantial re: two contributii

(ii) The Couloi rected for stn to the electroi increasing lonj (iii ) Concernii that the non-d: very different tic increase o:

Fig.l. Plan view of experiment These theoreti recent CERN ex

20b -

100 It I (&eV/c)%

Fig,3. Momentum transfer distribution 1. G. Faldt, D

0.8 1.0 1.2 /.V 2. G. Faldt, N MASS ( 3. C. Bemporad Fig. 2. Preliminary 3ir mass distribution. A) Raw data •£ 10. B) Data corrected for spectrometer acceptance.

-30-

** II.5

Coherent Non-Diffractive Nuclear Production Processes Goran Faldt University of Lund

We have studied coherent nuclear reactions a+ A "-* * + ^ where the underlying nucleon production amplitude a+^l-^a*^M vanishes in the forward direction. Examples of this type are K,aM = CK,tf*). fx#S) i (V>T:1 and f*-,o) • Also Coulomb production can be important but only at small momentum transfers. We have found the following improvements £i ,2} of the previous theory necessary.

(i) Since the Coulomb production mainly takes place outside the nucleus as opposed to the strong production there will be a substantial relative elastic Coulomb phase difference for the 1 two contributions.

(ii) The Coulomb production from within the nucleus must be corrected for strong absorption introducing corrections in addition "iM to the electromagnetic formfactor. Both corrections increase with increasing longitudinal momentum transfer. (iii) Concerning the strong production amplitude it has been found 1 that the non-diffractive amplitude yields a nuclear form factor very different from the diffractiv.e one. This leads to a drastic increase of the nuclear production amplitude. These theoretical improvemen.-tfs,have been amply verified in a recent CERN experiment [3.] -•/

3 . 1. G. Faldt, D. Julius, H. Pilkuhn and A. Mullensiefen, Nucl. 1 Phys. Bk± (1972) 125; m 2. G. Faldt, Nucl. Phys. Blj3 (1972) 591; i 3. C. Bemporad et al. , Nucl. Phys. B51 (1973) 1.

-31- II.6

Non-Diagonal Contributions to Incoherent Nuclear Production Processes. Inatyt Goran Faldt University of Lund We propose a aider the reactio Incoherent nuclear production processes A +* -*i>+k are intact; this is p studied within the Glauber model. The amplitude for a nucleus which makes a transition from an initial state IO to a final us describe the i state \i> is written as product b with A p IM * "Z. F'71 IM ^ IT and V being the for scattering (a The explicit form of F is given by the model. The index m signifies that the production step 4+ M -=» *> + N' taK.es the amplitude of place on the nucleon labelled m, the remaining nucleons merely Goldberger transf attenuating the incoming and outgoing beams. Further more

05- U) \ The sum over final states f is performed in the closure approximation and the result is specialised to incoherent scattering^, where ,1^ are R & •=•> ± • The diagonal terms in U) , C- e, «* =-v. | give the standard result. The non-diagonal terms are usually assu- waves, (|/ (i) ar med to vanish and they do in the Born approximation. In the and YJ.*)) are th present model they can be calculated and are .found to be important. Assuming the hadrons 1 and 2 to have the same strong For scatter: interaction with the nucleons gives second term desc tile, while the •us, MJpO i the target. We the final produc tile. The elect where T?'°) is the forward nucleon production amplitude and l^is1) only through the standard nucleon numbers. Examples, i) hai Numerically the non-diagonal terms are important and negative. coherently on bo The first few terms in the expansion (3) are typically reduced by a factor of two as compared to the standard theory (diagonal are absorbed in 3 terms only). Nuclear two-particle correlations do not appreciably of the beam part change our conclusions. in electroproduc

iij hadron excil resonances are v< excitation

-32- m II.7 SCATTERING, EXCITATION AND DISSOCIATION A* Malecki Instytut Fizyki Jadrowej, Krak6w 31-3^2, Poland.

We propose a classification of high-energy processes* Con- sider the reaction a+A -» b+B, asuuming that the target A is left intact; this is possible if the beam energy is large enough. Let us describe the interaction of the projectile a and of the final v oU +v product b with A by means of the potentials: a a a» ^b^b^b* U and V being the parts of the potentials which are responsible for scattering (a&b) and production (a^bj* respectively* We write the amplitude of the process* applying the generalized Gell-Mann, Goldberger transformations

MJU where H * H. are the free-particle Hamiltonians, fare the plane waves* w (£) are the exact solutions of the total Hamiltonian* and X^) are the scattering states* For scattering (H =H.,W=O) we have only the first term. The H aH ¥ second term describes the £5£i*2£i22 ^ i3» £°) of the projectile, while the third corresponds to its dissociation C^^S^) on the target. We infer that for dissociation the target distorts the final product to the same degree as it does for the projectile* The electromagnetic production of hadrons may thus proceed only through the channel of excitation. Examples*, i) hadron dissociation - multi-meson systems produced

coherently on bound nucleons in the reactions 7CN"*A|N } KK/-*QN are absorbed in nuclear matter with cross-section equal to that of the beam particle} the NM(l^70), being very little excited in electroproduction, is strongly excited in nucleon collisions

ii) hadron excitation - NN-»N* (l520)N, N* (l688)N - these resonances are very much excited also by photons and electrons* iii) excitation of and by photon -£N •* £ N, CO- Nf % N-*$ N*(l52OJ

-33- II.8

COHERENT PRODUCTION OF KW~ ON NUCLEI AND DETERMINATION OF THE - NUCLEON CROSS SECTION Thj T ] "*) C. Bemporad , W. Beusch, J.P. Dufey, E. Polgar, E ] **) P ( D. Websdale, 0. Zaimidoroga - CERN. D < K. Freudenreich, F.X. Gentit, and P, Miihlemann, ETH - Zurich An exi P. Astbury, J,G. Lee and M. Letheren, of 1= 1/2 Imperial College, London. tons with A 19 C ABSTRACT helium gas action are As a by-product of the coherent production of K (890) we have observed low-pressui about 25 000 events of K IT ir produced by incident K on different Fast forwat nuclei and at beam momenta of 9.7, 12.9 and 15.8 GeV/c. The K7nr strictive r mass distribution shows a broad structureless enhancement, centered magnet. A d at about 1.25 GeV. Two-particle subsystems show a very strong ging purpos K (890) and very weak p signal. The total cross section on a nucleon enable fast of the outgoing K ir TT - system is found to be around 22 mb (at Durit 12.9 GeV/c). the elastic lish that inelastic preliminai

*) Present address:1stituto di Fisica dell'Universita, Pisa, Italy.

**) Present address: JINR, Dubna, USSR.

-34- II.9

The Coherent Interaction of High-Energy Protons with He

T Ekelof and A J Herz (CERN, Geneva) : E Hagberg and S Kullander (GWI, Uppsala) P C Bruton, C S Curran, J K Davies, S M Fisher, F F Heymann, D C Imrie and G J Lush (UCL, London)

An experiment, with the principal aim of studying ntr and pir IT decays of I = 1/2 states produced by the coherent interaction of high-energy protons with He, has been installed recently at the CERN PS. A 19 GeV/c proton beam is incident upon a 50 cm long target containing helium gas at high pressure. Helium nuclei recoiling intact from an interaction are detected in a helium recoil spectrometer consisting of two coaxial, low-pressure cylindrical spark chambers surrounded by scintillator counters. Fast forward particles are detected in a spectrometer consisting of magneto- strictive readout spark chambers placed on either side of a large aperture magnet. A downstream picket fence of scintillator counters is used for trig- ging purposes and two atmosphere-pressure threshold gas Cerenkov counters enable fast pions and kaons to be identified. During the first cycle of operation, trigger rates were investigated, the elastic scattering angular distribution was measured, primarily to estab- lish that the equipment was functioning correctly, and one and three prong inelastic events were recorded. The data are currently being analysed and preliminary results will be ready in time for the conference.

-35- 11.10 P- He COHERENT SCATTERING AT 24 GeV OBSERVATION OF ELASTIC SCATTERING AND PRODUCTION PROCESSES BY A MISSING MASS METHOD

Co I laboration C lermont-Fd-Lyon-Strasbourg Division NP - CERN-CH 1211 Geneve 22

We use an intense proton beam (6 x 10l2p/p) from the CERN PS and an He gazeous target (1 atmosph.) recording the recoil nucleus with a telescope of 3 or 4 semiconductor detectors in coincidence.

Double identification of "*He is obtained with the two first AE detectors using the Goulding method (Fig. 1). Energy of the recoil is measured with a precision of 1 %. The detection angle can been varied from 90° to 57° (angular aperture = 4 mrad).

Fig. 2 exhibits the angular spectrum of '''He for each energy channel in the double scattering region (t > 0.2 (GeV/c)2). One can see in the inelastic region the contribution of the missing mass of the N* (1470) which maximum at 2 + = 33 MeV t = 0.25 (GeV) . He max The noise in this experiment has been reduced by an appropriate shulding at values like 1 % in elastic scattering and 5 % in inelastic.

Fig. 2 (Preliminar)

Fig. 1 £100

Elastic o 50 (second maximum) Number of events at 83,3° 0 -i

IQt . 50

I10

-36- .1.10 ii. n Study of nuclear interactions of 200 GeV protons in emulsion. M.Jurifi, O.AdamoviS, Institut de Physique, Belgrad, Jugoslavia. E.M.Friedlander, Institute of Atomic Physics, Bucharest, Romania. I.Otterlund, Univ. of Lund, Lund. Sweden. G.Baumann, R.Devienne, Univ. of Nancy, Nancy, France, J.Hebert, Univ. of Ottawa, Ottawa, Canada. J.Lory, C.Meton, D.Schune, B.Willot, B.Charquet, Tsai-Chii, Univ. of Paris, Paris, France. G.Baroni, Instituto di Fisica dell'Universita, Rome, Italy. P.Ciier, J.P.Massue, R.Kaiser, Laboratoire de Physique Corpuscu- laire, Strasbourg, France. J.Pellicer, G.Rey, IFIC, Facultad de Ciencias, Valencia, Spain. a Here we give some preliminary results obtained in two stacks of 'ular K5 nuclear emulsions exposed at NAL. The n}e§5_free_path measured by three different methods do not de- viates iignlEicantly from the values obtained at lower energies. the A (cm) No of Method Laboratory events at 35.3±0.9 1493 "along the track" 36.8±1.1 3632 "air scanning" Bucharest 31.5±2.2 357 "plates normally to the beam" Ottawa R at The mean charged multiplicity, of shower particles is 12.6±0.5. In Fig7~l"~is compared with multiplicities at lower energies and with intranuc- 150 lear cascaue calculations (Artykov et al. Nucl.Phys. B6,11(1968)). The dependence on tHe size of the

PROTON-PROTON AND target is also shown. The most PROTON -OUAS1NUCLEON INTERACTIONS striking property is the compara- "100 tively low multiplicities in p-N interactions. Fig. 2 shows the dependence between and N. . The largest multiplicity obtained in an event is n ,=51 (N, =15) . We o 50 also compare witn multiplicities at CERN-energies. The mean value of Nh is 7.0±0.3. Fig. 3 shows the angular_distribution of shower particleiT The"lack~of"structure 0 -4 -3 is obvious. Fig. 3 30

• 200 20 v

10 RIGHT SCAIE _ I 3^ s 2 § s 1 CASCADE O215CV raOTON-MKLEUS INTERACTIONS

_l t i i i i 3 5 10 20 50 100 200 500 5 ID 15 20 25 30 INCIDENT LAB. MOMENTUM. GeV/e NUMBER OF HEAVY PRONGS (N Fig. I Fig.2

-37- 11.12 ONE PION COHERENT PRODUCTION IN D-PINTERACTION

It. BALDINI-CELIO, P. ~U FAB3RI and P. PICOZZA. Laboratori Nazion&li di Fras-cati del CNEN - Frsscati Italy .

We present here a first rough calculation of the differential cross section for the process d+p-sd+missing ma^SH. at the kinemstical conditions of the 1 Saclay-fiacn-Frascati experiment ' (i.e', Pd inc~ 2. 945 Gev/c /for angles of scattered deuteron 0^ = 4. 6 and 7. 4 degrees) at. small momentum transfer. We assume the- dominant process to be: a P

The calculation has been done in the aim of the impulse approximation. We assume the elementary processus N+p^N+N'+rt to be dominated , at these energies and momentum transfers, by the O. P. E. model and formation of A 33 (1236) resonance. The dominant graph we consider is the following: a "^tn^^jni^'^

Our results ?.re presented in the figure. JNio normaiiiation to the cat a has been dene so, as it can ba seen., the order of magnitude of the calculated cross section is in a quite good agreement with tine data. The disagreement in the position of the peaks and in its fall out can. be due to the approximations done in this first estimation neglecting multiple scattering terms, interference with the graphs dominant at high mor-ncntum tranfer, Fermi rr.otion effects. More refined calculation aro in progress. 100 3 ( (*) -J. Banaigs, J. Berger, L. Goldzhal, I.,, V. Hai, M. Cottereau, C. J.,o Bi-un, 1 F. L. Fabbri and P. Picozza. -Contribution to this Conference. 90 \

80 .

70.

60.

50.

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30.

10.

f I

13 00 'ii.00

-38- 11.13 HIGH-ENERGY COHERENT INTERACTION OF DEUTERONS ON PROTONS. T. BANAIGS, T. BERGER, L. GOLDZHAL, L.VU.HAI CNRS and Departement Saturne, CEN, Saclay M. COTTEREAU, C. LE BRUN Laboratqire de. Physique (Gorpusculaire - UniyerBite'de Caen J F.L. FABBRI,P-. PICOZZA* :r>, ' '"'. '".[ \^^ '7:'.V - Laboratori Nazionali di Frascati del CNEN - Frascati, Italy We present the results of d +. p 7*d + (mm) experiment, performed with an extracted deuteron beam from Saclay synchrotron Saturne; at fl, 94 - - 3,41 and 3,i48GeV/c Incident beam momentum! The ExperimentalAppara- tus was essentially the same as that we used in studying d-d interaction (Phys. Letters B 43/6, 535 (1973)).

In this experiment the coherent production is cleary;separated from the incoherent and the missing mass, (mm), is produced in a T = 1/2 isospin state. We report in figure the momentum spectra of the scattered deuterons at 4,6-7,4 and 10,2 degrees for 2, 94 GeV/c incident beam. The spectra range from the elastic peak up to deuteron momenta of about 1300 MeV/c. The square of four-momentum transfer ranges from 6«10~2 to 1 (GeV/c)2. The spectra present three peaks: the elastic scattering peak and two structures in the region of coherent production.

1; i • r I I \

/ r

f 3 1 T L ' 1"T9001 i n ii . 13SD138013S0laOO«OO»O 900 140O1420H0O 1300 1100 « 13SO14OO14OO 1300 11C0 800

-39- 11.14

" Unfolded phase shift analysis " * G. Alberi + and P. Poropat

+ CB8U, Th.Division , Geneva and Istituto di Fisica Teorica , Miramare, Trieste * Istituto di Fisica dell Universita and TM&, Trieste

A method is given to unfold the Fermi motion in a phase shift analysis s using deuterium data; this method which uses the derivative formula t i practical and can be used, in a rainimization programme; in taking in account the Fernd motion, we have to assume an off-mass-shell dependence; the sensi = tivity to different assumptions is explored and the results are compared with numerical integrations, showing in this way that the method is good inside a few per cent.

1) G. 1) G.Faeldt and T.Bricson Nucl.Phys. B8 , 1 (1968) 2) R.J.C

-40- 11.14 11.15 "71 production on deuterium " + * G.Alberi and L.Rosa + CERN, Th.Division, Geneva and Istituto di Fisica Teoriea, Miramare, TriesteV * International Gentre for Theoretical Physics, Miramare, Trieste re, Trieste Recent' measures of K production on deuteron allowed a comparison of the total production rate on proton extracted from deuterium data and the same quan= tity directly measured on hydrogen.- Since the ratio Iietween the two numbers 6»/Si turned out to be 1,25, we started an analysis of all possible deuteron corrections, which can be calculated using present theories . Using a gaussian in account parametrization of the deuteron wave function, we found analytical formulas: he sensi = for various affection the total production rate on deuterium : the interference pared between the neutron amd the proton,: the interference between single amd double ; good scattering, the double scattering alone. Per instance the additivity formula for the total cross section on deuteron in the single scattering approximation beco= mes for the total production rate( for pure non spin flip production amplitudes) tti;

where b and b are the slopes of the differential cross section, the inverse mean squ ire radius of the deuteron; the formu= la is valid for any reaction on deuterium..

1) G.Giacomelli et al Nucl.Phys. B37, 577 (1967) 2) R.J.Glauber and V.Pranco Phys.Rev. 156,1685(1967) r 11.16

"High momentum tail in spectator distribution" + * * G.Alber-i, h.Gregorio and Z.Thome + CEEN Th.Division, Geneva and Istituto di Pisica Teorica , Miramare, Trieste •International Centre for Theoretical Physics, Miramare, Trieste

Various experiments on deuterium bubble chamber with different projectors ( K* p.,71) at high energy have shown a common feature, the tailing off at high momenta of the spectrum of the spectator(defined as the slower of the two nucleons resulting from the broken deuterium). We have explored the possibility of the presence of secondary interaction of the two .nucleons and double scattering of th fast particle. These interactions are calculated using Peynman diagram technique ;, which has the advantage to be relativistic invariant and connects low energy and high energy phenomena: for instance at low momentum tramsfer for the scatt<;= red particle, the energy of the recoiling nucleons is low and we can get analytic results for the final state interaction, using the non relativistic approximation of the triangular graph. Moreover, for the one pole representation of both the deuteron wave function and the nucleon nucleon amplitude at low energy, we can integrate the amplitude squared on the phase space and we obtain an analytic result for the effect of final state interaction as function of the momentum transfer, which coincides with the prediction of the closure sum rule . On the other side the double scattering, in the high energy limit is consist= ent with the Glauber formulat'tji

The result of the numerical calculation is reported in the figure: the process is K D-»K pp . The final state interaction, with the non relativistic model ( dot- dashed line ), is able alo= ne to explain qualitatively the tail. The continuous line if the single scat= tering approximation ar

i)G.Alberi,a.Castelli,P.Foropat nnd K.Sessa IMS - A3 - 72/3 , Trieste , June 72 PjBaillon CEfttf / D.Ph.Il/ PETS 72-50, August 1972 2)R.J.Glauber and V.Franco Phys.Rev. 156,1685 (1967) 3) L.Bertocchi Suovo CimenJ-; 50,1015 (1967) 4) Q.Giacomelli et al Mucl.Phys. B37, 577 (1972)

-42- 11.17

Coherent Particle Production in Huclei and the Diffraction Excitation Model

Tata Institute "of Fundamental Research, Bombay-5, India

Coherent production of pions by pions and protons on different target nuclei in the energy region 15-70 GeV have been examined^ in the light of the diffraction, excitation model' of multiparticie production for hadron-nuclebn collisions. It is noted that a wholly diffractive excitation mechanism predicts too high a cross section for coherent production on nuclei. A cross section of only;about 2-3 mb is expected for diffraction dissociation of either a pion or proton incident on a nucleon on the basis of available data on coherent production on nuclei. This estimate of cross section for diffraction dissociation on a nucleon is consistent with the estimates from a different type of 2- analysis onthetasls of the two cociponeht^^ model for multiparticie production in hadrbn-nucleori collisions.

1. M. Jacob and R. Slansky, Phys. -Rev. DJ,r 1847 (1972).

2. H. Harari and E. Rabinovici, Phys. letib. 42Bt 49 (1973).

-43- 11.18

Incoherent Particle Production in Nuclei and Hodels for Ilulti particle Production

A. Subramanian Tata Institute of Fundamental Research, Bombay-5, India

S. lal and P. Vyas Department of Physics, Jiv/aji University, Gwalior-1, India

Existing data on average multiplicity of charged secondaries in nucleon-nucleus collisions in the energy range 30-1000 GeV when compared with similar and more accurate data available for proton-proton collisions in the same energy range seem to suggest an energy independent and weak dependence of the average multiplicity on the mass number A like n(A)oc A * . Such a weak dependence is at variance with recent calculations of Fishbane and Trefil using the multiperipheral model and G-lauber theory of multiple scattering in nuclei. Although with the diffraction excitation model one predicts a weaker dependence of the secondary multiplicity on A than with the multiperipheral model, it appears that it is necessary to attribute a lower inelastic collision cross section for excited nucleons colliding with target nucleons than in the case of nucleon-nucleon collisions in order "to obtain an agreement with the data using this model.

1. P.M. S'ishbane, J.L. Newmeyer and J.S. Trefil, Phys. Rev. Lett. 29_, 685 (1972); P.M. Fishbane and J.S. Erefil, State University of New York at Stony Brook preprint ITE-3B-73-15, 1973. 2. A. Dar and J. Vary, Phys. Rev. £6, 24-12 (1972).

-44- III NUCLEAR SCATTERING III.l The Interaction of 50 MeV TT+ with Deuterons D. Axen, G. Duesdieker, I.. Felawka, C.H.Q. Ingram, R.R. Johnson, G. Jones, D. LePatourel, M. Salomon, and W. Westlund, Univ. of British Columbia, and L.P. Robertson, Univ. of Victoria. A 12.5 cm diameter plastic scintillation spectrograph was used to analyse the reaction products produced by bombarding a 2 cm thick liquid deuterium target with 50 MeVrpositiver'"pionsr deliveredTby a channel constructed at j-^g L.B.L. 184 in. cyclotron. The pion flux was about 1011 s"1. Data for each of the-following reactions were obtained simultaneously: -= - --• : ir - + d •*• d+ it (1) d p+n+ir (2) d 2p (3) The angular distributions of the elastic scattering and absorption cross- sections (1) and (3) were measured over an angular range of 30° to 150° with an accuracy of about 5%. Data on the inelastic cross-section (2) were also obtained. It is expected that 10% accuracies will be achieved for pion energy losses up to about 15 MeV. Pions in the incident beam were selected by time-of-flight and their momenta analysed to an accuracy of 1% dp /p. As the solid angle of the spectrograph was 50 msr, scattering angles for each event were determined using spark chambers. The energy-loss resolution of the whole system was about 2.3 MeV. Outgoing particles were identified by combinations of E, dE/dx and, for the case of pions, observation of the decay muon within 100 ns of detection of the pion. Preliminary values for the cross-sections are displayed in Fig. 1 and 2 (for reactions 1 and 3). The smooth curves in the figures are the results of recent theoretical calculations • . 1 D. Beder, private communication, 1973; Nucl. Phys. B34_ (1971) 189. 2 C. Richard-Serre et. al., Nucl. Phys. B20 (1970) 413.

/Trt. Z if+cl-* ZP

%o €o Bo too LAS AHGLE

-47- III.2

MOD.ua>-INDiiIPEND£NT DETERMINATION OP THJS COUPLING CONSTANTS 5 5 5 ?=:He dp %& ; fc He He /" ' S .Dubnidca*/, O.V*Dumbrais * *^-,P.Nichitiu* * *?, Joint Institute for Nuclear Research,Dubha,USSR

2 The determination of the coupling constants g He3 dp p aa3 and g jre3tre3 been carried out on the basis of the existing data on differential cross sections of the elastic p He-' scattering at 13.6 MeV,16.252 MeV,and 19.48 MeV. The method is based on the extrapolation of cky&£. parametrized in the experimental region, to the d- and 3T-poles. The conformal mapping is used to accelerate the convergence of the series representing dCT/clil. The explicit formulae expressing the pole terms ( d(T / dlL )d and ( d G" /cl XL )3T are also given.

Institute of Physics,Slovak Acad.of Sciences (Bratislava. Institute of Nuclear Physics, Moscow State University. Institute for Atomic Physics,Bucharest,Romania.

-48- III.3

O.V.Dumbrais v.FiNichitiu v/^Tu.A.Scherbakoy, Joint Institute for Nuclear Research,DubnatUSSR

ABS TEAcCf ; ; •<•'•'• * --' The vpossibility of cdetermination of the sTHe^ai coupling constant on the basis of the existing experimental data on the differential cross section^ of' t^ei ^fHe^rscattering at ^100 MeT has been investigated. The method is based on the extrapolation of dc/d Q. to the IK-pole exploiting the conformal mapping techniques in order to accelerate maximally the convergence of the series representing ai

'^Institute of Nuclear Phsyics .Moscow State University,USSR, • *, institute for Atomic Physics, Bucharest .Romania.

-49- III.4

PION COUPLING CONSTANT AND THE PION RADIOS V.Z.Kopeliovich Joint Institute for Nuclear ResearehtDubnatUSSR

ABSTRACT

The dispersion relations for the ^He pion form factor have been considered. The subtraction constant was found from the Goldberger - Freiman relation and the tritium decay data* The anomalous threshold contributions due to the -Tie- decay on the proton and the deuteron as well as the proton and the singlet deuteron, have been taken into account in the absorption part* Besides, the direct calculation of the corresponding Feinnan diagrams have been performed* The pseudoscalar coupling constant square relation was found to be G2/ g as 18. The ^He pion radius is R «, 1,52 M"! The %e charge radius has been also calculated in agreement with experimental data*

-50- III.4 III.5

ELASTIC SCATTERING OF 3T± MESONS ON \e AT 154 UE7. M.Albu *^,T*^**r V. J. Iyastenko, A .Mihul*/,P .Nichitiu*/, G.Piragiao* *{ I G.Pontecorvo,Yu.A.Scb.erbakov.

Joint Institute for Nuclear Rssearcb.,DubnafIJ5SRe ABSTRACT The elastic scattering differential cross section of 3T+ and 3T~ mesons on %e has been measured at 154 iffeV with a high pressure streamer chamber^ i The angular distribution for the elastic scattering was measured for angles between 25° and 165°. The total cross sections are presented. The obtained results are compared with data on elastic scattering

of «jf mesons on He in the region of the A ,2 resonance' '•

1. I.V.Falomkin et al. lett.Nuovo Cimento,5»757 (1971)* 2. I.V.Falomkin et al. Lett.Nuovo Giment0,5,1121 (1972).

*^ Institute for Atomic Physics tBucharesttRomania. **/ Istituto di Pisica dell»Universii;a,Torino. Istituto Nazionale di Fisica Nucleare .Sezione di Torino.

-51- III.6

APPLICATION OP ACCELERATED CONVERGENCE EXPANSION FOR THE PHASE SHIFT ANALYSIS OF THE ELASTIC X%e4SCATTERING. O.V.Dumbrais ' , F.Nichitiu ' ,Yu.A.Scherbakov. Joint Institute for Nuclear Re se arch, Dubna,USSR.

ABSTRACT

The phase shift analysis of the elastic jf-He scattering in the energy range of 25-180 Mev has been carried out by means of the accelerated convergence expansion. The results of this analysis are compared with those of conventional analysis. The possibility of the more realistic estimation of the higher partial wave contribution is discussed.

'Institute of Nuclear Physics,Moscow State Iniversity,USSR "^Institute for Atomic Physics .Bucharest,Romania.

-52- III.6 III.7

ON THE ELECTROMAGNETIC PION RADIUS COMING FROM ^He* SCATTERING F.Nichitiu^yfu.A.Scherbakov Joint Institute for Nuclear Research,Dubna,USSR tING. The aim of this work is to analyse the influence of ambiguity from phase shift analysis, of the total cross section and of the pion beam energy on the electromagnetic pion radius derived from JT-He elastic scattering measurements. , The ambiguity in the nuclear amplitude,the total cross section and the incident beam energy are very important and have sring much larger effects on the pion radius calculations than all r other Coulomb corrections* Lts The average value of the electromagnetic pion radius cal- ana- culated with solution I for phase shifts and taking into account >f the non-point Coulomb phase shifts is

ty in the x*

JSSR Institute for Atomic Physics,Bucharest,Romania.

-53- III.8

ELASTIC SCATTERING OFjf± MESONS OK 4He AT 70 AND 154 MEV. M.Albu*/,T.Besliu*{l.V.Falomkin,R.Garf afiirri.**/,M.M.Kulyu]d.n, V. J.Lyashenko ,A.Mihul*^ ,P.Nichitiu*/',G.Piragino* *^, G.Fontecorvo, Yu. A.Scherbakov. Joint Institute for Nuclear Research, Dubna,USSR

ABSTRACT The differential cross section for elastic scattering of fl+ and 3f~ mesons on He have been measured afe 70 and 154 Mev with a high pressure helium streamer chamber. These measurements present a development of former investigations of the elastic scattering in the A „ resonance region^ '»*' using the high pressure streamer chamber' K A phase shift analysis was carried out and a set of phase shifts obtained. The results are compared with phase shift values obtained from the analysis of angualr distributions at different energies, 1. I.V.Falomkin et al. Lett.Nuovo Cimento,3,461(1972), 2. I.V.Falomkin et al. Lett.Nuovo Ciaento,5,1121(1972). 5. I.V.Falomkin et al. Lett.Nuovo Cimento,5,1125(1972). 4. I.V.Falomkin et al. Lett.Nuovo Cimento,5,757(1972).

'Institute for Atomic Physics(Bucharest,Romania.

••/• Istituto di Fisica dell»Universita-Torino. Istituto Nazionale di Fisica Nucleare-Sezione di Torino

-54-

•i. III.8 III.9

TOTAL GROSS SECTION FOB THEDOUBLE CHARGE EXCHANGE REACTION + 4 4 p AT 100 MEV.

I.V.FalomkLn, C.Georgescu ' ,M.MaKulyuk±atV.J.Lyashenko, A.Mihul ' ,F,lTichitiu*'lG.Piragino**'fG.Pontecorvo,A.Sararu*{ Yu.A.Scherbakov.

Joint Institute for Nuclear Research, Dubna,USSR

ABSTRACT The cross section for the reaction 3f + He^—?-^r~+ 4 p has been measured with a high pressure helium streamer chamber triggered by a scintillation hodoscope^-7 .Measurements were made for angles between 25° and 165° • By supposing the angular distribution of the secondary pions to be isotopic we have obtained the] following total cross section for the double charge exchange: 27 2 <5"tofc# =( 0.30 r 0.15). 10" cm . The obtained value turned out to be somewhat smaller, than is expected from calculations using the model of pair correlations.

1. I.V.FalomkinfM.M.Kulyukin,V.J.Lyashenko.F.Nichitiu,G.Ponte- corvo and Tu.A.Scherbakov. Lett.Nuovo Cim.3,461(1972). 2. F.Becker and Yu.A.Batusov. Revista del Nuovo Cimento, (1970).

V Institute for Atomic Physics,Bucharest,Romania. **/ Istituto di Fisica delllBniyersita-Torino Istituto Nazionale di Fisica Nucleare -Sezione di Torino

•'/SSL III.10

Ambiguities in IT He Phase Shift Analysis

F. Nichitiu* Joint Institute for Nuclear Research, Dubna, USSR

In the practical case of analysis of the scattering of zero spin on zero spin (ir~ He - ir'He in the energy range 24-154 MeV) with a finite number of partial waves, taking into account unitarity conditions and the total 2 cross section (and of course x criterion) gives only two solutions for phase shifts. For the low energy interval (< 60 MeV) the difference between the phase shifts of solutions I and II is smaller than at larger energy and therefore it is simple to confuse the first with the second solution. The scattering amplitude has two zeros in the complex cos6 plane. For the whole energy interval the first zero is in the upper half plane for solution I and in the lower half plane for solution II, and its position is dependent on the total cross section. For both solutions the second zero is roughly in the same position and is independent on the total cross section. The total cross section information is very important (even at very low energy - for scattering length calculations) for a good continuity of zeros trajectories and therefore for removing ambiguities in the phase shifts.

Institute for Atomic Physics, Bucharest, Romania.

-56- III.ll

SMALL ANGLE $f ^He ELASTIC SCATTERING AT 3,48 AND 6,13 Gev/c

A.A.Nomofilov, I.M.Sitnic, L.A.Slepetz, L.N.Struhov Joint Institute for Nuclear Research, Dubna

The $f He elastic scattering differential cross - section were measured in the range of the small squared four-momentum transfers of 0,0056 £ /t/ ^ 0,087 and 0,0056 £ /t/ £ 0,0462 (Gev/c)2 at 3,48 and 6,13 Gev, respectively. The data were analysed by the Glauber theory. The slope parameter of the spin-independent differential cross-sections of the tfTN elastic scattering was obtained. The slope parameter of the diffraction cone, the total

-57- III.12 STUDY OF THE REACTION 12C(ir,ir)12G* at 4.5 GeV/c SMALL ANGL J.L. Groves, L.E. Holloway, L.J. Koester, W-K. Liu, L.J. Nodulman, D.G. Ravenhall, and J.H. Smith, University of Illinois at Urbana-Champaign Ins In a 4.5 GeV/c TT beam at the Argonne ZGS, we used the apparatus shown in Fig. l(a) to observe the 4.4 MeV y ray in coincidence with the scattered IT" The d from ir~C -*• ir~C*(4.44 MeV). The circles and crosses in Fig. l(b) represent independent experiments using annular counters and wire spark chambers, respec- in the Cou tively. The results of Scipione ejt all/ at 3 GeV/c are also shown. framework Ravenhall and Schult calculate the cross sections in absorptive DWBA. They use the transition form factor between the ground and C* state obtained the region from electron scattering data. Their results agree well in shape (Fig.l(b))but figures be are 2.0 times the measured values. This discrepancy is hard to understand'. sections)* The same model predicts populations of M states in C*. The M=0 state Good dominates, and RepQ2/P00=^'^^" Insofar as incoming and outgoing pions are absorbed equally, time reversal invariance predicts PQI=O. (In meson production MeV the mo experiments, the ratio RepQi/poo should be a sensitive test of the difference momentum in nuclear absorption between the outgoing meson and incoming pion.) The dominance of M=0 is shown by the distributions in Fig. 2. The curves are least ing at 120 squares fits to the experimental histograms corresponding to Rep /p =0.08+0.04 0 m nft This is pi f ^ real to in Scipione, Melhop, Garland, Piccioni, Kirk, Bowles, Sebek, Murty, Kobrak, Marraffino, and Allen, Phys. Lett. 42B, 489 (1972)^_ (0.6 in c< higher en< 25- 100- -0.30 in -0.28 +, 0,

H. Le M.L.

(Si 10

to -t (GeV/cr Fig.l(a). Top view. Nal(TJt) y counter at 8Y=9O°. T=target; H=hodoscope(1.2m)2; S=spark chambers. Rl-4 are concentric ring counters. 90 180 270 360 a (b).©=Ring data; X=spark data; PION AZIMUTH (DEGREES) V=Ref .1; =Theory*2 (See text) Integrated cross section=2.0 mb. Fig.2. Histograms of $ distributions. C* recoil toward v counter at <{>=18QO. Curves are least squares fits (see text).

-58- 11.12 III.13 SMALL ANGLE 7C _ C SCATTERING IN THE REGION OF THE(3,3) RESONANCE H. LESNIAK and L. LESNIAK iaign Instytut Fizyki Ja.drowejv 31-3^2 Krakow 231 Poland. wn in + 12 in- The differential cross-section for the 7T - C scattering ec- in the Coulomb-nuclear interference region is calculated in the framework of the multiple collision model [lj • New data [2] in ed the region &f the (3,3) resonance are compared with theory (see ))but figures belovf dashed lines give the purely nuclear cross- • sections)* e ab- Good agreement is found at 167 MeV and 2*t2 MeV but at 115 tion MeV the model gives about UO56 too small cross-section for the nee —12 momentum transfers A < 8 x 10 GeV • Por the dom- - C scatter- east ing at 120 MeV the model gives too large sross-seetion W-0.04 This is probably caused by a too large value of the ratio of the real to imaginary parts ef the forward scattering amplitude (0.6 in comparison with experimental value 0.2^ £ 0*06) • At higher energies 167 and 2*»2 MeV we obtained the ratios 0.12 and

-0.30 in agreement with the experimental fits 0.03 + 0*0| and

-0*28 +, 0a0<» respectively* [l] H. Lesniak and L. Lesniak. Nuclear Physics 228 (1972) 221 [2J M.L. Scott et al. Phys.Rev,Letters 28 (1972) 1209

360 Ql li- ter

-59- III.14 TC~.l6o ELASTIC SCATTERING IN THE REGION OF THE (3,3) RESONANCE R.C. Berca H. LESNIAK and L. LESNIAK K. Gowtow Instytut Fizyki J^drovej, 31-3^2 Krakow 23, Poland University Columbia.

Recent data [ l] for the 7C ~—O elastic scattering at the The dif£ kinetic energies 160, rj'O, 220, 230, and 240 M©V are compared calcitna we using expe with the Glauber multiple collision model* Coulomb interactions experiment are included. /For description of the model see ref. \_2j •/ from 15 de; absolute a [ll R.W. Bercaw et al. Phys. Rev. Letters 22 (1972) 1031 The crosi [2] H. Lesnlak and L. Lesniak, Nuclear Physics B^8_ (1972) 221 first dete is 6bserve< observed mi bombarding The data scattering quite succi ing data 2. ing studies' differentii underestimi factor of 1 1. R.W. B< Anders 1 2£ 15 2. R.H. 3. S.C. 4. R.P. B.C. D.H. 20030n

3fUc \ v-"o • (S9 y, TlaB -2*0M* !

1-^\

»' 1 i Dl 08 12 16 JO

-60- III. 15 ir~ + lf0Ca Elastic Scattering Near the Resonance Region R.C. Bercaw and J.S. Vincent NASA Lewis Research Centre, M. Blecher arid K. Gowtow Virginia Polytechnic Institute and State University, R.C. Minehart University of Virginia, R.H: Landau and RJR. Johnson University of British Columbia. - - - _ .-.--.- .

The differential elastic cross sections for negative pions scattering from calcium were determined at pion bombarding energies of 205±5 and 215±5 MeV using experimental apparatus similar to that used in an earlier' ir~ '•+16 0 experiment^-). The cross sections were measured in two degree increments from 15 degrees to 70" degrees, with a relative accuracy of ten percent and an absolute accuracy of about 15 percent." ,••"•"' The cross sections follow an oscillatory diffraction-like pattern with the first detectable minimum at about 30 degrees. A second diffraction minimum is observed at about 45 degrees. The cross section magnitude of the first observed maximum is 51±6 and 36±5 mb/sr respectively for 205 and 215 MeV . bombarding energies. . ,, The data has-been compared with cross section calculations based on multiple scattering theory performed in momentum space^). Such calculations have been quite successful in reproducing the ir" + *2C and the ir~ + 160 elastic scattering data-2)3). Nuclear density parameters were taken from electron scattering studies^) and pion nucleon phase shifts from reference 5; The calculated differential cross sections agreed precisely with the 215 MeV data while underestimating the first observed diffraction peak in the 205 MeV data by a factor of two. 1. R.W. Bercaw, J.S. Vincent, E.T. Boschitz, M. Blecher, K. Gowtow, D.K. Anderson, R. Kerns, R. Minehart, K. Ziock, and R. Johnson, Phys.Rev.Lett. 29_ 15 (1972) 1031. 2. R.H. Landau, S.C. Phatak, and F. Tabakin, Ann. Phys. _78 (June 1973). 3. S.C. Phatak, F. Tabakin, and R.H. Landau, Phys. Rev.£ (May 1973). 4. R.F. Frosch, R. Hofstadter, J.S. McCarthy, G.K. Noldeke, K.J. VanOostrum, B.C. Clark, R. Herman, D.C. Ravenhall, Phys.Rev. 17£ 4 (1968) 1380. D.H. Herndon, A. Barbaro-Galtreri and A.H. Rosenfeld, LRL Report UCRL 20030irN (1970) unpublished.

-61-

:>.st III.16 An Approach to Picn-Nucleus Scattering Near the (3*3) Resonance with a Dynamically Modified Optical Potential m Saul Barshay, The Niels Bohr Institute, Copenhagen, Denmark Victor Rostokin, Moscow Physical Engineering Institute, Moscow, U.S.S.R. I George Vagradov, Institute of Nucuear Research of the Academy of Sciences of the U.S.SuR.y Moscow, U.S.S.R. We develop a new approach to pion-nucieus scattering near the first pion- nucleon resonance which is based upon the.modification of the pion Green's function due to isobar-hole excitation in the nuclear medium. Pion-nucleon scattering in the medium is modified in at least two essential ways: (1) the wave number is changed from the free-space value and (2) the isobar mass (and width) are modified in the medium. These modifications are important because the elementary scattering amplitude is a resonant, and hence strongly varying function of these variables. We construct a dynamically modified effective optical potential. The essential results are: (1) the growth of the attractive real potential with nuclear density is limited, and thus so is the growth of the pion wave iucfibsr m the medium; (.2) the resonance structure is broadened and is shifted doitonard in energy, in the medium, since the increase in the real part of the wave number in the attractive medium compensates in the P-wave scattering amplitude for the lower beam energy* An essential new quantity appears in the formulation of the effective optical potential, denoted by (V* - V) = Am* • This quantity includes a shift in ths effective mass of the composite isobar in the medium due to the interactions of the component pion, and due to the Pauli principle restriction on the component nucleon. The quantity also includes a possible difference between the binding potential felt by an isobar and by a nucleon in the medium.

-62- 1.16 III.17 THEORY OF PION-NUCLEUS OPTICAL POTENTIAL* J. Barry Cammarata 'and M.K. Banerjee University of Maryland, College Park, Md., 20741, U.S.A.

Since Kisslinger's formulation of the pion-nucleus optical potential, developed in the context of Watson's multiple scattering theory, most theo-

.on- retical effort in this field has focused on adding physically motivated refinements to Kisslinger's proposed form for the elementary pion-nucleon >n •he amplitude (which was used in impulse approximation te form the optical and potential). Although the original proposal, consistent with Watson's theory, rase ring was for an optical potential to be used in the Schrodinger equation, one re finds in the literature examples of the use of Kisslinger's potential in the ictive Klein-Gordon equation. Furthermore, the important physics represented by of led crossing is absent from the Watson-type optical potentials so far considered. We have formulated a theory of pion-nucleus optical potential using the single-pion Green's function in the presence of the nucleus. The results of our theory are best expressed in terms of an operator D which, bhe like the Kiss linger potential, is constructed by adding elementary pion- ybion nucleon invariant amplitudes, and another operator C which is obtained from D by crossing;, i.e.,

The optical potential (to be used in the Schrodinger equation) is expressed

as •; «

whereJfcv.5^Tr^J-Wx and the fully'off-shell scattering amplitude is given by T The second term in U(<4 arises from the crossing property. For a spin zero isospin zero target D=C, and one?'gets .

where T= C*fcd T C*-A\7^ and gives the invariant pion-nucleon amplitude. The implications of this optical potential in the scattering of pions by an N^Z target and on distorted wave calculations of the pion production process will be discussed.

*Work supported in part by the U.S. Atomic Energy Commission

-63- III.18

Exclusion Principle Effects in Pion-Nucleus Scattering Near tha 3,3 Resonance* J.M. Eisenberg and H.J. Weber Department of Physics, University of Virginia, Charlottesville, Virginia

In the conventional approach to nuclear scattering, theoretical work attempts a description of the scattering of the projectile on a nucleus in terms of the projectile-nucleon scattering. Recently, Bethe pointed out1 that for pion scattering near the 3,3 resonance there are important effects arising from the exclusion principle as it acts on the nucleon during the fundamental scattering process. Indeed, this Pauli blocking affects the shift and the width of the 3,3 resonance in nuclei. We have studied this by adapting the Chew-Low theory2 to a nucleon immersed in a Fermi sea, with suppression of the internal nucleon contributions by the exclusion principle. This amplitude is then used in a local density approximation, along with a self-consistent determination of the pion energy in the nuclear medium. Results are shown in Fig. 1, and exhibit clearly the consequences of the exclusion principle effect. Comparison with the existing data3 on C indicates that the blocking effect brings theory into good agreement with experiment, without adjustment of parameters.

References *Work supported in part by the National Science Foundation 1 1. H.A. Bethe, Phys. Rev. Lett. 30_ (1973) 105. 2. G.F. Chew and F.E. Low, Phys. Rev. 101 (1956) 1570. 3. F. Binon et al., Nucl. Phys. B17 (1970) 168. 1

180 MeV

Fig. 1. Differential cross sections for pion scattering on 12C, in a local I density approximation, compared with the data of ref. 3; the dashed curve is for no Pauli blocking.

-64- III.18 III.19

Coulomb effects in IT -C and IT -C total cross-sections inia A.S. Clough, G.K. Turner ork Physics Department, University of Surrey, Guildford, Surrey, U.K. s in B.W. Allardyce, C.J. Batty, D.J. Baugh W.J. McDonald, R.A.J. Riddle, L.H. Watson, Rutherford High Energy Laboratory, Chilton, Didcot, Berkshire, U.K.

M.E. Cage, G.J. Pyle, G*T.A. Squier, Physics Department, University of Birmingham, U.K.

Due to the distortion of the incident pion wave function by the Coulomb field the total cross-section for the scattering of negative pions by a T™ = 0 nucleus is larger than that for positive pions at the same energy. Coulomb contributions to ir-nucleus total cross-sections have been calculated (1) using a semi-classical method assuming a completely absorbing spherical nucleus. Total cross-sections for positive and negative pions on carbon have been measured (2) for energies from 90 to 850 MeV and the observed differences found to be in agreement with those calculated from the semi- classical method (1) and the optical model.

The evaluation of total cross-sections from the measurements at the lower energies is considerably complicated by the. need to know Coulomb-nuclear interference terms. In ref 2 an optical model calculation using a Laplacian potential was used and this gave agreement with interference 4eV terms calculated from small angle elastic scattering data at 120, 180 and 260 MeV. At energies in the region of 90 MeV however the model gives values for the forward scattering amplitude:.Ke>f(o) rather larger than those obtained from dispersion relations; (3)*.?' Using a model giving rather better agreement changes the differences between ir"and TT+ cross- sections from 4.7 ± 4.95 to 15.1 ± 5.8%^at 87 MeV and from 6.7 ± 2.4% to 11.6 ± 2.5% at 113 MeV.

These values are still consistent with those calculated theoretically but the changes in the deduced differences emphasises the need for caution in the interpretation of data at these low energies. Measurements of elastic scattering cross-sections at these low energies would be very useful.

1 G. Fa'ldt and H. Pilkuhn, Phys. Lett. 40B, 613, 1972.

2 A.S. Clough, G.K.. Turner, B.W. Allardyce, C.J. Batty, D.J. Baugh, W.J. McDonald, R.A.J. Riddle, L.H. Watson, M.E. Cage, G.J. Pyle and G.T.A. Squier, Phys. Lett. 43B, 476,. 1973.

3 Birmingham - Rutherford - Surrey Collaboration. Contribution to this Conference.

-65- III.20

Optical Model analysis of pion nucleus total cross section data

A.S. Clough, G.K. Turner Physics Department, University of Surrey, Guildford, Surrey, U.K. B.W. Allardyce, C.J. Batty, D.J. Baugh W.J. McDonald, R.A.J. Riddle, L.H. Watson Rutherford High Energy Laboratory, Chilton, Didcot, Berkshire, U.K.

M.E. Cage, G.J. Pyle? G.T.A. Squier Physics Department, University of Birmingham, U.K.

In a recent experiment at the Rutherford Laboratory, measurements of iri-nucleus total cross sections, in the energy region 86-870 MeV, have been made for 6Li, 7Li, ^Be, 12c, 16o. (1) The predictions of various forms of optical model potential have been compared with this data. The two forms used are the Laplacian:-

V_# = -(A-l) f(b p.2- >] 41 Li •— C and the Kisslinger:-

V p 2p - K oo where b and bj are parameters derived from pion nucleon phase shifts. (2) Dedonder, in a recent paper, (2) discusses the approximations made in the derivation of these potentials and proposes modified b1 parameters where the 1 kinematic transformation between the pion-nucleon and pion-nucleus systems is treated more exactly. He also questions the replacement of A-l by A.

We have investigated all these possibilities as well as the effect of Fermi- averaging the parameters. The results show the Laplacian model gives better agreement with the total cross-section data than the Kisslinger model. The Fermi averaging improves the agreement as does using A-l rather than A. The b1 parameters give little improvement on the b parameters. Good agreement between the measured values and the predictions is obtained over the region of the (3,3) resonance but between 300 and 700 MeV there are significant discrepancies suggesting that further modifications to the parameters or the form of the potential are required.

A.S. Clough, G.K. Turner, B.W. Allardyce, C.J. Batty, D.J. Baugh, W.J. McDonald, R.A.J. Riddle, L.H. Watson, M.E. Cage, G.J. Pyle and G.T.A. Squier. Rutherford Laboratory Report No RPP/NS 11. J.P. Dedonder. Nucl. Phys A174 (1971) 251.

-66- III.20 III.21 it a 7 9 Pion-nucleus coupling constants for Li and Be G.T.A. Squier, M.E. Cage, G.J. Pyle, Physics Department, University of Birmingham, U.K. J.K. A.S. Clough, G.K. Turner Physics Department, University of Surrey, Guildford, Surrey, U.K.

U.K. B.W. Allardycey C.J. Batty, D.J. Baugh W.J. McDonald, R.A.J. Riddle, L.H. Watson Rutherford High Energy Laboratory, Chilton, Didcot, Berkshire, U.K.

It has been shown by Ericson and Locher (I) that the pion-nucleus coupling strength reff can be obtained from pion scattering by nuclei with Tz = J, lave been using dispersion relations. Using the notation of ref (1) they obtain ; forms of m^ f forms in da' In; f (-) ceff ) - — P T IT • n k'2 where ;(~} ^ - * [Vx

1 T.E.O. Ericson and M.P. Locher. Nucl. Phys.. A1A8, 1, 1970. LUgh, le 2 A.S. Clough, G.K. Turner, B.W. Allardyce, C.J. Batty, D.J. Baugh; 1. W.J. McDonald, R.A.J. Riddle, L.H. Watson, M.E. Cage, G.J. Pyle aid G.T.A. Squier. Phys. Lett 43B, 476, 1973. .

3 M. Ericson.* Ann. Phys. jjr3, 562, 1971.

-67- III.22

The forward ir-C elastic scattering amplitude

B.W. Allardyce, C.J. Batty, D.J. Baugh W.J. McDonald, R.A.J. Riddle, L.H. Watson Rutherford High Energy Laboratory, Chilton, Didcot, Berkshire, U.K.

M.E. Cage, G.J. Pyle, G.T.A. Squier Physics Department, University of Birmingham, U.K.

A.S. Glough, G.K. Turner Physics Department, University of Surrey, Guildford, Surrey, U.K.

Calculations have been made using pion-nucleus forward dispersion relations to determine the real part of the ir-12c forward elastic scattering amplitude

2to.r. 1 (+) u'dio Im f (u') Re f(+)(u>) Re X L i,i2 (,.j2-,.2\

U)0 where Im = ~ (a (a)') + a _ (u1) ) It X IT X 12, Total cross sections have been measured for IT and fr scattered from ""C in the energy range 90 to 860 MeV. The ir~ l^C data is in good agreement with those of Binon (1), Crozon (2) and Cronin (3). Following Ericson and Locher (4) the form of Im f(+)(u) in the unphysical region (

It was found that the general form of Re f (to) was fairly well determined, but the magnitude,, especially at low energies (Tw < 200 MeV) is very sensitive to the position and form of the matching between the physical and unphysical region. Two different fits were made to match at u = % and 0) = i% + 20 MeV while a third, was allowed to match freely (i.e. no constraints on the fit). The magnitudes at T^. = 80 MeV in the three cases where (1.53 fm, 1.921 fm and 2.36 fm) respectively, demonstrating how poorly Re fC+/(0) is determined.in the low energy region. All three curves are in fair agreement with the experimental values for Re f(+)(0) derived from differential cross sections by Binon (5) and Scott (6).

1 F. Binon et al. Nucl Phys. B17 (1970) 168 b 2 M.J. Crozon et al. Nucl Phys. 64_ (1965) 567

3 J.W. Cronin et al. Phys Rev. 1CT7 (1957) 1121 to1 4 T.E.D. Ericson and M.P. Locher. Nucl Phys. A148 (1970) 1 '1 5 F. Binon et al. Nucl Phys. B33 (1971) 42" " 6 M.L. Scott et al. Phys Rev Lett. 28 (1972) 1209

-68- •••'• -/ II. 22 III.23 THE ROLE OF THE 3-3 RESONANCE IN THE IT -NUCLEUS ELASTIC SCATTERING Ryoichi Seki, California State University, Northridge, California 91324 We are interested in a question which effects,included in optical potentials and Glauber's multiple scattering theory that reproduce the elastic scattering data (1) remarkably well, are really dominant in 7T-nucleus elastic scattering,or more explicitly what pion dynamics in the nucleus is really revealed in the elastic channel. In order to answer this question we formulated a multiple scattering theory so as to include in intermediate states only the ground state of the nucleus and the on-the-mass-shell contribution. All the excited states of the nucleus and all off-the-energy-shell contributions are neglected. Within these approximations all orders of multiple scatterings and the nuclear binding effect on the TV -nuclear scattering are explicitly included: The impulse approx- .s imation to the TT -nucleon and -nucleus scattering amplitudes is avoided com- ide pletely. In fact our formalism corresponds to the lowest order impulse approximation of the IT -nucleus K-matrix: Consequently it is similar to Heitler's radiation dumping equation and further does satisfy the unitarity condition. Fermi motion of the nucleons is included consistently to these approximations: The TT -nucleon kinematics in the laboratory frame is restricted by no change in nucleon momentum. Our formalism yields an analytical expression of the IT -nucleus scattering amplitude in terms of the free TT -nucleon scattering amplitudes in the form of a partial wave expansion. The results obtained by this expression are shown in Figs.l and 2: Good agreement up to the third bump below and above the 3-3 resonance shown in Fig. 1 guarantees soundness of our formalism. Figure 2 demonstrates a simple picture of the "TT-nucleus elastic scattering described by our formalism: These diagrams show simply the effects of the 3-3 resonance id spreading out over all the angular momentum states of the IT -nucleus scatter- lined ing. This is a kinematic effect due tb-ithe nuclear size. The total cross sections calculated show a shift-down of the peak to about 165 MeV for the nuclei considered. The real parts of the forward amplitudes do not shift down, while their over-all energy dependence agree with the experiments (1) and with dispersion calculations. (1) F. Binon et al. Nucl. Phys. B17, 168 (1970) ad, and B33_, 42 (1971); R. W. Bercan et al. Phys. Rev. Letters 29, 1031 (1972); M. L. id Scott, Phys. Rev. Letters, 28, 1209 (1972). aints

30 90 15Q 30 90 150 3090 150 30 90 150

-69- III.24

Some Problems with the Pion-Nucleus Potential"

Alfred S. Goldhaber University of California Los Alamos Scientific Laboratory Los Alamos, New Mexico 87544

Difficulties in obtaining an accurate optical potential for pions with kinetic energy of 200 MeV or less have been discussed a good deal recently. The focus here is on some restricted questions viewed in a one-dimensional model. Kujawski has studied corrections due to non-additivity of phase shifts and due to overlap of potentials (interaction with more than one nucleon simultaneously). These considerations are extended here to suggest that the optical potential in the nuclear interior is almost completely disconnected 2 from that in the surface region. That is, as in the Kisslinger model, elastic scattering is nearly all at the surface, and the character of the potential in the interior is very different from that near the surface. The above results are obtained in the fixed nucleon approximation, whose validity is also discussed. The application, to scattering in finite nuclei, of infinite nuclear 3 4 matter pion potentials ' is examined.

* yf Work supported by the U. S. Atomic Energy Commission; address after September 1, 1973: I.T.P., SUNY, Stony Brook, NY 11790.

1. E. Kujawski, Am. J. Phys. 39_, 1248 (1971), and "Multiple Scattering and Nuclear Information," MIT Preprint #299 (1972). 2. L. S. Kisslinger, Phys. Rev. £8, 761 (1955). 3. S. Barshay, V. Rostokin, and G. Vagradov, to be published in Nucl. Phys. B. 4. H. A. Bethe, Phys. Rev. Letters 30_, 105 (1973); M. B. Johnson, private communications.

-70-

. III.24 III.25

Low Energy Pion-Nucleus Optical Potentials Goran Faldt University of Lund

A low energy pion-nucleus optical potential is derived from the non-relativistic Schrodinger equation. The pion-nucleon amplitude has been parametrised both as -f (£,i&) - U+c &»dl and as -ft C-fc'.tL) =5 (b+ c fe*)~x< • V . The two forms are identical for on-shell pion-nucleon scattering.

In first approximation fNL yields the non-local Kisslinger potential. When short range nuclear two-particle correlations are included the non-local Ericson-Ericson potential is obtained. The correlation dependence enters in the so called Lorentz- Lorenz term.

In first approximation fL yields a local but energy dependent optical potential. When two-particle correlations are included the potential becomes rather complicated. Moreover, non- local terms are generated. However, the Schrodinger equation can be transformed to that of Ericson-Ericson and we find the following connection between the wave functions ^0 * <> with being the nucleon density. For the application to pion-nucleus scattering experiments it follows that the scattering amplitudes for the local and non- local potentials (including correlations) are identical since they are determined by the large distance behaviour of the wave functions. -ife;--

For the application to pionicwa^pms iffollows that the eigen- values are the same except .-for^possible differences in the treatment of the Coulomb potential caused by the transformation (1). The effect of a finite correlation length has also been investigated. It has been shown that the effective change in the Lorentz-Lorenz term is small, less than 5%.

-71- III.26

OFF-SHELL EFFECTS IN THE PION OPTICAL POTENTIAL*

J. T. Londergan, University of Wisconsin and E. J. Moniz, University of Pennsylvania Calculation of the first order pion optical potential1 requires knowledge of the nuclear single particle density and of the off- shell TTN transition matrix:

(p|VOpt(E)|q) Different off-shell extrapolations can lead to significantly different results for various pion-nucleus reactions, and one would like to perform the extrapolation according to a physically reasonable dynamical model. Landau and Tabakin have employed absorptive, energy-independent separable potentials to generate the off-shell transition matrix, the attractive feature being that the inverse scattering problem is explicitly soluble (i.e., given the complex irN phase shifts, t^Cp^q^E) can be generated directly). However, there are serious theoretical difficulties with this procedure: the presence of inelastic channels requires an energy-dependent effective one-channel potential , and violation of this requirement yields an unphysical off-shell transition matrix when the inelastic channels are important (this is seen explicitly in Ref. 2 for the Pn partial wave). We propose the following coupled-channel separable potential model for the TTN interaction:

where i,j=Tr,irl for TT1 an effective inelastic channel; A^ - A\n ; hV' - AI'W ; and the form factors ^ are real. The important features of this model are that one can still explicitly solve the inverse scattering problem and, since the physics of the inelastic channel is built in, avoid the diseases inherent in the absorptive separable potential approach. That is, the coupled-channel approach gives a "smooth" off-shell extrapolation even in the presence of strong absorption or closed channel resonances. We have investigated the consequences of employing this model to generate the pion optical potential and find off- shell effects appreciably different from those obtained with the phase-equivalent complex, static separable potential. It is interesting that this is the case not only in the immediate vicinity of strong absorption but even below the inelastic threshold. ^Supported in part by the National Science Foundation. 1) For a review, see A. L. Fetter and K. M. Watson in "Advances in Theoretical Physics", Academic Press, New York, 1965. 2) R. H. Landau and F. Tabakin, Phys. Rev. D5(1972)2746. 3) H. Feshbach, Ann. Phys. 5.(1958)357.

-72- lU- III.26 III.27

OFF-SHELL TTN AMPLITUDES FOR THE PION-NUCLEUS OPTICAL POTENTIAL K. W. McVoy, University of Wisconsin, Madison, Wisconsin 53706

Off-shell wN amplitudes are required for the construction of a pion-nucleus optical potential, and probably the best means so far available for the off-shell extrapolation of experimental irN data is the complex, separable, 1-channel Landau-Tabakin (LT) potential u(k) u(k'). However, in a contribution to this Con- ference, E. J. Moniz notes an apparent pathology of u(k) when the

elastic S-matrix element S W(E) shows strong absorption near E=E , |S ^(E )| << 1. The pathology is in fact a pole in u(k), which can be seen as follows. D(E), its Jost function, has as discon- + — 2 2 tinuity across the elastic cut, D (E) - D~(E) = iku (k)/8ir .

Further, S H(E) = D~(E)/D (E) extrapolates from the physical region into the lower half plane as S (E ) = D~(E )/D (E„),

with Ej = E_T, but E "below" E on the sheet reached from the physical region. If ]s (E )| « 1, S (E) must have a zero at

a complex E =£, near E . If £ is 6TT> the zero cannot be due to a zero of D (Ej), for it has none on the first sheet. Hence it is a pole of D+(E), and so of u (k), near E . This is entirely general, and will occur whenever S (E) passes near the origin of its Argand diagram with decreasing" "phase, which makes Imtfc) < 0. As Moniz notes, an alternative to the LT potential is the real coupled-channel separable potential = v (k )v , (k ,), which produces the on-shell T-matrix elements c c c c , -= v 2(k)/d (E). d(E), its Jost function, clearly has 1 cc' c a (real) phase 6(E) which is the opposite of that of T and so is experimentally accessible. The Omnes procedure thus gives d(E) from the on-shell data in one channel alone, permitting the

2 T-matrix equation to be solved for vc . This method is free of the LT pathology and so should provide a more reliable off-shell extrapolation when the absorption is strong.

•4?. H. Landau and F. Tabakin, Phys. Rev. pj_ (1972) 27^6.

-73- III.28

Comparative analysis of pion-nucleus elastic and inelastic scattering

J.-F Germond and J.-P. Amiet*

Pion elastic cross sections on ^He , 12C and 160 have been computed in the vicinity of the (3,3) resonance. Three standard high energy approximations have been used. In all cases the pion-free nucleon amplitude has been parametrized by a gaussian as a fonction of momentum transfer. Then a first order local optical potential has been constructed? if the nuclear density is described by the harmonic oscillator shell model, this potential beha- ves as a modified gaussian. The results obtained within the eikonal approximation are very close to the exact ones and to the ones yielded by Glauber's theory, even for a nucleus as light as 4He. A comparison with experiments shows a fairly good agreement for 12C and 160. However the first minimum occurs at too low momentum transfer, aspecially for 16O. In the case of ^He the agreement is quite poor and a better parametrization of the pion-nucleon amplitude is needed. Pion inelastic cross sections for transitions to the 2 (4.4 MeV) and 3 (9.6 MeV) states of 12Chave been computed using the eikonal D.W.I.A. Three different models for the transition form factors have been considered : a phenomenological one which is in fact a fit to electron scattering experiments, the volume-conserving vibrational model and the Gillet particle-hole model. The present experimental situation is such that no definite choice can be made among these models. However it is interesting to note that the transition form factors which fit electron scattering experiments a]so describe pion- *2c inelastic scattering in a satisfactory way.

An extended version of this work will be submitted to Nuclear Physics for publication.

•University of NeuchEtel, Switzerland

-74- L III.28 III.29

6 7 9 Measurement of the II Total Cross-Section for "He, Li, Lit Be 12C, 32S for Eu from 80 to 260 MeV

E. Pedroni C. Cox, J. Domingo, K. Gabathuler, J. Rohlin, P. Schwaller, N. Tanner, C. Wilkin.

We have determined the charged pion total cross section for several light nuclei by a standard transmission measurement. Pion beams of energy between 50 and 260 MeV were produced by bombarding a Be production target with the extracted 600 MeV proton beam of the CERN SC. The beam was momentum analysed (-*^ = 1% FWHM) and recombined to form a nearly parallel beam at the absorption target by means of v a double QQDQQ transport system. A DISC Cerenkov counter, time of flight and pulse height discrimination were used to eliminate the proton, muon and electron contaminates. The transmission counter assembly, consisting of 6 overlaping circular scintillators of increasing diameter, was mounted on a rail system accurately alligned along the beam axis so that the solid angles subtended by the counters could be continuously varied. Measurements were taken at each pion energy and charge for three targets to counter separations chosen such that systematic differences between the counters could be eliminated. The extrapolation to zero angular acceptance was made after the corrections for single and multiple Coulomb scattering and the Coulomb nuclear scattering interference term, as calculated with the help of forward dispersion relations, had been applied. Surprisingly, large differences were observed between the n+ and n" total cross-sections for self-conjugate nuclei : the n to n+ cross-section excess increased rapidly for pion energies below 150 MeV. At 80 MeV the n" total-cross section on C is approximately 151 larger than the H+ total-cross section. This effect is qualitatively understood in terms of Coulomb effects.

-75- III.30 PION CHARGE EXCHANGE REACTIONS J.Alster, D.Ashery, N.Auerbach, S.Cochavi, M.A.Moinester, J.Warszawski, A.I.Yavin, M.Zaider. Physics Department,Tel-Aviv University, Ramat-Aviv, Israel. The pion single charge exchange reaction is an important tool in the study of the pion nucleus interaction. We have measured*) the activation cross section from 30 to 90 MeV, using the secondary pion beam of the Saclay Electron Accele- rator for the reaction 13c(Tr+,ir°)l^N, corresponding to the excitation of the g.s. analog only ; and for llB(ir+,iiro)llc corresponding to the analog state plus nine bound states. A significant feature of the results is that the 13c excitation curve is relatively flat between 30 and 90 MeV. We have carried out calculations^) with optical potentials : both non-local (Kisslinger) and local. Only the local potential could account for the flatness of the excitation function of H>C. We found the excitation function to be very sensitive to the shape of the nuclear density while best agreement was obtained when the excess neutron density was determined by a lpj/2 wave function calculated in a Woods Saxon well. First order plane wave calculations3) predict a maximum for the cross section near the (3,3) resonance. More elaborate calculations including absorption predict a minimum in that region. We note that at low energies the cross section for HB is appreciably larger than for 13C (analog transition only). If the cross section for13 C decreases from 90 MeV towards the (3,3)resonance, as predicted by the calculations including absorption, then the difference in excitation functions for analog transitions (as in 13C) and non-analog transitions (as in HB) is striking. In addition, the measurement for 13C by Chivers et al.4) (see Fig.) at a single energy (180 MeV), which suggests a high cross section (3.3 mb), and the relatively high cross section4) (1.3 mb) for the two non-analog tran- 5.0 sitions in 1°B, call for further investigation. We have also measured1) the analog state transition at 30 MeV for the D 91 + Zr(ir ,irO)91Nb reaction. It will be in- 1) T. 1.0 teresting to see whether the excitation function for analog state transitions in 2) T. 91 medium weight nuclei (like Zr) is diffe- 3) T. 4.0 rent than for light nuclei, as might be - \ expected from optical model calculations, 4) J.V e L * / 'y >* i which may be very sensitive to absorption 5) S. "o I . \ ^-~=^\ Rairtn s. XI at the nuclear surface. e i.O — m X I ii\ Reitan 1) J.Alster et al., Phys.Rev.Lett 128,313 Sakamoto (1972) ; and to be published. 0.5 2) N.Auerbach and J.Warszawski,to be published. _J present 3) Y.Sakamoto, Nucl.Phys. B10^,299 (1969); Chivers F.H.Bakke and A.Reitan,Nucl.Phys.BIO, I 43 (1969). O.I etal. -J non-local, 4) D.T.Chivers et al.,Nucl.Phys.A126,129 0.05 local, (1969). 0.03 0 40 80 120 160 PION ENERGY (MeV)

-76- III.30 III.31 ERICSON FLUCTUATIONS IN HIGH-ENERGY HADRON PHYSICS irszawski, Per J. Carlson -Aviv, Israel. CERN, Geneva, Switzerland in the study cross section Fluctuation phenomena are well known in many branches of physics. In particular, ctron Accele- nuclear reaction and scattering cross-sections shew a randomness when the energy levels in the componed nucleus overlap. This phenomenon was first discussed by ion of the 2 og state plus Ericson in 1960 *), and later reviewed by Ericson and Mayer-Kuckuk ). e 13C excita- It was suggested that Ericson fluctuations may also be present in particle 3 both non-local physics ), and a search was made in proton-proton elastic scattering at 17 GeV "*) the flatness with negative results. m to be very In a recent paper, Frautschi5) re-raised the question whether high-energy hadron was obtained cross-sections exhibit fluctuations. Structures have been seen in many differen- iction calcula- tial cross-sections as a function of energy6). Contrary to the conventional in- te cross see- terpretation of the peaks and dips in terms of individual resonances interfering with a smooth background, Frautschi suggests that these structures are fluctua- ing absorption tions arising from a large number of overlapping resonances with fluctuating level density and coupling strength. rreciably for 13C In this paper we present evidence for Ericson fluctuations in large-angle the calcu- Tri-proton elastic scattering around 5 GeV: the differential cross-section is unctions 11 found to vary by as much as a factor of three upon changing the incident energy in B) is with 0.1 GeV for ir+p. For ir~p, the fluctuations were found to.be much smaller. (see Fig.) These results are interpreted in terms of a lower density of states for iT+p (3.3 mb), than for TT~p. A quantitative evaluation of the fluctuating differential s section^) cross-section as a function of energy for 0° and 180° i^p elastic scattering lalog tran- is shown to be consistent with the observation at 5 GeV. irther inves- 0 the analog References; for the [t will be in- 1) T. Ericson, Phys. Rev. Letters 5, 430 (1960). \e excitation 2) T. Ericson and T. Mayer-Kuckuk, Annu. Rev. Nuclear Sci. 16_, 183 (1966). transitions in 91zr) is diffe- 3) T. Ericson, CERN TH-406 (1964). , as might be 4) J.V. Allaby et al., Phys. Letters 23_, 389 (1966). 1 calculations, e to absorption 5) S. Frautschi, Nuovo Cimento JJ2 A, 133 (1972). 6) See for example, S.W. Kormanyos et al., Phys. Rev. 164, 1661 (1967); ev.Lett 128,313 A. Carroll et al., Phys. Rev. Letters 20_, 607 (1968); and ished. A. Citron et al., Phys. Rev. U4_, 1101 (1966). wski,to be

B10_,299 (1969); Nucl.Phys.B10,

..Phys.A126,129

-77- III.32 MOMENTUM COMPONENTS OF THE DEUTERON: 200-400 MeV/c G. J. Igo and M. Nasser University of California, Los Angeles

Analysis of 180° elastic proton-deuteron data between 150 and 350 MeV clearly demonstrates the interaction proceeds by neutron exchange. This is illustrated in the Figure. The data points fall in a narrow band when plot- ted versus the neutron-exchange T-matrix variable A [A = (pi"Pdi)/2, where p ,p , are momenta (CM) of the incident proton and scattered deuteron]. Deuteron momentum components between 200 and 400 MeV/c determine the cross section at corresponding values of A. For A >_ 275 MeV/c, sensitivity is to m 3 D components. We obtain 7-8% D1 (see Figure) in good agreement with deuteron wave functions derived from modern phenomenological potentials which fit low energy properties of the deuteron. Preliminary fits illustrated in the Figure result when the S.. momentum components in the Moravcsik II wave function near 200 MeV/c are reduced (smoothly) by <_ 30%. The corresponding alter- ation of the wave function is largest near 2 Fermis. It is comparable to the differences among the phenomenoiogical wave functions discussed above. We have employed a second order (distorted wave) exchange T-matrix previously employed by Fukushima to analyze the 1 GeV data. It might be expected that the effects due to distorted waves in the initial and final channels would be more important than at 1 GeV. We find the second order correction is only 10% of 2 1 the first order T-matrix (at 1 GeV it is 16% ). We thus conclude the data are consistent with the reaction proceeding almost entirely through neutron exchange. The Figure also illustrates the effect of the nucleon isobar component D* when A ^ 400 MeV/c. WOOr-

1st Order with new wovefuncfion (s-stalel w

* This work is supported in part by the U. S. Atomic Energy Commission. 1) G. Igo et al., Nucl. Phys. A195, 33 (1972); J. C. Alder et al., Phys. Rev. C6, 2010 (1972); H. Postma and R. Wilson, Phys. Rev. 12JL, 1229 (1961). 2) S. Fukushima, unpublished report, Carnegie-Mellon University (1972).

-78- III.32 111.33

Polarization Measurements in High Energy Proton-Deuteron Scattering O.E. Overseth d 350 MeV University of Michigan This is when plot- Since high energy (>1 GeV) forward proton-deuteron elastic 2, where scattering is well understood in terms of the Glauber model, data ron]. from this reaction can be used to provide information on the deii- he cross teron wave function and the nucleon-nucleon scattering amplitudes. ity is to We would like to stress here the importance of polarization mea- : with deu- surements in high energy proton-deuteron scattering. The polari- ils which fit zation data can be obtained either from elastic scattering off :ed in the polarized deuteron targets or from double scattering of acceler- '. wave func- ated deuterons by protons. Such experiments can provide informa- >nding alter- tion on the deuteron D-state probability, the ratio of real to rable to the imaginary parts of nucleon-nucleon scattering amplitude, and the love. We dependence of this ratio on four-momentum transfer and incident reviously em- energy. For example, analysis of our polarization measurements :ted that the from a double scattering experiment at 1.0 GeV favors the deu- jould be more teron wave function of Bressel, Kerman and Reuben. The data are mly 10% of less satisfactorily fit with Hamada-Johnston and Lomon-Feshbach the data potentials, and the Reid potential with either hard or soft core »h neutron gives a poor fit. The polarization data also require large real Lsobar compo- parts for- the scattering amplitude^independent -of the deuteron wave function used. Since the source of the measured deuteron polarization (actually a tensor polarization or alignment) is the deuteron D-state, these polarization effects can be expected to f remain substantial even at high energies. 1 ii

G. Bunce, O.E. Overseth, J. Walker, H. Halpern, R. Handler, L. Pondrom, and S. Olsen, Phys. Rev. Lett. .28, 120 (1972). ission. , Phys. Rev. (1961). 1972).

-79- III.34 MEASUREMENT OF DEUTERON-PROTON BACKWARD ELASTIC SCATTERING AT Scattering Cont "INCIDENT DEUTERON MOMENTA OP 3-43, 4.5, 5-75 and 6.6 GeV/c Wave Function. C K Hargrove, L. Dubai, R.J. McKee, H. Mes. National Research Council of Canada (Ottawa); L. Bird, C. Halliwell, E.P. Hincks, J. Hornstein, F R Morrison, A.C. Thompson and J. Walters, Carleton University The College of (Ottawa, Canada); and J. McCaslin and A. Smith, Lawrence Berkeley Laboratory. Any theoretical quiresj at leas We have measured the differential cross section for deutercn- nucleus. One o proton backward elastic scattering at four incident deuteron mom- change scatteri enta, 3-426, 4.500, 5.750, and 6.600 GeV/c, at the Bevatron of the sically relativ Lawrence Berkeley Laboratory. The measurements were made with a deuteron and on two arm proportional wire chamber rar-f.netspectrometer . Both tion, the only final particles were momentum analyzed and the slow backward turn, requires deuterons were selected by time of flight. A clean separation of ('positive ener this reaction from the relatively high background was achieved. intrinsically r The data are shown in Pig. 1. A strong backward peak is seen relativistic an at all momenta dropping to a minimum near 130° CM. A rapid drop kinematically s of nearly two orders of magnitude is seen from 3-43 to 5-75 GeV/c yet an open que and then only a slow drop of a factor of two to 6.6 GeV/c. ation has recen (3 > **) coupling The data have been compared with two models, that of Craigie + 2 3 i|A ) and the as and Wilkin as calculated by Barry and that of Kerman and p and, 0) exchan Kisslinger **. The calculation of Barry has been shown to fit the meson. The eff data well over most of the range of incident momenta with one par- the existence o ameter. This calculation has been based on the one pion exchange nation. Thus t model, and the dp cross section has been calculated from the + elastic N-H sea appropriate pp->dir cross sections. The existence of nucleon iso-^ the hard core, bars in the deuteron has been -postulated by Kerman and Kisslinger phenomena at si dD-»dD and the t)ackward Peak has tances* to be cc IOO, , 1 " i !-, , 1 1 been explained by the nucleon solve for iji("")-. • = 3-426 GeV/c pickup mechanism and by the 1.5 GeY and C.E • =4-5 GeV/c exchange of these isobars. knowing the ljA"* A = 5-75 GeV/c Preliminary calculations have ,2Mc to .TMc, J Reid functions • =6 6 GeV/c been made for our highest momenta with encouraging re- modified Reid c 10 sults. In addition the par- ameterization of the data, / usin_g the pickup parameter A=|Pin-d/2|, has been done, and, In agreement with the lower momenta, the .s depen- 10 dence of the data has been 1) E. A. Remle largely removed showing that the nucleon pickup mechanism 2) J. Hornste: is an important process in m this reaction. m 3) E. A. Reml< 1 H.L. Anderson et al., to be f h) F. Gross, ! 01 published.. 2 N.S. Craigie and C. Wilkin, 1 Nucl. Phys. BL4, 447 (1969). 3 G. Barry, Annals of Physics 71, 482 (1972). .0 " A.R. Kerman and L.S. 40 60 80 100 120 140 160 180 Kisslinger, Phys. Rev. 9 (CM) 180, 1483 (1969).

-80- III.35 Scattering Contributions of Intrinsically Relativistic Pieces of the Deuteron Wave Function.

J. Homstein, F. Gross, R. A. Miller, E. A. Remler. The College of William and Mary.

Any theoretical description of high energy nuclear scattering presumably requires, at least at some point, a completely relativistic description of the nucleus. One of us (E.A.R) has previously discussedO) nucleon-deuteron exchange scattering as a paradigm to assess measurable effects of certain intrinsically relativistic pieces of nuclear wave Hfunctions. . In this process the deuteron and one nucleon are on mass-shell and the D-NP vertex is, by definition, the only dynamical function entering the calculation. This vertex, in turn, requires four scalar functions for complete specification. Two of these ('positive energy1, ^'+') correspond to the usual S and D states; the other,two intrinsically relativistic components ('negative energy1, i|X~)) have no nonrelativistic analogs. Ref. 1 pointed out that while the effect of the ij>(~) was kinematically suppressed at low energies in this process, elsewhere it was as yet an open question awaiting evaluation of I|J'""' for an answer. Such an evaluation has recently been reported^ / by two of us (J.H. and F.G.). The equation 3 1 i * *) coupling I(J(+) and ijj(~) can be solved algebraically for i|/-) in terms of i|)(+ ) and the assumed interaction after making an adiabatic approximation. 7T,ot, p and, 0) exchange was assumed, the a being a phenomenological scalar-isoscalar meson. The effective potential seen in the ijn+' channel develops, by virtue of the existence of the M~),- an infinitely hard core in this adiabatic approximation. Thus the i|A~' already play an important role in intermediate energy elastic N-N scattering the analysis of which led to the "original discovery of the hard core. It is thus reasonable to expect that they will effect other phenomena at similar energies. Reid soft core functions modified at Short distances to be consistent with the effective hard core, were used for ijn+) to solve for i|i("")-. We investigated the incident.nucleon lab energy range .15 to 1.5 GeV and cm. angular range, 150° to 180°. Each energy and angle requires knowing the ij;(+) and i|>(~) at one point in momentum space. We thus.scan momenta .2Mc to .TMc, Me2 = .938 GeV.. Over this*range we have checked that the modified Reid functions do not differ significantly for present purppses from, either un- modified Reid or Humberston-Wallace. The result is that fhe presence of the ijn") raises the exchange cross-section by about 10$ at .15-GeV, 150°; 2.%= at .15 GeV, l80°; 25$ at .5 GeV, i50°; 50$ at .5 GeV, 180°; 150$ at 1 GeV-, 150°; 20$ at 1 GeV, l80°; 100$ at 1.5 GeV, 150°; 20$ at 1.5 GeV, 180°. One must conclude that calculations dominated by exchange processes will, be in error -by corresponding percentages if their negative energy contributions are not included.

1) E. A. Remler, Nucl. Phys. B^, 69 (1972).

2) J. Hornstein and F. Gross, Bull. A.P.S. 18, Ser II, No. k, 621 (1973K

3) E. A. Remler, Nucl. Phys. Bjj2, 56 (1972).

h) F. Gross, SLAC preprint PUB-1138, Nov. 1972, submitted for publication. a

-81- III.36 FERMI MOTION AND DEUTERON RECOIL IN THE RBLATIVI3TIC, COVARIMT, EIKONAL FORMALISM J. M. Namysafbwski Department of Theoretical Fhysies, Manchester University Depi

Covariant eikonal formalism can be extended to treat both the relative motion Covariai ofSTwith respect to dnuteron (d), as well as the relative motion within d itself. in the schemi The momentum used in the eikonal approximation within d is usualy chosen to be the help of the \ direction of the deutsron recoil. However, the 4-vector needed to define an como- ensional sub: mentum dynamics, or equivalently, the; 4-vector needed, in the reduction of the re- scheme provii lative 4-momentum within d is not uniquely defined. The relation between the known all particlei nonrelativistic df-uteron wavefunction and the covariant deuteron wavefunction de- by Alberi ani pends crucialy on this choice. tained from i The recently proposed by Cheng and V?u recoil correction in the scattering off The Blai deuteron corresponds to the choice of the above mentioned 4-vector along the momen- ring term in tum of the incoming pion. This gives them the recoil correction which has an eff- sfer and ene: ect on the single scattering term in the Glauber formula, but practiealy has no round 1 GeV/ effect on the double scattering term. In the very good approximation of a large gle and doub d in comparison with the range of forces responsible for the STp and^fh interac- itself, wher tion, the Cheng-Wu recipe for the recoil correction in the double scattering term U tion for TT d of the Glauber formula, boils down simply to 1. Without this approximation, the it is 0.79. ' Chen^-Jffu recipe makes an effect on the double scattering term only for momentum with the ran transfers comparable to I6(nucleon marf,-) for a Gaussian deuteron wavefunction. A symmetrical choice of the 4-vector used for defining an eo momentum dynamics, i.e. used for the reduction of the relative momentum within d is iCf^-t-f'nk where where pfl * are the total initial, and final d 4-momenta. From this choice it fol- lowg, that in the Breit frame the energy component of the relative 4-momentum within d is zero, and that the covariant deuteron wavefunction is related with the The right h nonrelativistic deuteron wavefunction in the Breit frame, as it was proposed by independentl Licht and Pagnamenta. The Blankenbecler-Gunion-Gottfried recoil correction, which For th is present even without the Fermi motion, and which by itself is much more important for the double scattering term in the Glauber formula than the Cheng-Wu minor correction, undergoes some modification in the presence of the Fermi motion. This where (J. - modification is numericaly very small, and it amounts to bringing in essentialy The quantity the factor to&fafflflfawhere ^- onj/fcf^ ,*/^rfn%&%!&J%&\ terms of Daw This factor is numericaly very close to 1 for the present day experiments, and it * has the property of approaching 1 for 00 energy, contrary to a similar factor of On leave of Faldt which is I + *£i * On leave of absence from the Institute of Theoretical Physics, Warsaw University

-82- III.36 111.37 COVAHIANT RECOIL CORRECTIONS IN THE GENERALISED GLAUBER FORMULA J. M. NamysZbwski Department of Theoretical Physics, Manchester University e motion Covariant generalisation of the Glauber formalism can be uniquely defined itself. in the scheme of eo momentum dynamics, and then it can be rewritten with the io be the help of the Wightmar-GSrding relative momentum q, reduced to a covariant 3-dim- in como- ensional subspace by the condition qP = 0, where P is the total 4-momentum. This the re- scheme provides a unique prescription of the off-energy-shell continuation-for ;he known all particles involved in a process, contrary to rather arbitrary recipes used ;ion de- by Alberi and Bertocchi in their relativistic formulation of Glauber model, obtained from only some Feynman diagrams, yet distorted by extra assumptions. jring off The Blankenbeeler-Gunion-Gottfried recoil correction of the double scatte- bhe momen- ring term in the Glauber formula depends in a covariant way on the momentum tran- an eff- sfer and energy, and it goes to 1 for oo energy. For the laboratory momentum a- ias no round 1 GeV/c it is very important both in the region of interference of the sin- large gle and double scattering terms, and in the region of the double scattering term iterat- itself, where at t = - 0.8(GeV/c) it reaches the value 0.28 in the cross sec- ing term tion for Tr d-^STd. For energies around 10 GeV, and momentum transfer t = -2(GeV/c)*: , the it is 0.79* Assuming a very good approximation of a large deuteron in comparison nentum with the ranges of forces responsible for the Trp and TTn interaction, we get iction. a dyna-

where 5 it fol- rtum wi- Lth the The right hand side can be calculated from the known deuteron wavefunction, and 3ed by independently measured n, which For the scattering of electron and positron on deuteron we get e impor- -Wu minor on. This where Q. — ^(jZtCf>\y 1\/\"ri»~"^' /"£ f\t ^.> aa^ nuc^eons are spinle88* itialy The quantity Im G can be expressed, for a Gaussian deuteron wavefunction, in terms of Dawson integral, and it has a maximum, reaching 61$, for 'Q = O.145GeV/c. and it On leave of absence from the Institute of Theoretical Physics, Warsaw University ctor of m iversity

-83-

•••.-•JiB III.38 F0UR-M0MEN1 IN HYDROGEf B.C.Allad I.S.Saito

pd-=»-ppn RSSCATT1SRING EFFJCTS. B *M. Golovin, G. I • Lykasov, F .Sh.Khamraev

Joint Institute for Nuclear ResearchfDubna,USSR.

AES1BACI

The reaction pd —r ppn at T = 600 MeV is investigated within impulse approximation taking into account the rescattering effects of the incident protons on the deuteron nucleons. The results of the differential cross section calculations are given in the symmetry kinematics of the energy spectra of the polarization effects* The rescattering in the given reaction and the sensitivity of the obtained results to the deuteron wave function are investigated. The D-wave contribution to the deuteron ground state and the N-N amplitude real spin structure are taken into account*

-84- III.38 III.39 FOUR-MOMENTUM DISTRIBUTION IN dp->ppn REACTION AT 3.3 GeV/c IN HYDROGEN BUBBLE CHAMBER B.C. Alladashvili, V.V.Glagolev ,R.M.Lebedev, J.Hassalski ,M.S.Nioradze, I.S.Saitov,A.Sandacz,T.Siemiarczuk,J.Stepaniak,V.JT.Streltsov Dubna-Warsaw Collaboration We report the further results on deuteron break up in the interactions of 5.3 GeV/c deuterons with protons in the hydrogen bubble chamber. Use of deuterons as incident particles is more convenient in the spectator analysis /see JIHR report P1-6714, 1972 and Batavia conference, 1972,paper 868/. The deuteron break-up channel contributes to about 50% of all re- interactions and presently the collected number of events in this channel is about 8400. four-momentum transfer distribution from the proton target to co- the slowest proton in the laboratory system is given below. Curve represents the results of the Glauber model calculations using closure approximation without taking into account spin-

I ; effects and with gaussian deuteron form-factor and exponentials for elementary nucleon-nucleon amplitudes. The discrepance for 11| £.2 can be probably explained by the uncertainties in elementary nucleon-nuclebn data,whereas for low Itl the difference may be significant. More detailed calculations are in progress.

a A* M10mb<&cMfcr ,a

i .4 -t

-85- III.40 AMBIGUITIES in the TREATMENT of CENTER-of-MASS CORRELATIONS in £1 HIGH ENERGY PROTON and PION SCATTERING by the ALPHA PARTICLE. C. Ciofi degli Atti, Physics Laboratory, Istituto Superiore di Sanita and INFN Sezione Sanita, Rome, Italy R. Guardiola, Department of Theoretical Physics and GIFT, University of Barcelona, Barcelona, Spain. WE thin Shell mode] wave functions (|)(^ •••*"* ), being referred to some external po tential frame, violate the requirement of traslation invariance. In this_case, Tl various prescriptions to remove the center-of-mass (CM) coordinate R in the thin evaluation of intrinsic matrix elements lead to different results (Lipkin, Phys. sion Rev. 110, 1395). The intrinsic electron or hadron cross sections Th the f (1) Mi p or ;•••-! have often been evaluated using either the Gartenhaus-Schwartz (f(R) = 1) or the fixed center-of-mass (f(R) = 6 (R)) prescriptions. Both amount to calculate intrinsic matrix elementft(i. e. dependent only upon A-l intrinsic coordinates (rj ); they lead to identical results in case of factorable functions (l|)( "Fj. . .ijj) =(|>G?&X(^)e. g. harmonic oscillator), but give rise to large differences in the high momentum part of the He electron form factor when other shell model wave functions are used (Friar, Nuclear Physics. A173 257; Ciofi degli Atti et al. (V Phys. Lett. 42B 27). For this reason we have calculated high energy (IBeV) (2) proton and pion scattering by He using Glauber theory and the non factorable density (Bassel and Wilkin, Phys. Rev. 174, 1179). f%) ft) The two ways of removing the CM coordinate lead to large differences in the single-scattering term (a factor of •vlO in the magijjmde of the second maximum) whereas in multiple scattering terms the difference is less (about 50% at q -*3 fm ). Due to the interference of the various terms and to the dominance of double and triple scattering over single scattering at high momentum transfer, the diffraction maxima in the total scattering amplitude differ by 20% only in case of protons and by 40% in case of pions (The difference between protons and pions in mainly due to the difference in the total hadron-nucleon cross section and not in the the slope). On the basis of these results, we conclude that although non-traslation invariance effects in hadron-nucleus scattering are not as large as in the case of electron-nucleus scattering they nevertheless seem to be large enough as to mask very small effects (short range correlations, ratio of the real to the imaginary part of the hadron-nucleon scattering amplitude, etc) that have usually been studied using non-traslation invariant (non factorable) wave functions of the type (2) or of similar types.

-86- III.40 i III.41 riONS in P-6Li ELASTIC SCATTERING AT 600 MeV EtTICLE. m and INFN J. GARDES, F. Le MEILLEUR, L. MERITET, J.F. PAUTY, G. PEYNET, •••?> M. QUERROU, F. VAZEILLE 3ity of m Laboratoire de Physique Corpusculaire - Clermont-Ferrand We use an intense proton beam (2 x 1011 p/s) from ths CERN SC and a very thin 6LiF target (200 yg/cm2). external po lis case, The recoil nucleus is identified by means of semiconductor telescope with a e R in the thin AE detector C50 ym), using the Goulding method. We measure with a preci- •kin, Phys. sion of 1 % the recoil energy at various angles. The identification of6 Li allows the rejection of all quasi elastic events : the 6Li excited states at 2.18, 4.52, 5.35 MeV etc... desintegrate giving a, d, p or n particles. The 3.56 level gives by y emission a 6Li, similar to initial state ; but the major contribution of this excited state is in very forward •) = 1) or direction (13 and is negligeable in our transfer region (0.05 < t < Q.32 (GeV/cD2, :o calculate irdinates The experimental result exhibits (Fig. H3 the absence of a minimum at tfte. 2 (*(-,...rA) expected value t = 0.13 (GeV/c) . R. RaphaSl (2) in a recent calculation, s in the high supposing an a-d cluster configuration, explains this result by some interfe- model wave rence between single and double scattering on a-d quasi free substructures. tti et al. (1) Jaemcwt - Thesis, Orsay (1964) p. 32 T (IBeV) 3 (2) R.B. Raphael, Nuol. Phys. A204 (1973) 640 factorable 3 —. mb/fGeV/c)2 dt Fig. 1 -101 I \s in the maximum) \ p-6Li at 600-MeV (exp.) % at q minance of — Raphael calculation transfer, only in protons cross include 10s ttering are ;heless :orrelations, ng ampli- nt (non

10"

3x10 0.1 0.2 0.3

-87- III.42 GOOD RESOLUTION pp' SCATTERING ON 12C AND 't0Ca AT 155 MeV AND THEIR ANALYSIS IN FINITE RANGE D W I A V.COMPARAT,R.FRASCARIA,N.MARTY,M.M0RLET and A.WILLIS Institut de Physique Nucleaire, B.P. n°l, 91406 - ORSAY(France) Glauber protons With some improvements on the achromatic beam of the synchro-cyclotron and the use of a multiwire proportional chamber with a spatial resolution of 1 mm and 96 wires covering a 6 MeV range at 155 MeV (ref.l), a 105 keV overall resolution has been reached for a mean intensity of 6 nA. With this equipement the proton inelastic scattering has been studied on 12C and lf0Ca over a range of 35 MeV excitation energy. A typical spectrum is shown on the figure For some of the levels the theoretical interpretation of the results has been carried out within the frame of the DWIA, in the zero range as well as the finite range approximation (ref.2). The nuclear models used were those of V.GILLET (ref.3). The optical potential parameters were settled in a previous experiment with the same equipment, for a systematic study over 11 targets ranging from 1ZC to 209Bi. For C, the values of the parameters are : UR RR AR WV RI Al USO WSO RSO ASO RC 12.84 1.40 0.52 25.45 0.80 0.71 1.84 -2.29 0.92 0.45 1.42 On the figure the results are given for three levels of 12C. For these levels, as well as the first levels of "°Ca, the agreement is mainly improved by the introduction of the new optical potential. The improvement afforded by the finite range approximation is not significant for the two levels where the calculations were done, except for the 4.4 MeV level at small angles. zero range zero range opt.pot.of ref.4 ..... finite range

-Jo

V / is

-I ID

References

1) V.COMPARAT et al. Nucl. Inst. and Meth.(to be published) 2) V.COMPARAT, These 3e cycle Orsay (1970) 3) V. GILLET, Rapport CEA n°2177 (1962) '-0 C. ROLLAND et al., Nucl. Phys. 80 (1966) 625

-88- III.42 111.43 10 Elastic and Inelastic Scattering by 1 GeV Protons on C, Ni, Pb Y. Alexander and A.S. Rinat, Weizmann Institute of Science, Rehovot, Israel

Glauber theory has been used to analyze recent data on scattering of 1 GeV 1 2 protons ^ . dael/dSJ is related to the phase x ) (Y is the profile function) ron and 1 iran 2 1 reso- Xoo(b)=iA||cr)Y(^4)dr-|A || CD The first terms respectively describe scattering from the average density P ed on (the optical limit) and from fluctuations in p related to the pair correlation m is function g. We calculated daeJ!/dfifor Ni and Pb in the optical limit employing Woods-Saxon densities p and found only qualitative agreement. Application of s has several approximations to the correlation correction in (1) based on a as the specific g^) did not yield detailed agreement. It could however be shown that f minor modifications in the phase xoo may produce large changes in dael/dR. vious This sensitivity will ultimately maEe accurate high-energy hadron scattering ts data on a variety of targets a unique tool for the study of correlations. 4)5) The Glauber series for inelastic scattering has been summed to a DWlA form

RC A (2) 1.42 •£l ese = The transition operator in (2), Xijn(b)(b>AJA|pip m(r)Y(b-s)dr, contains the inelastic roved by mass density and is assumed to be equaqual tco the corresponding transition charge density. The latter with the elastic phase may be taken from experiment and can ignifi- the inelastic distributions danl/dfi= Mfj,m| thus be calculated without 4.4 MeV additional information or parameter fitting. The results (some of which are displayed below) are in good agreement with the data for protons exciting the lowest states in C, Ni and Pb1-' The outcome shows that the excitation of discrete levels is essentially the same process whatever the projectile W. This should'also be.true for planned experimentriments using pions. A fuliwreport will be published elsewhere' -\ m •Ssl"..

J. to

4 S h u 13

1. B. Bertini et al., Phys. Letters to be published. 2. R.J. Glauber, Lectures in Th. Phys. Vol. 1 (1959), High Energy Phys. and Nucl. Structure (Ed. S. Devons) Plenum Press, N.Y. 1970. 3. E.J. Moniz and G.D. Nixon, Ann. of Phys. 67^ (1971) 58. 4. Y. Alexander and A.S. Rinat (Reiner), submitted for publication to Nucl. Phys. 5. C, Wilkin, CERN report 71-14. 6. Y. Alexander and A.S. Rinat (Reiner), Phys. Lett, to be published.

-89- 111.44 I.ADRONIC SHADOWING EFFECTS AND SUM RULE CONSTRAINTS IN IIIGIi-ENERCY PHOTON-NUCLEUS INTERACTIONS W. Weisc Institute for Theoretical Physics, (Jniv. of lirlangen, Germany Total plioton-nucleus cross sections in the range 2 GeV£ <«? £ 2o GeV of piioton energies exhibit pronounced shadowing effects: the effective number of nucleons, Aeff , defined by A r<"uo r where o>A and o~ror are the photon-nucleus and photon-nucleon cross ri sections, is experimentally observed to be roughly Ae« = A°' . This is commonly interpreted as an evidence for the admixture of hadronic components to the photon propagator £i!J. Ar. analysis of these shadowing effects has been carried out, combining the existence of hadronic fluctuations of the photon with Glauber's multiple scattering theory, without explicit reference to the Vector Dominance Model. The experimental data in the above Mentioned energy region can well be described if one assumes the average cross section for the interaction of hadronic fluctuations with a nucleon to be about 2o mb, which is smaller than the commonly adopted % -nucleon cross section. Furthermore, the energy dependance of A«ff (&J) turns out to be closely related to the energy dependence of <*>«<•(<*»): if

where \t. is the TT meson mass, Fj^ and FyA are the forward photon- nucleon and photon-nucleus scattering amplitudes, and S = 6o MeV mb is the classical dipole sum. «• is some fixed photon energy very large compared to p- . The value of Y(A,Z) is determined by the low energy data £3](namely, o.Si Y(A,Z)4 1.1). This sum rule clearly introduces strong constraints on the properties of A€ff (w) at very large energies t->. In particular, a straight- forward discussion shows that the limiting cases, Aef^ -* A and Aeff -» AA/a for w-»<* are both ruled out. A more detailed investigation proposes that even at energies u> > 2o GeV, Aef* should not be too far from the already observed A°"9' -behaviour, unless there are dramatic changes in

1 V.N. Gribov; JETP 3£C197o)7o9 2 W. Weise; Proc. Asilomar Coni. on Photonucl. React.,Vol.II(1973) 3 B. Ziegler et al.; Proc. Sendai Conf. on Photonucl. Reacttions, (1972), p.213

-90- III.45 HBAVY-ION COLLISION IN THE EIKONAL FORMALISM

L.J.B. Goiafarb and J.M. Namys*owski Department of Theoretical Physics, Manchester University

Infinitely many Born terms, being of particular importance in a collision of heavy ion?, are summed up in such an eikonal formalism, that it allows for the initial energy to be different from the final energy. Eikonal off-energy- shell effects, especialy relevant in the Coulomb excitation processes, show up as an infinite series of hypergeometric functions. This series, after an appropriate analytical continuation, is truncated, and terms with the highest power z z e are of n = 1 2 I ^ Preserved. sum of several Coulomb potentials, with centers shifted from the origin, is considered. The whole T-matrix in momentum space naturaly splits into a large contribution, corresponding to large values of impact parameter, and a negli- gably small contribution, associated with a formaly included small values of impact parameter. Addition theorem for Bessel functions, and an explicit expression for the off-shell eikonal 3-body T-matrix in terms of the off-shell eikonal 2-body t-*natrices, established by Karlsson and one of the present authors, allows to reduce the problem of scattering off several shifted Coulomb centra to a supperposition and a product of scattering off one Coulomb potential. The structure of this result resembles that of the ordinary Glauber formula. The eikonal formalism is superior to other approaches because: 1) for the on-shell T-matrix it gives the exact answer for scattering off one Coulomb potential, as it was shown by Moore,

2) it allowsAthe full treatment of infinitely many Born terms, 3) it avoid3 the complexity of coupling of different angular momenta, since there is a diagonality in the impact i>»rameter space, 4) it enables an explicit account cf the off-energy-shell effects, which can also incorporate the Presnel type diffraction of heavy charged particles.

On leave of absence from the Institute of Theoretical Fhysics, Warsaw University

-91- III.46

Nucleus-nucleus collisions at relativistic energies G. Faldt, University of Lund, Sweaen H. Pilkuhn and H. G. Schlaile , University of Karlsruhe, GFR

Inelastic collisions of d, t He and oi-particles with heavier nuclei are comp_uted using Glauber's theory and Gaussian wave functions. They allow e. g. the computation of pion multiplicities in nucleus-nucleus collisions from those of proton-nucleus collisions. Let CT(A N) denote the cross section for the inelastic (i.e. pionproducing) collisions of N out of A incident nucleons, such A that the total pion-production cross section is &0,aA -Z = can be used to estimate the expectation values of the total pion energy and multiplicity. For comparison alsc> the geometric cross sections cc t .z arare given. cr(A A) U)

4He 17.5 25.4 2.1 7.5 52 .2 1.99 53 .6

The numbers correspond to an elementary inelastic cross section of 4 fm . Except for the three lightest nuclei, the production cross section is close to the geometric cross section and practically independent of energy. To obtain the total inelastic cross section, one must add the breakup without pion production.

-92- III.47 The Energy Dependence of the Real Central Optical Potential for Proton-Nucleus Scattering* W.T.H. van Oers, and Huang Haw Cyclotron Laboratory. Department of Physics University of Manitoba, Winnipeg, Canada The nucleon-nucleus optical potential vhich describes the overall features0of the nucleon-nucleus interaction is energy dependent and non- local. ' Pnencmenological optical potentials are usually chosen to be local potentials. Consequently, these potentials will exhibit an energy dependence which is due •oartly to the intrinsic energy dependence of the non-local optical potential and partly to its non-locality. To study in detail, the energy dependence of the phenonenological optical model over a considerable energy range we made cysteratic optical nodel analyses of p + l"0, p + ^Ca, anc* ? + ^uPb elastic scattering in the energy range 10-klOO I-leV.3) One defines the volune integral per nucleon of the real central fart of the optical potential as: J/A = [/V(r)d3r]/A = UTT V r3

where Vc, ro, and ao are the strength, radius and diffuseness of the real central potential with a Woods-Saxon forn factor. If proton energies below 25MeV are excluded then J/A exhibits a linear energy dependence (J/A =Jo/A + aTp) over a limited energy range. At the lower energies one expects the effects due to core polarization and the lack of an explicit treatment of exchange to becorr.e important.^' The energy dependence of J/A is given in Table I. The optical model parameters for 12c and 27A1 were adopted from the literature. energy' range Jo/A a r> + J-^C 30-100 535 -3.29 ^ O.Ch *r> + 16O 25-100 5m -3.50 ± 0.72 Table I T> + 27AI 25- 60 517 -3.5? - 0.81: r + h0Cs. 25-lCO Jt55 -2.05 t 0.U9 I, + 203pt 25-180 LL5 -1.U2 ± 0.52 (MeV) (MeV fm-) (fn-) It snould be noted that a is decreasing rabidly for increasing nass nunber A. Although less pronounced this decrease of c; with increasing A was also found by Oven and Satchler in their discussion of exchange effects.5) Secondly, the large values of a for the light nuclei :.ial:e the real central potential for these nuclei repulsive at relatively low energies in disagreement with available data for the energy range 200-1000 I'eV. Consequently, the energy dependence of J/A ir. the range 25-1000 I-'cV cannot be represented by a linear relation. In fact after inclusion of values of J/A above ?C0 !"eV, calculated fror. optical r.cdcl parameters for the five nuclei considered, the energ lependence of J/A in each case is essentially of the for™. J/A = ."->/+r a /'n(ivj **.-.'ork supported in part by the A.F.C.1}. of Car.ade . 3) ;:. Feshbach, An.'phys. 5.,357 (1955) 1) r. Lipper;:ei0e, ?.. Pivsih ££i2_,'/:• (l?'-7) Z) -..T.ii. van Oe^s, hu&ng ::aWj'.'..'£. Daviscr., A. Ir-gerarsson, aria r;. Tiboll, to be publis-ied ;0 "..". :.fe.kofsl:e, CJ.'.v. Oreenlees, i:.". Liers n.J.

Owe-, ar.a O.K. 3f.tchler, Ph;-s. Rev. Letters 1J2O (1970)

-93- III.48

"A three-parameter nucleon-nucleus optical potential on the energy shell" Bikash Sinha and Feroze Duggan

The nucleon-nucleus optical potential is calculated in first-order within the framework of the impulse approximation. The real-central part is generated by folding in a realistic effective interaction with the nucleonic density function, known a priore from Hartree- Fock calculation™. The second-order contributions are empirically simulated by using a density dependent effective interaction. For the exchange term a simple plane wave approximation has been used'). The imaginary potential is calculated assuming that the absorption arises entirely from the imaginary part of the two-body forward scattering amplitude. The forward scattering amplitude is determined by using the optical theorem which relates the forward scattering amplitude to the total nucleon-nucleon cross-section within the nucleus, such that, only those energy conserving single particle excitations allowed by the Paul! exclusion principle are taken into account '. Previous authors^/ used a zero-range interaction. We have modified the formalism to take into account the finite range of the interaction, so that the imaginary potential now becomes,

where D is the density, V. the two-body effective interaction evaluated at S = Ij^-Xi! and Jfi is the volume integral of the interaction Vp is the velocity of the incident nucleon inside the nucleus such that mVp =/2m(E-UoPT(n) ~ VC(rj) where E is the incident energy, UQPJ the real central part and VC the Coulomb potential. Thus, the real central and imaginary potential is calculated self-consistently. <j>{, is the average total nucleon-nucleon cross-section^). Clearly eq. (2) reduces to ordinary density for a zero-range force. The spin-orbit potential is generated using the Blin-Stoyle prescription. The three parameters varied to fit the data are the three depth parameters of the real, imaginary and the spin-orbit potential respectively. The fits to the data obtained by using this model are of comparable quality with that of using a standard ten parameter phenomenological model, Fig. 1. The full line shows the fits obtained using eq. (1), the long dashed line by using ordinary density and the small dashed line by using phenomenologicai model. It is clear that the fits greatly improve by using eq. (1) compared to that obtained by using ordinary density. However, the fits using this model tend to deteriorate at backward angles, sig- nifying the importance of non forward scattering amplitude contributions and possible off- shell effects. The volume integrals of the imaginary potential per nucleon within the energy range 30^E^50 ivieV remains constant and independent of the nucleus. Interest- ingly enough, they are of the same magnitude as found by Thomas et al^) using a phenomenological imaginary potential.

1) G.L. Thomas, B.C. Sinha and F. Duggan, Nucl. Phys. A203 (1973) 305. 2) G.W. Greenlees et al, Phys. Rev. ]T\_ (1968) 1115 and refs. therein.

-94- III.49

:'High Energy Elastic Scattering of Protons by Nuclei", by John Ullo and H. Feshbach, Massachusetts Institute of Technology, Cambridge, Massachusetts. — The multiple scattering theory of Kerman, McManus, and Thaler is extended to include triple scattering effects. The triple scattering term in the optical potential is approximately proportional to the triple correlation

function. The methods of Feshbach, Galr and Hufner are generalized to provide a coupled channel description of the elastic scattering of fast particles including triple scattering. The coupling potentials depend directly on the pair and triple correlation functions. Numerical calculations are performed for protons of

• ' •' 4 .\ 1.69 GeV/c momentum on He. Center-of-mass correlations and •:i phenomenological short-range dynamical correlations are tested °| using a spin-isospin averaged nucleon-nucleon amplitude. The - ; differential cross section around the second diffraction minimum v; and third diffraction peak is particularly sensitive to triple y\ scattering effects while only minor effects at the second •j diffraction peak are obtained.

-95- III.50

Effect of Nuclear Deformation on High Energy Elas- tic Hadron Nucleus Scattering*

,Alexander Wu Chao Institute for Theoretical Physics SUNY, Stony Brook, New York 11790 and Alfred S. Goldhaber University of California Los Alamos Scientific Laboratory Los Alamos, New Mexico 87544

In the first work on multi-GeV hadron-nucleus scattering, Bellettini, et al., made two remarkable observations: First, that large nuclear targets gave rise to Fraunhofer diffraction patterns. Second, that the pattern with a uranium target was much less sharp than with a lead target. Similar results 2 have been obtained by a Stony Brook-Northeastern collaboration. Already in the original publication, it was suggested that the fuzziness of the uranium diffraction pattern was a consequence of the deformation of uranium, an 3 2 explanation endorsed later. The new data have impelled us to reexamine this question, leading to the conclusion that the blurring of the first diffraction minimum cannot be a deformation effect (It is probably due to multiple Coulomb scattering in the target. In addition to the higher atomic charge, at least in 2 the recent experiment, the uranium target was thicker.). At the second minimum, there may be a significant contribution from electric quadrupole scattering, but not from deformation of the strong potential. In short, an electrifying possibility turns out to be merely an electrical reality. We discuss the accuracy which would be required in future experiments to see the effects of nuclear matter deformation.

* / Work supported by the U. S. Atomic Energy Commission; address after September 1, 1973: I.T.P., SUNY, Stony Brook, NY 11790. 1. G. Bellettini, et al., Nucl. Phys. _7£> 609 (1966). 2. H. R. Blieden, G. Finocchiaro, P. D. Grannis, D. Green, D. Hochman, R. Kephart, J. Kirz, Y. Y. Lee, C. Nef, R. Thunn, W. Faissler, and Y. W. Tang, private communication. 3. A. S. Goldhaber and C. J. Joachain, Phys. Rev. 171, 1566 (1968).

-96- III.51

High-energy approximations to nuclear scattering

W.E. Frahn and B. Schlirmann

Physics Department, University of Cape Town

We have developed systematic approximation methods for high-energy nuclear scattering which improve upon Glauber's eikonal approximation. These methods are based on expansions of the free-space propagator in terms of the eikonal and the Fresnel propagator, respectively, and emphasize different aspects of the scattering process. While the "eikonal expansion" describes deviations from the asymptotic energy limit and proceeds in powers of the reciprocal wave number, the "Fresnel expansion" emphasizes the deviations from geometric- optical propagation caused by diffractive distortion of the propagating wave front in transverse direction.

We show that the Fresnel and eikonal propagators are connected by a unitary transformation. By means of tbis transformation, which is analogous to the one that leads from the SchrBdinger picture to the interaction picture in time-dependent perturbation theory, we derive a closed expression for the scattering amplitude in Fresnel approximation which is formally similar to the

Glauber expression. However, it differs from the latter by involving a characteristic Dyson-type ordering of the interaction operators with respect to the z-ccordinates. From the general expression we calculate, to first order in k~l, the Fresnel correction to the Glauber amplitude.

In the present contribution these methods are formulated for potential scattering; application to multiple scattering in nuclei is made in a companion paper.l

1. B. Schumann and W.E. Frahn, these proceedings.

-97- III.52

Fresnel diffraction in high-energy multiple scattering

B. Schttrmann and W.E. Frahn

Physics Department, University of Cape Town

The Fresnel approximation method described in an accompanying paper1 is

applied to high-energy multiple scattering of hadrons in complex nuclei.

Starting from a finite Watson-type multiple scattering series, we approximate

the free-space propagators by Fresnel propagators. By employing the unitary

transformation that connects the Fresnel and eikonal propagators, we derive

a closed expression for the multiple scattering amplitude which is formally

similar to the corresponding Glauber expression. However, the Fresnel

diffraction effects manifest themselves in a characteristic Dyson-type ordering

of the transformed profile operators with respect to the z-coordinates.

The general formulae are then applied to elastic scattering by a target

nucleus represented by an independent particle model. The resulting amplitude

is again formally similar to the Glauber series for multiple scattering by A

independent nucleons, but involves a Fresnel-transformed interaction operator

which is defined in terms of the nucleon-nucleon scattering amplitude, the

nuclear form factor and the transverse kinetic energy operator. It is shown

that in the "optical limit" A •+• « the multiple scattering amplitude is

identical with the Fresnel approximation to potential scattering described in

ref. 1. For A = 2 we recover essentially the result previously derived by

Gottfried2 for Fresnel diffraction in deuterium. Fresnel corrections to order k"1 have been calculated for other light nuclei (A = 4 - 16) and compared with experimental data.

1. W.E. Frahn and B. SchUrmann, these proceedings.

2. K. Gottfried, Ann. Phys. (N.Y.) 6£ (1971) 868.

-98- a * III.53 Cancellations in Watson's Multiple Scattering Series and Additivity of Phase Shifts. D. Agassi, Weizmann Institute of Science and A. Gal, Hebrew University of Jerusalem. The scattering of high energy projectiles on nuclear targets is considered within the freezing assumption for two extreme cases. The first one corresponds to scattering from non-overlap- ;=f ping potentials, a case which has recently been considered by some authors for the construction of n-nuclear optical potential. It is well known by now that the multiple scattering series description of such a scattering involves only on the energy shell projectile-nucleon scattering amplitudes. This (trivial) pattern of cancellations in Watson's series, however, is insufficient for establishing connection with Glauber's additivity assumption. It is shown by us explicitly for scattering on deuterium that the cancellations necessary for the above mentioned connection arise from an average, over a smooth target density, in which terms osci- ,§% llatory over a wavelength distance k"1 are dropped out. This 'is! sj averaging procedure does not show up in the (small angle) eikonax 'M formulation due to translational symmetry of constituent poten- 4'sf tials, each separately, along the beam direction. VI The second case corresponds to scattering from completely jt overlapping potentials in which case the notion of averaging ,1 obviously does not show up. High energy conditions g<>l H are used to obtain additivity of phase shifts for each partial Is wave. The derivation is based on a proper eikonalization of the ?!| radial SchrOedinger equation; for semiclassical values of &>>1, 5,+2^kb, the connection with Glauber's additivity can be established. The main result is summarized by the formula

h (kr) |2V(r)dr .

-99- III.54

KINEMATICS IN NUCLEAR MULTIPLE SCATTERING"*" E. KUJAWSKI Laboratory For Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, Massachusetts, U.S.A. and E. LAMBERT Institut de Physique de 1'Universite, Neuchatel, Switzerland

One of the basic problems in any multiple scattering formulation is to relate the matrix elements of the relevant many-body modified operators to the free two-body scattering matrix elements. The multiple scattering series may be expanded in terms of rather general t-matrices, and we investigate two formulations relevant for intermediate- energy elastic nuclear scattering: (i) the "fixed scatterer approximation" (FSA) kinematics, (ii) the "on-energy-shell impulse approximation" (OEI) kinematics. In the FSA the scattering amplitude in the center-of-mass system is calculated from the scattering by fixed scatterers using the reduced mass of the total system and averaging over the internal eigenstates. For non-overlapping potentials the scattering in the FSA is determined fully in terms of on- shell quantities [1]. In the OEI the target nucleon in lowest order is effectively treated as recoiling freely, and unless the internal motion is neglected off-shell effects need to be taken into account. The significance of the above two formulations will be thoroughly discussed and illustrated for several cases of relevance to intermediate-energy elastic nuclear scattering. Our results suggest that at intermediate energies the scattering is still quite sensitive to the kinematics, and it may be inappropriate to use the scattering amplitudes obtained from two-body scattering.

+ Supported by the Atomic Energy Commission under Contract (11-1)-3069 and the Swiss National Science Foundation. [1] E. Lambert and E. Kujawski, this Conference.

-100- III.55

OFF-ENERGY-SHELL EFFECTS IN MULTIPLE SCATTERING

E. LAMBERT Institut de Physique de l'Universite, Neuchatel, Switzerland

and E. KUJAWSKI Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology, Cambridge, Mass., USA

The elastic scattering from a two-body bound system is studied in order to investigate what information about the nuclear structure and the projectile- nucleon interaction may be obtained at intermediate energies. This study is made within the framework of the fixed scatterer approximation. As a result of averaging the scattering amplitude over the ground-state density, these potentials generally overlap thereby mixing up information about the nuclear structure with information about the off-energy-shell part of the two- '- body interaction. Two approximations whereby the scattering is expressible simply in terms of on-shell information are investigated : (i) the "non-overlapping potentials ; approximation" in which the scattering amplitude is calculated assuming that the potentials do not overlap, (ii) the "on-energy-shell scattering approximation" in which the principal part of the propagator is neglected. ', The results up to double scattering terms are compared for two phase equivalent interactions namely the S-wave square well and equivalent separable po- ' tential and the above mentioned approximations are investigated. ; In addition for the Yamaguchi interaction the results keeping up to double j scattering terms are compared with the exact ones in order to study the impor- [' tance of the higher order terms. !' Numerical calculations are performed for three spherically symmetric densities at 100 and 500 MeV projectile incident energy. The "non-overlapping" and "on- energy-shell scattering" approximations lead to very similar results, but they differ significantly from the exact ones. Although the convergence of the multiple scattering series, the validity of the various approximate treatments and the agreement among the results for the phase equivalent interactions improve with increasing energy, the importance of the off-shell effects remains comparable to the effect of the nuclear structure. This observation plus the sensitivity to the kinematics [l] suggest that elastic scattering is not well suited to obtain information about two-body nuclear correlations or the two- body interaction.

The details of the present investigation are included in a paper submitted for publication in Annals of Physics (N.Y.). [lj E. Kujawski and E. Lambert, this Conference.

-101- IV

PRODUCTION PROCESSES IV.1 Cross Sections for -n^ from He-* on Complex Nuclei N.S. Wall, J.N. Craig, R.E. Berg, D. Ezrow, and H.D. Holmgren University of Maryland An experiment to detect ITO mesons produced by He3 incident on nuclei at energies slightly above threshold has been performed using the Maryland Cyclo- tron. He ions of 180 and 200 MeV were used to bombard targets of C-^2 and natural Pb, and the annihilation quanta of the irO mesons were detected by two total energy Ph glass Cerenkov counters which had been calibrated utilizing the 60 MeV electron beam from the NRL Linac. The electrons in turn were used to calibrate light emitting diodes; one for each phototube. Each Cerenkov counter was viewed by two phototubes which were in coincidence with a revolving time of ^20 ns. The two detectors were then put in coincidence with each other, with an overall resolving time about 50 ns. The fourfold coincidence signal was used to open a gate on a linear gate and stretcher which integrated the signals from each pair of photomultipliers. The stretched signals were then fed into one of two two-dimensional pulse height arravs, depending upon whether the fourfold coincidence was due to the light pulser of represented two y-rays. Cerenkov counters and this method of recording data were utilized because we expected a low cross-section and such an arrangement permitted good discrimination against pile-up from target produced y-rays. The background y-radiation was minimized by a beam optic design which permitted the beam to see no significant material within about 5 meters from the detectors, which in turn were usually less than 25 cm from the target. Finally a thin tungsten plate was placed between the detector and target to further eliminate low energy y-rays. Since the TTO decays in its rest frame isotropically with the emission of two back-to-back y-rays it is necessary to transform that isotropic probability to the laboratory frame. To perform this folding it is necessary to assume both an energy and angular distribution in order to relate the observed told v-energy two-dimensional spectra to d^o/dfidE, the quantity desired. It is also necessary to know the resolution function in angle and y-ray energy to be able to completely construct the bi-dimensional spectrum. The results we give in the table, however, integrate over the detector resolution function and over the solid angle determined by the geometry of the detectors. The complete technique was essentially verified by measuring the TT^ production cross-section for 300 MeV protons on C^2 utilizing the SREL Cyclotron and the results are comparable to earlier published results on such a cross-section.

Element He Energy Angle of y-detectors dQdE C12 180 MeV ± 90° 2 x 10-36cm2/sr 200 MeV + 90° 7 x 10-36 Pb 200 MeV + 90° 7 x 10-35 While there are, to our knowledge, no direct theoretical calculations that can be compared with our experiment there is a calculation by Shusterl) which can be utilized to get a rough estimate of what the theory would give under our conditions. Shuster gives an approximate total cross-section for TT" production for 200 MeV He3 which is 10~26cm2. Assuming isotropy, and a flat energy spectrum, and further lowering the estimated cross-section by 10"3 to account for absorptive processes, we deduce his calculation would predict an estimated d2o/dftdE>2 x 10-32cm2. ^he discrepancy WJth our results is disturbing in light of the agreement of the theory with the Uppsala proton TT+ production results. 1) M.D. Shuster, Ph.D. Thesis, Univ. of Md., 1970

-105- IV.2 The (p,ir ) Reaction and Nuclear Structure* J.M. Eisenberg, J.V. Noble and H.J. Weber Department of Physics, University of Virginia, Charlottesville, Virginia

We have studied the (p,ir ) reaction at 185 MeV and 600 MeV in a distorted wave Born approximation theory in order to compare with recent experiments^-' . As is well known, the application^ of the usual Kisslinger potential to this problem leads to disastrous off-shell effects which generate errors of two or three orders of magnitude in the resulting cross sections. We have therefore attempted to apply eikonal and Sopkovich formalisms to this problem in order to minimize these off-shell effects. We have utilized Eckart wave functions to insure appropriate asymptotic behavior for our single-particle bound states. As is shown in Fig. 1, we are able to produce cross sections which are of the correct size, but we are not readily able to account for their shapes with normal nuclear size parameters; there are also substantial changes if a static absorption vertex is used in place of a Galilean invariant vertex. We have examined the consequences of isobar exchange for the (p,n) reaction as well as the effects of using a coupled-channel approach, and modifying the form of the single-nucleon wave functions. Within reasonable ranges of parameters , these mechanisms are separately able to account for the observed data. There are thus still so many ambiguities in the theory that it is difficult to extract definitive information on the behavior of the nucleon wave function at the small distances involved (^0.5 fm), but there is hope that with further systematic data these ambiguous points may be clarified.

References *Work supported in part by the National Science Foundation. 1. K. Gabathuler et al., Nucl. Phys. B40 (1972) 32 and references quoted therein. 2. S. Dahlgren, B. Hoistad and • 1 1 P. Grafstrom, Phys. Lett. 35B (1971) 219; preprint and private communication. 3. W.S. Jones and J.ti. Eisenberg; Nucl. Phys. A154 (1970) 49. :io* Fig. 1. Cross sections for the C(p,ir+) ^C reaction, leading to the c // • * vv j A ground state (lpi/2> and low- lying excited states // • A * iiO2 (2si/2+ld5/2), at 185 MeV lab kinetic energy. The dot-dashed •5 f \ • A A \J ' r \ 2s curves represent coupled-channel 1/2 calculations with — "* *lp^- IS'?#>"J2-I collective 6 \v 1d s.p.*, using a single-particle 10 wave function with modified 5/2 short-range behavior. N, rmGal. inv. \ * -Tr.r static \ 1 • \ 0° 40° 80° 120° angle

-106- IV.3 MICROSCOPIC DESCRIPTION OF PION INDUCED NUCLEAR REACTIONS M.Dillig and M. G. Huber Institute for Theoretical Physics, University of Erlangen The interaction of pions with nuclei seems to be a sensitive test of nuclear models, since such processes generally involve the transfer of large momenta. Therefore it is to be expected that the contributions from the two nucleon mechanisme have to be taken into account. - - Consistent with a previous analysis of the absorption rates of bound pions(1) the short ranged two body correlations are introduced phenomenologically in the framework of the Jastrow Model. The effect of the SRC on the differential cross section of the recent Uppsala experiment on ^C(P,TC+) 13c is generally an increase of the rate by a factor 50 to 100(2) (see Pigs.1,2,3) over the IPM predictions - in agreement with the experimental data. - - In the same model a mechanisme for the (p,7t~) reaction is provided; the (n+/n;-)production ratio has been calculated within the Jastrow Model, the results are shown in Fig.4 for Ep=185 MeV(Uppsala) and Ep=600 MeV(CERN)(3). Conclu- sions: Within the framework of the Jastrow Model both the absorption and production rates of n* and it~ can be accounted for consistently provided the correlation factor has been choosen properly. Furthermore it should be noted, that within the same model several photo-and electroinduced reactions in the intermediate energy range can be explained quantitatively. (1) K.N.Chung et.al.;Z.Phys. 240 (1970) 195; (2) M.Dillig et.al.; Phys.Lett.(in press); (3) M.DTTTig et.al.; to be published.

Sr "*'"' "**" 1JC!p.n*)l3C(V}->

'«» PWBA 1 \ V IPM ru q < 300 Me\* q.3OO MtV* q.32SMcYfc q.325Mctt

10 f{ tO I0O 120 1(0 W) M0 6 0 20 (0 M N SO 120 UO K0 1M •

9Be(p.n*l EpiUSMtV PW8A PWBA IPM ^.^-.q.MO MeV.'c qi325M«t/c -CERH 100= - Uppsala—

10= Pi".

0 20 (0 tO M BO 120 U0 zto

-107- IV.4 Complete Differential Cross Sections for the Reaction p+p-»d+TT* from 3 to 5 GeV/c. D.A.LARSON*, H.L.ANDERSON, AND L.MYRIANTHO- POULOS, University of Chicago; L.DUBALt, CK. HARGROVE, and R.J. McKEE, National Research Council of Canada; E.P.HINCKS, D. KESSLER, H.MES*. and A.C.THOMPSON?, Carleton University A multiwire proportional chamber system was used at the Lawrence Berkeley Laboratory Bevatron to measure the entire differential cross section for the reaction p + p-*-d+ir+ at eight values of incident proton momentum between 3 and 5 GeV/c. Deuterons and pions produced in a small liquid hydrogen target passed through a single magnetic field and were detected in coincidence in two moveable spectrometer arms, each containing six 255-wire multiwire proportional chambers and various scintillation counters, including a deuteron time-of-f1ight system. By using the multiwire proportional chambers in an event selection mode, based on the unique kinematics of the desired reaction, it was possible to select good events from among the 104-105 times more probable elastic and multiparticle production processes. For example, if a particle was detected at a certain wire in the pion arm, then kinematics would allow an associated deuteron from the reaction of interest to appear only at certain wires in the deuteron arm. In order to select these good events, four hardware comparison tests were carried out, in parallel, as the data came out of the multiwire proportional chambers. These tests involved comparisons of horizontal or vertical coordinates of the trajectories as determined by specific wire planes and served to check coplanarity, opening angle, and the correct correspondence between the angle of emission and the momentum of the particle detected in each of the two arms. As a result, mainly good events were recorded on magnetic tape, with only a moderate sample of the unwanted variety. At each incident beam momentum approximately 60-80 data points were measured, each with 5-10% statistics. The measured cross sections exhibit a strong dependence on momentum transfer and energy. At 3.83 GeV/c, for example, the differential cross section falls from 14 ub/sr in the forward direction to 0.2 yb/sr at 90°(CM). The total cross section falls from 37 yb at 3 GeV/c to 3.4 yb at 5 GeV/c. The data show that the previously observed enhancement in the forward cross section between 3 and 4 GeV/c is an effect which damps out quickly as the production angle departs from zero degrees, in contrast to the well-known enhancement at 1.35 GeV/c, which is evident at all angles. The coefficients of even-order Legendre polynomial fits to the data increase smoothly with momentum. There is no evidence that any one angular momentum state plays a dominant role in the process between 3 and 5 GeV/c. Available data between 2 and 24 GeV/c show that the total cross section decreases as s~n with n~4.

Presently at Cornell University Ithaca NY. Presently at SIN, Zurich, Switzerland, Presently at National Research Council of Canada, Ottawa, Ontario Canada Presently at Carnegie-Mellon University, Pittsburg, PA.

-108- IV.5

The Reactioinn pd -» tir , by C. P. PerdrisatJ W. Dollhopf, C. Lunke, W. K. Roberts,! P. Kitching,^ W. C. Olsen? and J. R. Priest, CCollego e of William and Mary, Williamsburg, Virginia 23185.

We report the results of an experiment performed at the Space Radiation Effects Laboratory in Virginia. 590 and 4j0 MeV protons were scattered from CDg-targets 0.20 cm thick. The tritons were detected in a l»-counter telescope; their time of flight, specific energy loss and range were measured. The associated pions were detected in a 3-counter telescope containing also 3 wire spark chambers; their specific energy loss and range were measured. The incident proton intensity was monitored by scattering the beam from a secondary Al target into a 3-counter telescope. The pt> and pd elastic cross sections were also measured at one angle to check the efficiency of the system. Multi- dimensional on-line analysis of the data was used to check that the background from pd -*• nd vr+ was properly rejected. The tritons could be identified from either their time-of-flight or their specific energy loss, but the pions associated with pd -*• tir+ could not be separated from those produced in 3- or It-body final states. In the final analysis, cuts were applied on the triton time-of-flight and dE/dx-spectra. A residual background remaining after subtraction of the carbon contribution was removed using a least-square fitting procedure simultaneously on the triton time-of-flight and dE/dx-snectra. The results are shown in Fi^. 1 and 2. Whereas a distinct backward peak is seen at 470 MeV, in agreement with a previous experiment at 325 MeV2, no such backward peak is apparent in our 590 MeV data. A backward peak does not appear in the twp-nucleon process considered in^ or in the one-nucleon process discussed, in ; one may conclude that an exchange process is important in the production of pions in the backward direction.

• NEW DATA o - 20 - SOLD 6 DATA 4 \ Fig . 2 10 - \ • \ 8 Fig. 1 2 \ 590 MeV T \ \ 6 1+70 MeV \ do/dQ do/dQ 4 : -\ 1 — \ IN IN /ib/sr .8 — \ /iWsr • _ 2 .6 L \ i \ J .4 \ 1 ' \ .8 .2 .6 ii .4 " i i 1 1 f 1 T 1 1 1 I i i 0 30 60 90 120 150 180 0 30 60 90 120 150 180 6, CM 8. CM tNow Physics Inst. University^of Neuchatel; iN.A.S.A. Lewis Research Center; SNucleai- Research Center, Uni. of Alberta, Edmonton; *Miami University, Oxford, Ohio. 1) W. Dollhopf et al. N.A.S.A. TM X-69187 (1973) 2) K. R. Chapman et al N.P. 57, 499 (196*0 3) C. H. Q. Ingram et al N.P. B31, 331 (1971) U) S. Dahlgren et al. preprint (1973); to be nublished in N.P.

^Supported in part from a Research Corporation grant.

-109- IV.6

MECHANISM OF THE REACTION p + d -> t +X AND pt BACKWARD SCATTHKING AT HIGH MiSRGHS. V,Z»Kopeliovich,I,K,Potash»ikova. Joint Institute for Nuclear Research, Dubaa,TJSSE

ABSTRACT

As the Ruderman mechanism for the reaction p + t +T does not describe the data at large angles and high energies, the OPE mechanism has been proposed similarly to the Yao model for pp —* d 3* and to that of Craigie - Wilkin for the p-d backward scattering. The data on 3T -d backward scattering have been used in '4 our calculations. There is a maximum in the differential J - s cross section energy dependence at T p s 1,1 GeV which -/fI; agrees with experimental data* Using the considered I ki mechanism the isovector exchange amplitude in the sea- | ttering and proton backward charge exchange on %e and J t nuclei has been calculated.

-no- IV.7 PION PRODUCTION FROM NUCLEI

MORTON M. STERNHEIMJ Department of Physics and Astronomy, University of Massachusetts, Amherst, Mass., USA and RICHARD R» SlLBAR» LOS Alamos Scientific Laboratory, University of California, Los Alamos, NM, USA. We have calculated it~ production by protons from nuclei using a semi-classical model. Production is assumed to occur via a one step NN -»• NNir reaction, with the relative probabilities of various charge states determined by the isobar model. The incoming nucleon and outgoing pion fluxes are attenuated by absorption, and both fluxes are modified by charge exchange reactions. The model requires total cross sections for IT and J. N absorption and charge exchange, and differential cross % sections for pp -*• pmr . 3* Initially1 we used a uniform sphere nuclear density; 'i we fitted the absorption cross sections and used experimental ••i data on free nucleons for the other inputs. The overall agree- •| ment with the data2 at 740 MeV was quite good. '! We have now3 used realistic densities and have corrected ths input cross sections for the effects of the Pauli principle, Fermi motion, and nuclear optical potentials. These modifica- —i tions produce substantial changes in some of the inputs and in ] ••'I the fitted ir absorption cross section. However, the final re- r^ suits for ir production are only slightly altered, so that the •<•*.'} agreement with experiment is similar to that obtained earlier. ;'( Ambiguities arising from the nuclear corrections are found to ^1 be larger than the effects of moderate variations of the '.'j nuclear surface parameters. f a J Research supported in part by the U.S. Atomic Energy .J Commission and the National Science Foundation. i >| 1. M.M. Sternheim and R.R. Silbar, Phys. Rev. D 6, 3117 (1972). 3 2. D.R.F. Cochran et al., Phys. Rev. D £, 3085 (T972). 3. M.M. Sternheim and R.R. Silbar, PhysT Rev. C, to be published.

-Ill- IV.8 Effective icNN Interaction Il-T. CHEON and J. CUGNCN Institut de Physique, Universite de Liege, Liege, Belgium

An effective TtM interaction which can be applied to the problems of pion absorption and production at low energy is proposed in an elegant form. Although our theoretical treatment is, in principle, the same as the previous work(Ch. 1968), the present form of the itNN effective interaction includes no free parameter in the sense that it does not contain any phenomenological quantity. The interaction proposed here has been examined in the processes, p+p j± d+ic+ , p+p-» >rp-f-TC° at threshold. The two—nucleon wave functions for the initial and final states have been obtained by solving the Schrodinger equation with the Hamada-Johnston potential. Our results are as follows: cr^p-dit*) =24oii jib (0^ =24011 pb)(Ko.l967). =32±7?f (Dun.1959); 27* 1011* (St.1958)). V.'e have Also calculated the absorption rate of it* mesons from the IS atomic orbit by the 16 —1 deuteron, W=0.995x10 sec . Since our effective "ON interaction is connected to the TTN scattering length, it may be possible to determine this quantity from the processes considered here. By the method of X—fit for the process it + d-»-p+p ( <20Me\O, we have obtained

at+2a3= 0.00193 which is very close to the values calculated by Hamilt- on et al. (Ha.1963; Ha.1966) and Samaranayake et al. (3am.1972). It must be very interesting to apply our effective interaction to the problems of It* absorption by various light nuclei. Reference. Cheon Il-T. et al., Nucl. Phys. _§6(1968)586. Rose CM., Fhys. Sev. 154(1967)1305. Dunaitsev A. F. et al., Soviet rhys. JJTP 9(1959)1179. Stallwood 3. A. et al., Phys. Rev. 109(1958)1716. Hamilton J. et al., 3ev. Mod. I>hys. 35(1963)737. Hamilton J., Fhys. Letters 20(1966)687. Samaranayake V. K. et al., tfucl. Phys. 848(1972)205.

-112- IV.9

A STUDY OF THE REACTION d+p-»-He3+ir •», d+p-*H3+ir+ AND d+p-»-He3 + rio

J.Banaigs, J.Berger, L.Goldzahl, T.Risaer3 L.Vu-tiai CNRS et DSpartement Saturne CEN SACLAY FRANCE M.Cottereau, C.Le Brun Laboratoire de Physique Corpusculaire, University de CAEN FRANCE

These reactions have been studied in two conjugate inclusi- ve reactions : d+p-*-H3+(mm)+ and d+p-»He3+(mm)° with an incident deuteron beam of momenta between 2.83 and 3.82 GeV/c from the Saclay synchrotron Saturne. For each selected incident momentum, we measured the missing mass spectrum of the H3, or He3 nuclei emitted at a fixed angle in the laboratory. The salient results on the production cross sections da/dft* of if ° and n° are : i) The angular distributions of ir° at = 3.28 and = 3.44 GeV and of n° at WCM = 3.44 GeV are flat in the backward hemisphere K i.e. e- 3 >90°, and peaked forward (Fig 1), 3 ii) The backward cross sections for ir° and nQ pproduction show a maximum for a total CM energy near 3.47 GeV (Fig 2). The estimated total cross sections in the CM are : otot ' 3-57 *0.46 pb at 3.28 GeV and 1.76 *0.25 ub at 3.44 GeV for n° and otot; = 0.65 ±0.15 yb at 3.44 GeV for n°.

nb/sr. 1200 Fig. 1 ®->r7° Pincm 2.65 GeV/c 1000

Pine" 5.50 GeV/c 600 A- r

600

400

200

-7 -0.5 0 0.5 +1 3.25 335 3.45 3.55 cos.e' W*GeV

-113- IV. 10 OBSERVATION OF THE "ABC" EFFECT IN n+p-*-d + (nun)°

y F.Bonthonneau, M.Cottereau, J.L.Laville, C.Le Brun F.Lefebvres, J.C.Malherbe, R.Regimbart Laboratoive de Physique Corpuaoulaire, University de CAEN FRANCE

J.Bergev, J.Duflo, L.Goldzahlt F.Plouiny L.Vu-Hai CNRS et Dipartement Jaturne CEN SACLAY FRANCE We present preliminary and partial results of two separate missing mass experiments obtained with the extracted deuteron beam from the Saclay synchrotron Saturne : I - momentum spectrum measurements of the final deuteron in the reaction d+p-*-d+(mm)° ( fig2) This reaction can be interpreted as the sum of the two nucleon-nucleon interactions + ns+p+p-»-d+ (mm) +ns o and ps+n+p-»-d+(mm) + ps in the impulse approximation and of the coherent interaction d+p->d+(mm)+ II - momentum spectrum measurements of the deuteron in the reaction n+p-»-d+(mm)° where the monoenergetic neutron beam is obtained by stripping of the deuteron beam. (fig.1) We observe : I - A large "ABC" effect in both experiments, II - The existence of a bump located at the maximum missing mass (backward-forward transition). Such an effect has been predicted by T.Risser and M.Shuster (Physics Letters t3B,68 (1973)).

o f•> + p—d+ (mm)" /V+p-H»d +

t 1 h z I pu d GeV/c i p/z d GeV/c .3 10 1.2 1.4 7.6 7.8 2.0 1.0 1.2 0» i • I •< I 1 • I IIQ 0» .1.2.3 A 2 21 .1.21 .5 A .5 fmmj GeV/c A .5 .2.1 (mm)

-114- IV. 11

ON THE NATURE OF THE ABC EFFECT

M. D. Shuster, Institut fiir Theoretische Kernphysik, Universitat Karlsruhe, 7500 Karlsruhe, Germany T. Hisser, Depjirtment of Physics, University of California, Santa Barbara, California, USA * I. Bar-Kir , Institut fur Hochenergiephysik, Universitat Heidelberg, 6900 Heidelberg, Germany

The ABC effect, a dramatic enhancement at a missing mass around 300 MeV observed in the reactions p + d—» He + MM and n + p-—•» d + MM, has been the subject of much dissatisfying speculation. Originally thought to be the vector meson v/hen the earliest searches for this were made, this idea was abandoned when the study of other reactions showed that there was no resonahce structure in the nit-scattering amplitude at this energy. Recently some light has been cast on the nature of this process by the Saclay deuteron group who observed that the ABC enhancement is -largest when the total c.m. energy is larger than the masses of the incident particles by about 600 MeV. This would lead one to suspect that the effect is tied somehow to the excitation of two ^(i236)-resonances. This possibility in the reaction np—»dim was explored by two of the authors (T.R. and M.D.S., Phys. Letters 43B(1973)68). who were able to reproduce the enhancement, its supposed isoscalar nature, and its dependence on the total c.m. energy,without adjustable parameters. An enhancement at vcr,>- laroe /;iibf;in£- na.oses predicted by the :>odel has been observed recently by the Saclay deuteron group (see elsewhere in this volume). That this mechanism might be responsible for the low-mass enhancement was ohown also by the Tel-Aviv-Heidelberg bubble-chamber collaboration in a not altogether different approach analysing slightly different data (I. Bar-Nir et al., to be published). The ^^-excitation also accounts for the c.m. energy at which the ABC effect occurs in other reactions and there are indications that,it may account as well for certain peculiarities of the reaction pd 'He Jtn. on leave from Department of Physics and Astronomy, Tel-Aviv University, Tel-Aviv. Israel

to 12 1.4 1.6 1.8 Puttdcuteron) in GeV/c

. Calculated deuteron recoil-momentum spectra in the laboratory for the isospin-zcro and isospin-one channels for . Feynman diagrams for the reactions NN -»NNwn and deuterons emitted at 0 deg. NN -> dira.

-115- IV.12

"ABC" AND "DEF" EFFECTS POSITION, WIDTH, ISOSPIN, ANGULAR AND ENERGY DISTRIBUTIONS

J.Banaigs, J.Berger, L.Goldzahl, T.Riaser*3 L.Vu-Hci CNRS et DSpavtement Satuvne CEN SACLAY FRANCE M.Cottereau, C.Le Brun Laboratoire de Physique CovpusoulaiTe, Vnivevsiti de CAEN FRANCE The spectrum of mesonic missing mass produced in the reaction (1) dtp-»-He^+(mm)° has been studied with a beam of deuterons extracted from the Saclay synchrotron Saturne, this spectrum being deduced from the momentum distribution of the He^ nuclei emitted in a given direction 0 in the laboratory. Thirteen spectra in the ranges of incident momenta (2.8^p<3.8 GeV/c) and laboratory angles (O°-«:0

f Dept. Phys* University of California, Santa Barbara, USA

-116- IV.13 A STUDY OF THE REACTION d+d+HeVdnro)°

J.Banaigs, J.Bergert L.Goldzdhl, T.Risser3 L.Vu-Hai CNRS et D4partement Saturne CEN SACLAY FRANCE M.Cottereau, C.Le Brun Laboratoire de Physique Corpusoulaire, University de CAEN PRANCE F.L.Fabbri, P.Picozza Laboratori Nazionali di Frascati del CNEM, FRASCATI ITALY The reaction did+He +(mm)° is presently under study at the Saclay synchrotron Saturne. The study of this reaction is particularly interesting because of the fact that the missing mass is in a pure state of Isospin 1 = 0, the deuteron and He1* having isospin zero. The momentum spectra of He1* nuclei emitted at 0° in the Laboratory (180° CM) has been measured so far at incident deuteron momenta of 2.49, 3.34 and 3.82 GeV/c. The results show clearly : 1) The production of the "ABC" effect at 2.49 (Physics Letters 43B p535-538) and 3.34 GeV/c with a cross section do/dn*(0*=O° or 180°) of 0.66*.18 ub/sr and .026*.007 ub/sr respectively, 2) The production of the well known

nanobarn/sr. GeV/c? he? 8fabr0.3deg.

150

100-

tr .5 .6 .7 .8 .9 1.0 (mm) masse manquante GeV/c2

-117- IV. 14

Analysis of p + d •» He3 + X° Experiments*

H. Brody

Physics Department University of Pennsylvania Philadelphia, Pa. 19174 U.S.A.

The production of TT , ^ and a) mesons in the reaction

p + d .» He + X° with protons of 2 GeV and 3 GeV has been

analyzed. Using a simple nucleon exchange model and assuming that

the variation in cross section with respect to the momentum 3 transfer is dominated by the He form factor, - particularly at 3 these large momentum transfers - information about the He form

factor can be obtained. With this momentum transfer dependence of 3 the He form factor it is then possible to explain why there is an

enhancement above phase space in the neutral missing mass 3 spectrum at the two pion threshhold (the ABC effect) when a He

nucleus is produced, and show that a relatively small TW scatter-

ing length will now fit not only the 2 and 3 GeV data, but also

the 750 MeV p + d data. Hence the ABC effect is not a pion

resonance or large final state interaction, but due to the fact 3 that it is difficult to form a He nucleus when the relative

momentum of the constituent nucleons is high.

Supported in part by the U.S. Atomic Energy Commission

-118- IV.15

NUCLEUS EXCITATLON MODEL FOR ABC EFFECT

M. BLESZYNSKI, F. L. FABBRI, P. PICCHI, P. PICOZZA. Laboratori Nazionali di Frascati del CNEN-Frascati Italy

It is well known that at present time does not exist any theory of ABC enhancement successful in describing all the available experimental data for the production of D, He , He . Recently the Saclay-Caen group has measured the ABC effect in the n+p*d+(mm) reaction (contribution to this conference ). It is possible now to start from the first step in the knowledge of this effect. We would like to present a possible theoretical model which tends to explain the ABC effect as an enhancement due to the excitation of the nucleus. In this model the reaction n+p*d+(mm) should go through the intermediate step n+p»d*»d+(mm). The initial input for our model is the d form factor preserving the final product of d* decay to be a deuteron. Our very preliminary calculation for n+p->d+(mm) seems to be encouraging. The advantage of this model is that it can be applied for all nuclei, with the appropriate choice of the final nucleus form factor.

~\ * OU/L. fitOh A\ -\ SACLAV ~>aA- A\

\ X \ \

{$00 2ooo

3oo

-119- IV.16

DYNAMICAL MODEL FOR THE ABC EFFECT by J.C. AMJOS. 0. LEVY qnr A. SANT'vZ Service de Physique Theorique - CEN Saclay B.P. N°2 - 91190 GIF s/Yvette - FRANCE

We present a modal for the ABC production, experimentally observed in the missing mass spectrum of the reaction dp-*He S+(HMo). The reaction is assumed to be splitted in two successive steps, namely : (i]-NiD-»dini followed by (ii) N2di-»- 5HeII2, N1 and N2 being the two nucleons of the incident deuton and di an intermediate deuton. The total amplitude is factorized into the product of the two amplitudes of reactions (i) and (ii). We Know that at low energy these two reactions are dominated byAproduction. This involves that the total cross sections are given by Breit-Wigner type formula and that angular distributions are peaked in the bacward -4nd forward directions.

The two main results are :

- At given incident energy the ABC effect results from the angular distribution of the two intermediate reactions.

- the energy dependence of the ASC is deduced from those of intermediate processes.

The resulting fits are very good when we taKe into account the fermi motion in the initial deuton (see figs. 1 and 2).

tf-cr 1 ABCetfecL al l Incident 50 fwi Enerey deyen

Zlm 2-7 U 2-1 ID U U i) 3* 35 31 M S-8

-120- IV.17

POLARIZATION IN PRODUCTION REACTIONS ON DEUTERONS

K. Bongardt and H. Pilkuhn University of Karlsruhe,GFR

The polarization of baryons in two-body meson-baryon collisions such as 7C~p-»K°A vanishes in the forward direction. When the target nucleon is bound in a deuteron, this need no longer be the case. The effect comes from double collisions and is therefore most pronounced in events with relatively large momentum p* of the spectator nucleon. At energies where the matrix elements for double collisions can be calculated from Glauber theory, the ef- feet can be used to measure Re f (q')g(q') (weighted over intermediate momentum transfers q1), where g and f are the spin-flip and non-flip amplitudes of^-production. If p is not too large, one can neglect the spin-flip amplitude in the elastic scattering of T or K on the spectator and keep only the interference between single- and double scattering: £ 5) 4 j> c«J2 A I.a«o 71 k where 12 is the solid angle between fc and K, f is the sum of >z - spectator and K°-spectator non-flip amplitudes, k is the incident momentum, and

For larger p, both <$>$ (f>) 'PfifP ~y') and the square of the double scattering enter, p must not be too small in order to suppress final-state interactions between the two baryons.

•121- IV.18

A COUNTER EXPERIMENT ON THE PRODUCTION OF ^C BY K" IN FLIGHT

G.C. Bonazzola, T. Bressani, R, Cester, E. Chiavassa, G. Dellacasa, A. Fainberg, D. Freschi, N. Mirfahkrai, A. Musso and G. Rinaudo

Istituto di Fisica Superiore dell'Universita - I 10125 Torino (it) and Istituto Nazionale di Fisica Nucleare, Sezione di Torino

We report the first results concerning the reaction :

K" + 12C -» A2C + it" induced by K~ of 390 MeV/c and n~ detected at forward angles. The interest in studying these reactions was stimulated by the theoretical ^' on the possible existence of the "strangeness analogul e states", i.e. hypernuclear states which could be imagined as arising from the replacement of a nucleon with a A-hyperon, in the same orbital and spin state of the shell model. It was also emphasized 2»5) that these states would be preferentially excited in reactions induced by K~ in flight rather than at rest, due to the lower momentum transfer.

In our experiment the determination of the hypernuclear levels is obtained from direct kinematical analysis (missing mass). We use a double magnetic spectrometer consisting of a single magnet, with the target in the middle. The trajectories of the incident and outgoing particles were measured by means of six pairs of multiwire proportional counters placed behind, inside and after the magnet* The instrumental total energy resolution for the hypernuclear levels is 5 MeV. The trigger and the rejection of it" contaminating the beam (100 u" for 1 K") was performed by a set of fierenkov and dE/dx scintillation counters. The experiment was controlled by a PDP-ll/20 on-line computer and the data written on magnetic tape for further off-line analysis and reconstruction. 12 The first nuclide we studied was C, because the use of a plastic scintillator as target will hopefully allow a separation between mesonic and on-mesonic decays of the hypernuclear levels. In the energy spectrum of °C two peaks are seen. The first corresponds to the production of ^C in the ground state, the second one to an excited state at ~ 10 MeY, in accordance with the theoretical predictions*) about the location of the strangeness analogue state. The differential cross section for the production of this last state is of the order of 1 mb/sr.

1) A.K. Kerman and H.J. Lipkin, Ann. Phys. (N.Y.) 66 (1971), 738

2) H. Feshbach and A.K. Kerman, in Preludes in Theor. Fhys. (North- Holland, 1966), 260

3) R.H. Dalitz, Proc. Int. Conf. on Hyp. Phys., Argonne (1969), 708.

-122- IV.19 SPECTROSCOPY OF HYPERNUCLEI VIA THE AZ (K",TT ) jfz -REACTION. M.A.Faessler, G.Heinzelmann, K.Kilian, U.Lynen, H.Piekarz, J.Piekarz, B.Pietrzyk, B.Povh, H.G.Ritter, B.Schuerlein, H.W.Siebert, V.Soergel, A.Wagner and A.H.Walenta. Max-Planck-lnstitut f. Kernphysik and 1. Phys. Institut, Heidelberg. Inst. of Nuclear Research and Inst. of Expf .~imental Physics, Warsaw.

In a recent experiment*^ y -transitions of light hypernuclei have been observed. One of the major difficulties of this experiment was the assignment of the observed hypernuclear ^-transition to a specific hypernucleus. A possible way to overcome this difficulty and to study also heavy hypernuclei is the spectroscopy of pions emitted from the A - - \ A two-body production process Z (K , "IT ) ^ Z. A further advantage of this method is that all excited levels - particle stable and particle unstable - including the ground state can be investigated. The experiment has been performed at the low energetic K-beam of the CERN Proton Synchrotron. The K-mesons were stopped in an active target consisting of six plastic scintillators, each of 1 cm thickness. This target was used in order to discriminate against *~ and T emitted from K~ decaying in flight. The energy of the outgoing particles was measured with a magnetic spectrometer, the overall energy resolution being^rf MeV/c at 27o MeV/c. At the end of the spectrometer *Twere discriminated from iT by use of a range telescope. The continuous part of the spectrum can mainly be explained by the production of free A and Z hyperons. Two peaks are observed at h 273.3 * 1 MeV/c and 261 ± 1 MeV/c with production rates of (4i2)-1o and (6t3)-1o~ per stopped K-meson, corresponding to the ground state

and an excited state of A C. The binding energy of the ^in these two states is 11*1 MeV and 0^1 MeV, respectively. The excited state had already been observed in emulsion 2) TT-SPECTRUM experiments. Its configuration is 1000 8MO8 K"stopped most probably that of an excited 12 „ in A -particle coupled to a C-core 261 MeV/c in the ground state. C 500 V* A 1) A.Bamberger et al. >*, 273 Mev/c Phys.Lett. ]& B (1971) 2) G.Bohm et al. Nucl. Phys. Bk? (1972) 36 225 250 275

-123- IV.20

Pion Photoproduction and > vs. T< Analog States in N>Z Nuclei Anton Nagl and H. Uberall* Catholic University of America, Washington, D.C. 20017 Giant resonance levels in N>Z nuclei with ground state isospin T are split

into T^ = T + 1 and T< = T components, which are sometimes seen as separate peaks in photonuclear experiments . However, photonuclear reactions cannot unambiguously identify the T> character of a given peak. Charged pion photoproduction may achisve such an identification (at least for the spin-flip levels), through a comparison of pion (or particle) spectra after TT , TT photoproduction: T^, levels are excited in both TT— production, and T^, levels in TT" production only. Moreover, this process may be more reliably calculated than the nucleon reactions1 where the method has been first mentioned. We have calculated the differential cross sections of TT— photoproduction on a 13C target with excitation of 13B (lsN) analog levels, using the wave functions of a 2 particle - 1 hole shell model . Fig. 1 shows the calculated level scheme in 13B, 13C and 13N and Fig. 2 the spectra at 3O0 of TT- produced by 200 MeV photons. The levels present in the TT spectrum but absent in the TT spectrum are T< = ~ . 1M. Obu and T. Terasawa, Prog. Theor. Phys. h±, 1231 (1970).

*Also at U.S. Naval Research Laboratory, Washington, D.C. 20375 tSupported in part by the National Science Foundation

K-2OO M»V d

il 1 - 111 IT T =' = : = 11 I T ! BrSggWa 1 i " .* 20 i 40 so T, (M.V)- ss.*ss___.-rs_. 533S

2mrr 20 «MQ» " "•' Ij i - n i n ii i 1

/ 2.221 ft iL-nJll i 30 40 50

Fig. 1 Fig. 2

-124- IV.2I Pion Photoproduction and Spin Flip States in Self-Conjugate Nuclei * t # # B.A. Lamers , G.B. Lamers , C.W. Lucas ^, A. Nagl . H. liberal l5# and C. Werntz* Catholic University of America, Washington, D.C. 20017 Differential cross sections have been calculated for n (rr ) photoproduction on a 1£C target with excitation of 12B(12N) analog states, and on a 160 targeL with 1SN(16F) analogs. Charged pion photoproduction excites predominantly the spin flip states, so that the corresponding experiments may determine the degree of spin flip strength of a given T = 1 level. The transition matrix elements were obtained on the basis of the generalized Helm model, whose parameters were determined by fitting the experimental form factors for electroexcitation of the levels of 12C and 160 obtained at Sendai. Figure 1 present angular distributions of positive pions produced by 200 MeV photons on a XsC target with the excitation of (a) magnetic and (b) electric levels. The cross sections are dominated by the spin flip Ml and E2 states (No, 1,2) and especially by the spin-flip El giant resonance No. 16 (or integrated over wider excitation energy intervals: Nos. 18 or 19), and by its M2 counterpart (No. 10).

•Computer Sciences Corp., Silver Spring, Md. 20910 tHarry Diamond Laboratories - EMEL, Woodbridge, Va. 20^38 %Also at U.S. Naval Research Laboratory, Washington, D.C. 20375 ^Supported by Office of Naval Research and National Science Foundation

10"'

10-

iff* id* 60* ECf 60*

Fig. la Fig. lb

-125- IV. 22 COHERENT PHQTOPRODUCTION OF Tl+ ON He D. Bachelier, M. Bernas, J. L. Boyard, J. C. Jourdain, C. Lazard, P. Radvanyi, Institut de Physique Nucleaire, BP. 1, 91406 Orsay (France) and Z. Marie", Institute of Physics, Beograd (Yugoslavia). ^ 3 The coherent photoproduction reaction He(v,ll+) H has been studied in a coincidence experiment performed at the Saclay electron accelerator"/. Mea- surements have been performed at fixed values of the transferred four-momentum q2. From Ey = 228 to 453 MeV, and at a fixed C. M. angle from q » 3.1 to 13 fin"2. The first resonance appears to be shifted towards lower energies (see Figure 1) as compared with the predictions of the simplest model ; this shift seems to become smaller at smaller q2. The minimum of the charge form factor of 3He observed near 11. 6 fm~2 does not appear here (see Figure 2). The shift of the 3-3 resonance might be explained in the frame of impulse approximation '2', by two effects which add-up together in the case of He : (i) In coherent photoproduction, the central value of the proton momentum involved inside the ^He nucleus is not zero, but - q/3 (inthe lab. system) ; for this particular value the elementary process is also on the energy-shell ; this accounts for about half the observed shift ; a similar result has been obtained by D. Ezra in a calculation performed in the Breit frame (3\ (ii) The other half of the shift might be explained by the effect of the S1 and D state components which modify the relative weight of the spin-flip and non-spin-flip terms of the elementary process (see calculated curves on Figure 1). The qualitative behaviour of the cross section versus q can be understood by an estimation of the pion rescattering terms (2) (on Figure 2 : . without rescattering, and with rescattering) : the impulse amplitude seems to dominate until about 6 fm"2, whereas rescattering predominates at higher values of q2. (1). D. Bachelier, M. Bernas, J. L. Boyard, J. C. Jourdain and P, Radvanyi Phys. Letters, B 44 (1973) 44. (2) C. Lazard and Z. Marie1, Nuovo Cimento A (1973) to be published. (3) D. Ezra, to be published.

200 250 300 350 Ey MeV

Figure 1 Figure 2

-126- IV. 23

PION PHOTOPRODUCTION ON 3He by G. Goggi, G.C. Mantovani, A. Piazzoli and D. Scannicchio The results of an experiment of pion photoproduction on He carried out with a diffusion chamber at the Frascati Electronsynchrotron(E 800 MeV) are presented and compared with some available theoretical prelictions based on the impulse approximation (I.A.) model. Cross-sections per equivalent quantum are given in Tab. 1 for various processes. The comparisons with theory for IT photoproduction, both elastic and inelastic, show a satisfactory agreement with the I.A. assumptions (Figs. 1 and 2). The double photoproduction processes are characterized by cross-section values much higher than one would expect from free nucleon cross-sections. In the framework of the I.A. this would require the contribution of large positive interference terms among the production amplitudes on the single nucleons. Yet, some features observed in the angular and invariant mass distributions and

TABLE 1 Th. Th. Y(3He,T)ir+ 7O±1O - 69 64+11 3 3 Y 332±35 312 Y( He, He)*"V 249+31 3 + 0 Y(3He,3He)Tr° 770±200 Y( He,T)ir ir 188±48

400,

140 220 soo 5 Hevi y f He -*1T* so i 1 20 A i 40 | f s V 40 80 120 460 4.0 4.4 4.4 1.6 4.8 ft* (Tf*p)

-127- #••

CAPTURE AND ABSORPTION V.I

Gross Theory of Muon Capture Y. Kohyama & A. Fujii Department of Physics, Sophia University, Tokyo 102, Japan

I) The gross theory of beta decay is extended to the muon capture reaction. The single particle nuclear matrix elements associated to the transition M> -* \f> with neutrino momentum q are reduced to the follwing 5 types after due approximations in gross treatment, „ . 7 r fl allowed transition: J -- h t%«i, J r._ a>/c tf) , Ji.»h( t first forbidden transition: Jr. tr J, c?yj, fc. c®"r) j, <•%• •> ne where v. transforms the proton into neutron and j7(%r) is * spherical Bessel function of order 1. R }i (?y> inside the nuclear radius is expanded in Chebyshev's polynomial and well approximated by a power series in (.r/gy2- . The strength functions become the linear combi- nation of the form

The functional form of {w..-.is is assumed as the superposition of 2 Gaussian or modified Lorentzian functions, whose peak and width are chosen to be consistent with the sum rules and gross theory parameters of beta decay.

Some illustrative computation is summarized in the following table. The capture rate is given in an unit of 10* sec . The first line is for the Gaussian and the second for the modified Lorentzian functions. The nuclear radius is taken as R -

Nucleus Allowed First forbidden Total transition transition 0.28 1.55 1.65 SCa 0.18 1.42 1.60 2.55 0.62 2.15 2.77 4.41 ill Fe 0.43 2.09 2.52 1.37 5.85 5.22 5.74 0.81 3.74 4. 55 Reference 1) K. Takahashi, Prog. Theoret» Phys. 45 (197D, 1466: K. Takahashi, H. Takeda and M. Yamada, Prog. Theoret. Phys. 46 (197D, 1637.

131- V.2 DYNAMICS IN TOTAL MUON CAPTURE MATRIX ELEMENTS. Renzo Leonardi Istituto di Fisica dell'University and I.N.F.N., Bologna, Italy. Some dynamical properties of the unretarded dipole muon-capture matrix elements Mj[ y p are examined. A more complete discussion on the possibility of utilize commutators algebra in studing the miiLtipole components of I| y p, their relative importance as a function of the SU(U) symmetry breaking and the isospin properties of the target will be published elsewhere^D. Here we reanalize the widely accepted statment that the perturbative calculations of M| y p fail both in predicting the total dipole strength and the ratio M^/My of the doubly closed shell nuclei. Very accurate perturbative calculations'^' give as a result MJ^ =1.12 M^, In particular the spin-orbit interaction, so active in spreading the pure p-h configurations over a range of 10 MeV, play no role in modifing MA/My. This result, combined with the photoabsorption data as input for MS;, makes worse the agreement with experiments. With commutator algebra and sum rules it has been shown^) that 2 Aw MA/% = 1 - and Aw = 2 _,_, . A v _ Bartlett Em-W where E - 90-100 MeV, to is the peak energy for the photoabsorption and Aw is the separation between the S=0 and S=l peaks. Experimental data on partial muon capture (and electron scattering) support the idea that the spin flip excitation S=l has a mean energy higher than the S=0 excitation^) and from the previous formula this would imply M^

-132- V.3 TOTAL MUON CAPTURE RATES MI THE AVERAGE NEUTRINO ENERGY

J. Bernabeu, CERN - Geneva F. Cannata, Istituto di Fisica dell'Universita, Bologna

Total muon capture rates on nuclei are usually analyzed, within the general framework of a universal theory of weak interactions, by using closure approximation. The rate can then be written in terms of expected values of two-body operators on the initial state. However, the uncertainty on the average neutrino energy if is so important that conclusions for the adequacy of the nuclear model used cannot be reached. In order to avoid this difficulty, a first order expansion of the partial capture rates around y is proposed. The sum over final states gives two corrective terms besides the usual one. One of them is related to the iJ slope of the main term. The other one is a first order energy weighted sum rule, which is related to the expected value of a double commutator between the effective transition operator and the nuclear Hamiltonian.

For nuclei in which spin-dependent forces can be ignored and only the Wigner potential is retained, a generalized TEK sum rule is used. Application to ^B.e, 4He and 6Li, for which the L-S coupling is • rather good, is given and good agreement with experiment is found, quite independent of the specific value of »» within a large range of plausible values.

The effects of central, spin-orbit and tensor potentials are present in the main term through the complications induced in the ground state wave function, such as configuration mixing. In the framework of SU(4) symmetry higher supermultiplets are admixed to the supermultiplet to which the ground state belongs, and allowed axial transitions are present. Of completely different origin are the allowed transitions which arise in non-scalar supermultiplets, like ^Li, even neglecting SU(4) impurities. The modifications to the sum rule due to the various potentials are worked out, and it is shown that in the short range limit, the expected value of the commutator is related to the effective matrix elements of the potentials. Application to ^C is made, using the effective interactions in the 1p shell.

-133- V.4 Atomic Collision Quenching of the Metastable 2S State of Muonic Hydrogen and Muonic Helium V.W. Hughes, R.O. Mueller, H. Rosenthal1" Physics Department, Yale University, New Haven, Connecticut, USA C.S. Wu Physics Department, Columbia University, New York, New York, USA The possibility of measuring the fine structure and Lamb shift of the n=2 state of muonic hydrogen [y.-p] requires the metasta- bility of the 2S state, and hence crucially depends upon how rapidly atomic and molecular collision quenching processes deplete the p.~p(2S) atoms after they are formed by stopping negative tnuons in hydrogen (H2) gas. Such precision measurements would be of great interest for the study of proton structure and as a sensitive test of quantum electrodynamics. The 2P states of (j."p lie about 0.2 eV above the 2S state and foi relative kinetic energies of p,~p and H(or Hp) above this threshold of 0.2 eV the principal quenching process will be inelastic excitation to the 2P states. Calculations2 carried out in the impact parameter straight line approximation yield a cross section of about 10"ie> cm2 at 1 eV, which is extremely large and hence unfavorable for the fine structure measurement. However, for relative kinetic energies below threshold, this inelastic process is energetically forbidden, and the dominant quenching mechanism will be radiation to the IS state during a close encount- er of |i~p(2S) and a IU molecule when the Stark mixing of the 2S and 2P states is large. We have calculated the quenching cross section utilizing an interatomic potential energy between p.~p and H, a quantum mechanical partial wave treatment of the relative motion, and an adiabatic approximation whereby the inelastic channels are completely neglected and the scattering corresponds essentially to elastic scattering by an optical potential, the imaginary part of which accounts for the radiative decay process. The quenching crosSoSection for fx~P is of the order of 1B 2 (YTC) x 10-16 cra2 _ io~ cm , (y=radiative decay rate for 2P+1S, TG= collision time), and for relative kinetic energies below 0.2 ev detailed theoretical results will be presented. Due to the complexity of the formation process3 of u~p(2S), it has not been possible to predict quantitatively the fraction of |j.~p(2S) atoms with kinetic energy below 0.2 eV. An experiment to measure delayed 2P-*1S 1.9 keV X-rays as a function of H2 gas pressure would provide information about the number of p.-p(2S) atoms formed and about their quenching cross section. For (p.~a)+ formed in the 2S state where the kinetic energies are expected to be below the 2P-2S threshold energy of 1.6 eV, the quenching cross section was calculated to be about 0.25x10-20 cm^.j. This theoretical result is consistent with experimental observations. tDeceased. V.W. Hughes, H. Rosenthal, and C.S. Wu, Bull. Am. Phys. Soc. 16, 617 (1971). 2G. Kodosky and M. Leon, II Nuovo Cimento lB,"~5l (1971). 3A.S. Wightman, Ph.D. thesis, Princeton University, 1949, Phys. Rev. 77, 521,, (1950); M. Leon and H.A. Bethe, Phys. Rev. 127, 636 (1952). 4A. Placci, et al., II Nuovo Cimento 1A, 445 (19TT).

-134- V.5 Formation and Hyperfine Structure of Muonic Helium (ap.~e~) M. Camani SIN, CH 5234 Villigen, Switzerland K.N. Huang, V.W. Hughes, and M.L. Lewis Physics Department, Yale University, New Haven, Connecticut, USA

It may be possible to form the muonic helium atom ap.~e~ and to measure1 its hyperfine structure interval in the ground state. In helium gas a stopping \i~ will be captured and cascade to the ground state of the ion (a|x")+ with both electrons being lost by Auger processes.2'3 p>or thermal (

•""V.W. Hughes and S. Penman, Bull. Am. Phys. Soc. 4, 80 (1959). 2V.W. Hughes, et al., Bull. Am. Phys. Soc. J5, 75 (I960). ^D.C. Buckle, J.R. Kane, R.T. Siegel, and R.J. Wetmore, Phys. Rev. Letters 20, 705 (1968). \. Camani and V.W. Hughes, Bull. Am. Phys. Soc. 17, 454 (1972). %.H. Fleischmann and R.A. Young, Phys. Rev. Letters 19, 941 (1967). . ~

-135- V.6

FORMATION OF PIONIC AMD MUONIC ATOMS IN LIQUID HELIUM AMD HYDROGEN

*) **) +) *) G. Backenstoss , J. Egger , T. von Egidy , R. Hagelberg , C.J. Herrlander J, H. Koch ', H.P. Povel ', A. Schwitter , *) and L. Tauscher ,

CERN, Geneva, Switzerland University of Karlsruhe, Germany Technical University of Munich, Germany Research Institute of Physics, Stockholm, Sweden

Energies and intensities of pionic and muonic X-rays in liquid ''He have been measured with a Si(Li) detector. The energy shift due to strong interaction effects of the pionic Is level in ''He was determined to be -75.0 ±2.0 eV. The natural line width of this level is 45.2 ± 3.0 eV. These values are not in agreement with optical potential calculations. Cascade calculations, including Stark mixing and external Auger effect, have been performed to reproduce the yields of the transitions.

X-rays from muonic and pionic transitions in liquid hydrogen have been searched for with Si(Li) and Ge(Li) detectors. An 8.1 keV transition, which is delayed by about 1 ysec, was found in the muon run. This X-ray corresponds either to the muonic-2-1 transition in 3He after the fusion pud -*• y3He, or to the muonic transition of the molecule state pyd to the y3He ground state. The 5.49 MeV gamma-ray from the fusion of p + d -*• 3He was observed.

*) Visitor from Karlsruhe. **) Visitor from ETH-SIN, Zurich, Switzerland. +) Visitor from Munich. ++) Visitor from Stockholm.

-136- V.7

MUON CAPTURE BY 14N NUCLEI

H.B.. Kissener and A. Asvad Zentralinstitut far Kernforschung, Bereioh 2, Rossendorf bei Dresden, DDR

R.A. Eramzhian and H.U. Jager Joint Institute for Nuclear Research, Dubna, USSR

A recent analysis of the excitation and decay of the states of giant 14 resonance of photo absorption in K has shown that the theory, that takes into acoount all 1 "fcc») excitations, reproduces well the available experimental data '. Using the same approach, the excitation and decay of the giant resonance in muon capture by N is considered in this paper. A characteristic feature of this process is the large yield of two neutrons ; the states of the giant resonance are strongly coupled with the excited levels of C which are above the neutron threshold. The most populated one of these levels is the 5/2"", 7.55 MeV state (24 j6 of the total capture rate). The study of the neutron spectrum in coincidence with the secondary neutrons from the decay of this level provides information on the structure of the high-energy part of the giant resonance. This spectrum has resonance character and is shown in the figure. The 4 -1 muon capture rate is calculated to be 8x10 sec . The next strongly populated levels are the 3/2~, 3.68 MeV (by 21 $) and the g.s. (by 18 #). Only 1.5 f> of the transition strength goes to excited levels of 0 above the oL threshold. From this one concludes that the observed high yield of charged particles in nuclear emulsion experiments is due to the 12 14 muon capture by C and not by H. 1) R.A. Eramzhian, H.U. Jager and H.R. Eissener, Dubna Preprint 24-6895, (MeV-secr1! u 13 N(jufn) v.

3000 5/2~, 7.55 MeV

0 10 En (MeV) _ _i—i—I H—i~i. —i—

•137- V.8

Capture Rates of Negative Muons in 0 Leading to Bound States in

M. Eckhause, F. R. Kane, G. H. Miller, B. L. Roberts, and R. E. Welsh, College of William and Mary

Negative muons from the muon channel of the Space Radiation Effects Laboratory synchrocyclotron were brought to rest in an oxygen (H2O) target. From measurements of the intensities and energies of the nuclear y-rays emitted following capture of the muons, we obtain the following capture rates to bound states in 16

16N State Rate (103 sec"1)

l" 1.31 ± 0.11

0" 1.56 + 0.18

2~ 8. 0 + 1. 2

3~ < 0.09

These rates can be compared to the experimental results obtained by other groups as well as to various nuclear model calculations which depend on . the value of the induced pseudoscalar coupling constant in muon capture ,

*Work supported in part by the National Aeronautics and Space Administration and the National Science Foundation.

tPresent address: Lawrence Livermore Laboratory, Livermore, California 94550.

1) J.P. Deutsch, et jal^., Physics Letters 29B, 66 (1969) and references cited therein and T. W. Donnelly and J. D. Walecka, Physics Letters 41B, 275 (1972).

-138- V.9

Muonic X-Rays in Lead Isotopes.

D. Kessler, H. Mes, and A.C. Thompson (Carleton University, Ottawa), H.L. Anderson and M.S. Dixit (University of Chicago), C.K. Hargrove and R.J. McKee (National Research Council of Canada, Ottawa).

High resolution spectra of muonic lead isotopes 204, 206, 207 and 208, previously published in preliminary form1 were re-analyzed, using an improved calculation of the higher order vacuum polarization term for all energy levels.2 The conclusions reached previously are essentially unchanged except for the anomalous 3d-splitting. (The nature of this anomaly is that the experimental fine-structure splitting is found to be larger than the calculated value by about 250 eV or 8 standard deviations in all four isotopes of lead). Whereas previously it was thought that only one of the levels was shifted with respect to its predicted position, it results from the new calculation that both levels are displaced in opposite direction, so as to preserve the center of gravity of the doublet. Other highlights of this experiment are : 1. Observation of the natural line width. 2. The charge distribution of the lead isotopes can be described with the help of a two-parameter Fermi distribution. There is no evidence for a central depression. The nuclear density increases regularly in going from Pb-204 to Pb-208, while the skin thickness remains essentially unchanged. 3. The weak transitions involving the 2s-levels were measured in all four isotopes. This information is used to determine the nuclear polarization in the Is-level. We find values ranging from -7.1+2.3 to -10.0+0.9 keV which are slightly higher, but not inconsistent with,the best theoretical prediction of -6.8 (±2.0) keV. This analysis is, however, model dependent and may be subject to revision.

1 D. Kessler, Invited paper presented at the Muon Physics Conference, Fort Collins, Colorado, September 6-10, 1971. 2 M.K. Sundaresan and P.J.S. Watson, Phys. Rev. Letters 29_, 15 (1972) and unpublished results.

-139- V.10 NUCLEAR EXCITATION AND ISOMER SHIFTS IN MUO1MIC ATOMS

H. K. Walter 5 H. Backe 1 R. Engfer 5 E. Kankeleit t) **) R. Michaelsen H. Schneuwly , W.U. Schroder and A.Zehnder

CERN, Geneva, Switzerland

Excitation probabilities and isomer shifts for nuclear rotational levels, quadrupole and octupole vibrational levels, and single- particle levels in muonic atoms have been measured. It turns out that the effect limiting the accuracy of the extracted isomer shifts is the correction for the magnetic hyperfine splitting of the nuclear levels. The data for 153Eu are used in comparison with isomer shifts from the Mossbauer technique to evaluate electron density differences in rare earth compounds. A nearly model independent interpretation of the isomer shifts in terms of the 2. and 3. moment of the charge distribution differences is given, which facilitates the comparison with results from other techniques or from calculations. The study of isomer shifts is a very powerful, in seme cases even unique means of distinguishing between models for excited nuclear levels.

Fig. 1 Muonic isomer shifts (with the

CERN assumption, that •xp. Columb.o AR, AR, Sp«lh th»Oty where

for first excited states.

-•-I

•) Visitor from SIN, Zurich, Switzerland **) Visitor from Institut fur Technische Kernphysik, T.H. Darm- stadt, Germany ***) Visitor from Hahn-Meitner Institut fur Kernforschung, Berlin, Germany t) Visitor from Institut de Physique de l'Universite Fribourg, Switzerland

-140- v.n OP THE STRUCTURE OP K DEPENDENCE OP MESIC X-RAY SPECTRA UPON NEGATIVE MUON DEPOLARIZATION R.Arlt,V.S.Evseev,G.H.Orthlepp,v.s.Roganov,B.M.Sabirov,H.Haupt Joint Institute for Nuclear Research,Dubna,USSR ABSTRACT The depolarization of negative muons undergone various ways in the mesic atom cascade have been measured for the first time. In order to detect the K-series of mesic X-ray radiation (in the coincidences with pulses of >•-stopped in the target > a Ge-spectrometer was used; electrons from muon decay were detected by a hodoscope of some telescopes consisting of scintillation counters. Depolarization was measured by the muon spin precession method in a weak transversal magnetic field when muons were stopped in graphite and paraphine for four lines of the Ca mesic X-ray spectrum. Residual polarization was observed to increase with increasing transition energy for each of the targets. The comparison of experimental data with the depolarization theory in the mesic atom cascade allows one to draw a conclusion on the primary population of mesic atom states. Residual polarization turned out to be twice smaller in paraphine for any of the K-series lines than in graphite. This corresponds to the results of measurements in detecting only mu-decay electrons. This fact proves the hypothesis on the presence of the depolarization mechanism taking place after the end of the mesic atom cascade and depending on the properties of the medium surrounding the mesic atom.

-141- V.12 j .NEUTRON SPECTRA FROM THE NEGATIVE MUON ABSORPTION BY HEAVY • MJCLEI AND THE RESONANCE MODEL OF NUCLEAR REACTIONS « V.S.Evseev,T*N.Mamedov °4 Joint Institute for Nuclear Research,Dubna,USSR '1 ABSTRACT ;j

It is considered at present that according to the resonance r, model the absorption of negative muons for all nuclei occurs -,\ through the production of few-particles quasi-stationary states \ of the intermediate nucleus. The fact that the energy spectra ;* of neutrons from mu-capture in heavy nuclei are of "evaporatio- nal" character allowed one to assume the mechanisa of fast ener- '~\ gy dissipation in these states over the composite nuclear sta- '{ tes. :; We have been the first to measure very precisely neutron ~j spectra from mu-capture in some heavy elements remoted from % double magic region in the lead range. The calculated "tempera- 4 tares" of the final nucleus and the parameter of nuclear level -% density for mu-capture coincide with those for the reactions de- €$, liberately described by the statistical model only in the lead ;;| range and remain practically constant for all heavy and middle ;

~~-142- V.13~~

~~NEUTRON SPECTRA FOLLOWING MUONUCLEAR ABSORPTION J. JOSEPH Institut de Physique Nucleaire, Lyon, France B. GOULARD Laboratoire de Physique Nucleaire, Universite de Montreal, Montreal, Canada.~~

~~We wish to report calculations on spectra of neutrons following muon absorption by Ol(> and Ca40, i.e.~~

~~16 _N16 *.„-.- 15 * 1 3. + o (0,1,2 ) + V 2 40 40* - - - +' V Ca -K (0,1,2 ) + i/-K39 * i 3. ( 2 ' 2 '~~

This type of reactions is important to characterise the intermediate states excited in N*" and K4^ in order to demonstrate that they are the analog counterparts of the giant dipole resonance of O* and Ca [L.L. Foldy and J.D. Walecka, Nuovo Cimento 34, 1026, (1964)].

Our approach involves the factorization of some channels whenever they appear in the continuum-continuum matrix elements and only in those cases. This allows us to keep the basic simplicity of the method [V.V. Balashov and E.A. Eramzhyam Atom. En. Rev. 5, (1967), 3] and to keep a good control over its convergence [N. Van Giai and C. Marty, Nucl. Phys. A150 (1970), 593].

In a first stage the method has been tested in the case of photonuclear absorption by O and Ca^" against "exact" coupled channel solutions -.-•i [M. Marangoni and A.M. Saruis, Nucl. Phys. A132 (1969), 649]. Then, it has been applied to muon absorption by those two nuclei. To separate out the effects of the continuum, calculations based on a Tamm-Dancoff appro-

~~.•-' I'' ximation are presented and shown together with our improved factorization method.~~

Although this approach reproduces the main features of the currently available data, as more phenomenological calculations do [For example, L. Hill and H. ifberall, Nucl. Phys. A190, (1972), 341], its real interest is due to appear with the forthcoming meson factories, because of its ability to incorporate more complicated structure and reaction aspects of nuclear theory.

~~-143- V.14~~

~~INVESTIGATION OF MJ~ MESON CAPTURE BY I2GHT NUCLEI~~

~~Yu.A.Batusov,S.A.Bunyatov,L.Vizireva,G.R.Gulkaniant F.Mirsalikova,V.ll#Sidorov,Ch.Chernev Joint Institute for Nuclear Re search,Dubna,USSR~~

ABSTRACT Negative muon capture in photoemulsion by C, N, 0 nuclei has been studied. The relative probabilities of capture with charged particle emission have been determined and their spectra have been measured. The schemes of capture on C have be been identified. The relative probabilities of the vC^G —*• QLi-pEe + ntS> and ^ C —^ 2a + T+zwreactions have been found. The energy and angular distributions of charged secondary particles have been obtained*

~~'"•§~~

~~-144- 7* J V.15~~

3 9 3 Pion-Nucleus Total Cross-Sections on He and Be , and Pionic X-Rays in He . C. S. Hsieh, J. R. Kane, B. Sapp, C. B. Spence, and R. J. Wetmore; College of William and Mary. J. B. Carroll, Lawrence Berkeley Laboratory. (Presented "by R. T. Siegel.) + 30 12 The total cross-sections for TT on He , Be , and C have been measured at several energies spanning the (3,3) resonance. A standard technique involving a transmission counter and four annular counters was used. The beam definition was 2.5 cm at the target, with energy determined by range measurement and beam composition by Cerenkov counter and time-of- flight techniques. •:< 3 j-i The pionie x-ray energies and widths in He are of special interest * because of the proton excess. An experiment was performed to observe the ' pionic (and muonic) x-rays from beams stopping in a liquid He scintillation 'i counter-target by means of a Si(Li) detector. At the resolution of this ); experiment pionic energy shifts are observable, while widths are consistent ,;; with experimental resolution. j Results for both total cross-section and x-ray measurements will 3 "be presented.

~~f'-'i~~

-145- V.16 ANOMALIES IN THE STRONG INTERACTION SHIFTS AND WIDTH OF THE Is LEVEL IN PIONIC 6Li, 7Li, AND 9Be On *) .. **) ***) *) G. Backenstoss , I. Bergstrom , J. Egger , R. Hagelberg , C.J. Herrlander**) H. Koch , H.P. Povel '.R.H. Price^, A. Schwitter and L. Tauscher , Rutheri CERN, Geneva, Switzerland. Institut fur Experimentelle Kernphysik der Universitat und des Kernforschungzentrums, Karlsruhe, Germany. Research Institut for Physics, Stockholm, Sweden.

Godfrey and \ Using high-resolution Si and Ge X-ray detectors the strong interaction shifts 6 7 9 mesons were £ of the Is level in pionic Li, Li, and Be have been determined with high of 55jin and i accuracy. The experimental values of the Is level shifts are: times that oi coupling to i -(330 ± 3) eV, -(576 ± 4) eV, and -(1620 ± 7) eV, respectively. We have obsei Using a parameter set for the optical potential obtained by a least square fit ', this case th< the corresponding theoretical shifts are: For a 5gm/cm' (4 -*• 3) pioni -456 eV, -679 eV, and -1816 eV, respectively. thickness of (b) and (c)) The experimental and theoretical Is level widths exhibit similar discrepancies, reduced in a] but here, the theoretical values are significantly lower than the experimental indicating tl ones. The discrepancies for the shifts and the widths cannot be removed simul- varies as th< taneously by changes of the different parameters. With the beai with a neutr< The precision of the experimental data makes it possible to study nuclear struc- 6 Diagram (e) i ture effects with high accuracy. The Li data reveal a drastic change in the a copper tarj systematic for light elements with T = 0, which is also confirmed in later z in the regioi experiments on ''He '. with target 1 KeV line is The results show that the optical potential for the ir -nuclear interaction as of the type: used at present, neglecting I/A terms, is not sufficient for light nuclei. Furthermore, the results show a very pronounced isospin dependence. hadron

1) L. Tauscher, Proc. Int. Seminar on ir-Meson Nucleus Interactions, The magnitud Strasbourg, 1971 (CNRS, Strasbourg, 1971), p. 45. neutron sour 2) G. Backenstoss et al., contribution to this conference. interpretati We would con explanation *) Visitor at CERN from Karlsruhe. and Wiegand, **) Visitor at CERN from Stockholm. from studies with caution ***) Visitor at CERN from ETH-SIN, Zurich. process is e t) Present address: TRIUMF, Univ. of Victoria, Victoria BC, Canada.

~~G.L. Go LBL 776~~

~~-146- V.17~~

~~On the origin of the 126 KeV transition previously observed when K~ mesons stop in $->Mn.~~

~~R.A.J. Riddle, G.T.A. Squier, R.E. Welsh Rutherford High Energy Laboratory, Chilton.Didcot, Berkshire, U.K. \ N. Berovic, G.J.,Pyle Physics Department, University of Birmingham, U.K.~~

Godfrey and Wiegand (1) recently observed a strong line at 126 KeV when K~ mesons were stopped in 55Mn. This is the energy of the first excited state of 55jm and the 9 -* 6 kaonic transition; however the intensity is about 20 times that of other observed An = -3 transitions. They propose a resonance coupling to explain this.

We have observed y and X-ray spectra when pions are stopped in Mn. In this case there is no pionic X-ray transition of energy close to the y-ray. For a 5gm/cm2 target the intensity of the 126 KeV line is comparable to the (4 -> 3) pionic atom transition at 113 KeV (diagram (a)). However when the thickness of the target is reduced (diagrams (b) and (c)), the ratio of these two lines is (o) reduced in approximately the same proportion, indicating that the intensity of the y ray varies as the square of -the target thickness. With the beam off, the target was irradiated with a neutron source (diagram (d)). Diagram (e) shows the spectrum obtained with a copper target, showing no spurious effects in the region of interest. The variation with target thickness suggests that the 126 KeV line is the result of a two stage process of the type: _

IT + Mn -*• X + hadrons A (O hadrons + Mn •*• hadrons + ^Ha •*y(126KeV) The magnitude of the peak observed with the neutron source is consistent with such an interpretation. (a) We would conclude that this is a likely explanation of the observations of Godfrey and Wiegand, and remark that y-ray data from studies such as these should be treated with caution until the direct nature of the process is established.

~~G.L. Godfrey and C.E. Wiegand J LBL 776 (1972) its Enerqy(kev) 15 t On~~

~~-147- V.18 STUDY OF E-HYPERONIC ATOMS~~

~~G. Backenstoss, A. Bamberger, I. Bergstrom, T. Bunaciu, J. Egger, S. Hultberg, H. Koch, U. Lynen, H.G. Ritter, A. Schwitter, and L. Tauscher~~

CERN, Geneva, Switzerland, Institut fiir Experimentelle Kernphysik der Universitat und des Kernforschungszentrums Karlsruhe, Karlsruhe, Germany Max-Planck-Institut fur Kernphysik, Heidelberg, Germany Research Institute for Physics, Stockholm, Sweden

The X-ray spectra of E hyperonic atoms produced by stopping K mesons were investigated for the elements C, P, Ca, Ti, Zn, Nb, Cd, and Ba. Energies and intensities of the E X-ray lines, which appear simultaneously in the kaonic X-ray spectra, have been measured.

From the E /K ratio the production of E hyperons by kaons has been studied as a function of atomic number Z. It turns out that the E production is in qualitative agreement with the calculation of Zieminska1', which is based mainly on E production rates and the strong absorption of the E in the nucleus. Nuclear correlations contribute about 25% to the E production, according to the calculation of Zieminska. Thus E hyperonic atoms might be sensitive to nuclear correlations.

The strong interaction of the E with the nucleus in the E atom was observed via the intensity of the last observable E X-ray transition in the E cascade. The absorption was compared with the analysis of E nucleon scattering at low energies from Gell, Alexander and Stumer2). It is found that out of the four different sets of scattering amplitudes of Gell et al. only two are compatible with our data. These two sets are, on the other hand, not compatible with a E N bound state, whereas the remaining two sets are. Thus our data seem o to exclude a E N bound state. a. ao. REFERENCES

~~1) D. Zieminska, preprint Dubna El 6064 (1971). 2) Y. Gell, G. Alexander and I. Stumer, Nuclear Phys. B22_, 583 (1970).~~

~~-148- 18 V.19~~

ATOMIC CAPTURE OF NEGATIVE MESONS*

M. Leon, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87544, and Ryoichi Seki, California State University, Northridge, California 91324 This is the first of a series of papers on the intensities of the x-rav lines observed in mesic atoms. In order to understand the initial formation of the mesic atom, we em- ploy the Fermi-Teller model (1); this treats the slow meson classically and the electrons as a degenerate Fermi gas. While there are two energy loss mechanisms, electron ejection (Auger process) and radiation, only the former is significant for initial capture. The model enables us to calculate capture cross-sections and distributions in angular momentum of the captured mesons. Figure 1 shows an example of such a distribution for K~ with Z=40 expressed, both in terms of the incident angular momentum £ and the angular momentum at E=0 •£'. The model also enables us to compute how this distribution changes as the meson de-excites through the electron cloud; we find in fact that the shape of the distribution doesn't change at all! The final stage, when the meson is below the electron cloud, is handled by a quantum-mechanical cascade code (G. Godfrey, LBL). This part is novel, only in that instead of a pertur- .es bation calculation for the Auger rates, we use Ferrell's formula (2): It gives the Auger rates in terms of the photoelectric cross-sections of the ionic Z-l atom for which extensive experimental data are available. (Electron depletion is assumed not to affect the calculation significantly.) Nuclear absorption (for K~) is calculated by integrating the Klein-Gordon equation idied including a phenomenological optical potential which reproduces existing

I shift and width data ifc'Kfatoms of light nuclei. (3) Correction to the x-ray intensities for the motibnlbf the nucleus (significant for K" and heavier dnly particles) is included .^Resulting intensities as functions of Z are shown in Figure 2 for various transitions n+l-*n. *Work supported in part by the U.S.A.E.C. (1) E. Fermi and E. Teller, Phys. Rev. 72_, 399 (1949); see also J. Rook, Nucl. Phys. B20, 14 (1970). (2) R. A. Ferrell, Phys. Rev. Letters 4_, 425 (1960). (3) G. Backenstoss et al, Phys. Letters 38B, 181 (1972) and 32B, 399 (1970); R. Kunselman, Phys. Letters 34B, 485 (1971).

~~:ter- F,*.l : of a :ible seem~~

~~TO 60 tO '«0~~

~~-149- V.20~~

~~Fred Myhrer, The K-mesic Atom, NLHT, Trondheim~~

Assuming that Y (1405) dominates the KN amplitude at threshold, it is shown in a three-body K d model that to get the correct sign of the real part of the K-nucleus optical potential, we must use an off-shell KN amplitude, and that higher KN multiple scatterings including intermediate nuclear excitations are important. In the fig. K d amplitudes are displayed. I through IV means increasing bound Hulthen deuteron models. The broken lines display the contributions from single KN scatt, double KN scatt., double KN scatt. with intermediate N-N interaction, triple KN scatt., and terminate at the values for the K~d amplitudes obtained by solving the Faddeev three-body integral equations for the different deuteron models. The single scatt. on-shell amplitudes with (a) or without (b) the impulse approx. are included. The fig. shows that in order to reproduce the experimental K-atomic levels and level-widths, we must solve the K-nucleus many body problem.

~~-.25 .25~~

~~-150- V.21 Optical Potential for Kaonic Atoms~~

~~M. Alberg, E. M. Henley, and L. Wilets Physics Department, University of Washington Seattle, Washington 9E195 U.S.A.~~

In an earlier paper,! We reported on the derivation of a non-local, energy- dependent K~-nucleus optical potential by means of a t-matrix method and the independent pair approximation. It was found that the equivalent local potential did not follow the form of the nuclear density, as had been assumed in earlier calculations.2*3 Non-locality and off-energy-shell behavior of the t-matrix were shown to appreciably affect the nuclear surface density distributions extracted from the analysis of experimental data.

Shifts and widths.of the energy levels in the light elements measured by Backenstoss4 were calculated in a local approximation and found to be in fair agreement with experiment. These calculations were carried out using Kim's5 M-matrix and effective range analysis of low energy kaon-nucleon scattering, and harmonic oscillator densities for the nucleus. A more realistic nuclear density, the two-parameter Fermi function, has now been used in our study of 31 32 the heavier elements P, s.t 35c£. our agreement with the experimental widths for these elements was improved, but the shifts were too large. We have also made a study of the dependence on the two-body parameters of the energy level shifts and widths in these elements. This study included calculations in which Kim's analysis was replaced by that of Berley.6 Berley's parameters yielded excellent agreement with experimental shifts, but the widths were too small. '-"'•}...

The effect of the Pauli exclusion principle on the optical potential has been taken into account.? The changes in the energy level shifts and widths due to this effect have been found to less than 5%. Experimental data8 on shifts and widths in Ni and Cu have recently been obtained, and calculations for these atoms are now in progress.

References Supported in part by the U. S. Atomic Energy Commission. 1M. Alberg, E..M. Henley, and L. Wilets, Phys. Rev. Letters 2!0_, 255 (1973). 2W. A. Bardeen and E. W. Torigoe, Phys. Letters 38B, 135 (1972). J. H. Koch and M. M. Sternheim, Phys. Rev. Letters 28, 1061 (1972). 4G. Backenstoss et al., Phys. Letters 38B, 181 (1972). 5J. K. Kim, Phys. Rev. Letters 19, 1074 (1967). . 6D. Berley et al., Phys. Rev. Dl, 1996 (1970). We thank S. Barshay for pointing out this effect. 8,R. Segel, private communication*.

~~-151- V.22~~

ABOUT POSSIBLE AKISOTROFY OF X-RAY RADIATION OF MESIC ATOMS t Istituto G. Ya» Korenman § Institute Groningei Institute of Nuclear Physics,Moscow State University;Moscow Strong : USSR with the o| context th effects in the optica In atomic capture of fast mesons to the high angular mo- its finite scattering mentum states i the sublevels with different M are populated crossed Bo o o significan irregularly. The cascade of the radiative and Auger transitions To esti we write does not totally destruct the alignment of the meson orbital angular momentum. Therefore X-rays are radiated even from the where t3 a lowest mesic atom transitions anisotropically in respect to t-matrix a the momentum of projected meson, while for

If we take into account only the principal dipole transitions We have Cc first ordt &.-*£.-± in the cascade then the anisotropy coefficient for VI3 and y^, a value cc any observed transition t-* t-L is determined only by the full-shifi sublevel population pC*tt) of the initial state fo

~~Q (2) 2~~

To the ex If, for example, only the sublevel Mo = 0 is populated then interacti cannot be - Qz (e-* 4-t) > 0.25. CD M.Kr The experimental observation of the mesic X-ray anisot- [2] M. E [3] A. D ropy should indicate the fast meson atomic capture and give the possibility of investigating the mechanism of the mesic atom formation. One may expect that the effect under consideration is revealed in rare gases most strongly.

-152- .22 V.23 FINITE SIZE EFFECTS IN PIONIC ATOMS t § F. Iachello and A. Lande t Istituto di Fisica, Politecnico di Torino, Torino, Italy § Institute for Theoretical Physics, Groningen University, Groningen, The Netherlands Strong interaction shifts in ir-mesic atoms have been succesfully analyzed M with the optical model of Ericson and Ericson [2]. In a purely phenomenological context the finite range of the IT- nucleon interaction may be ignored and its effects included in the effective parameters. However any attempt to derive the optical parameters from the IT - N interaction must also take into account its finite range, particularly in view of the near cancellation of the s-wave scattering lengths 2a3+ a, . We note furthermore that both the ranges.of the L crossed Born (M/m^M ,4fm ] and a - exchange (M/2m ^ 0.7fm ) terms are not significantly smaller than internucleon distances..ir To estimate the finite range contribution to the s-wave isoscalar potential we write 3 V(r) = / \{ 2tq[r-rJ - t,(r-rj} pCr ] d ? CD u J u 10 O Q where t3 and t<] are the s-wave, isospin | and £ , projections of the IT - N t-matrix and p(r0] is the nuclear distribution. For zero range this reduces to V(r) =-,-^12113* a^ ) p(r) C2) while for finite range it takes on the more general form

We have calculated the level shift associated with the potential, eqn.(3), to first order in perturbation theory, for" a Yukawa type t-matrix, with ranges y3 and y^. These shifts increase rapidly with Ay = y-p y3. For Ay = 0.3 fm, a value consistent with theoretical estimates (3), the shift is "v» 15% of the full-shift. Typical values for the 2p level of Ca40 are shown in the table.

y3 [fm] (fm] AE CeV] 0.05 0.27 215 0.30 0.70 304 0.5 1.0 502 Full theor. shift [1] 1520 eV To the extent that distortions of the wave function by the additional strong interaction itself are small, our estimate suggests that finite size effects cannot be ignored. The role of the distortion is currently being investigated.

CD M.Krell and T.E.D. Ericson, Nucl. Phys. B11_, 521 (1969]. (2] Fl. Ericson and T.E.D. Ericson, Ann. Phys. (N.Y.) 3I3, 323 (1966). (3] A. Donnachie, J. Hamilton and A.T. Lea, Phys. Rev. 135, B515 (1964].

~~-153- V.24~~

~~TRANSITIONS TO DISCRETE LEVELS IN RADIATIVE PION DE-EXC CAPTURE BY LIGHT NUCLEI~~

~~V.V. Earapetyan, G.Ta.Korenman, and V.P. Popov Fj Institute of Nuclear Physics, Moscow State University; Moscow Coj USSR~~

The probabilities of radiative pion capture from the S and P states by light nuclei with the transition to the bound Prc states of the daughter nuclei have been calculated. The shell from ab£ detectec model with residual interaction was used. We have shown that [1]. Tl identifi the structural features of the nuclei are revealed differently Th« 32s, anc for the P and S capture. The following states of the daughter formed 1 nucleoiu I4l + + I0 nuclei 0* in Ste and 0, 0 and 2 in Be, T* and 2* in *%t are rel< target x 2~,O",3""|I~ in TT were taken into account in calculating the involve The spec yields R-JTU • The average pionic atom data of various groups strong 1 four nuc were used. » DO{ the trar Table I. The yields of the d?V^, /J fc~ 1) reaction correspc possible mechanic I0 I2 work on Target B 0 absorpti

~~0.052 0.063 0.028 0.19 Suppc~~

~~i /5/ Suppt O.l5 O.3 [1]SREL /2/ [2]J. L: O.39±o.l Enerc [3]W. J, Lankj~~

~~I.J. Deutsch et al, Phys.Letters,26B(1968)315 2. H. Baer et al. Bull. Amer.Phys.Soc.IZ( 1972)585 3. J. Bistirlich et al. Phys .Rev. 05.(1972)1867 4. H. Hilscher et al, Nucl.Phys. AI58(I970) 584~~

~~-154- V.25~~

DE-EXCITATION GAMMA RAYS FOLLOWING NEGATIVE PION REACTIONS AND ABSORPTION ON LIGHT AND INTERMEDIATE NUCLEI H. S. Plendl* Florida State University, Tallahassee, Florida 32306, H. 0. Funsten** and W. J. Kossler** College of William & Mary, Williamsburg, Virginia 23185, V. G. Lind*** Utah State University, Logan, Utah 84321, C. E. Stronach Virginia State College, Petersburg, Virginia 23803. Prompt Y-rays from reactions of 220 MeV negative pions and from absorption of stopped negative pions on A = 19-51 nuclei were detected with a large Ge(Li) detector at the SREL synchrocyclotron [1]. The resulting spectra showed many distinct lines that were identified with transitions in residual nuclei. The spectra following 220 MeV ir~ reactions with 24Mg, 28si, 32s, and 4"Ca are dominated by transitions in residual nuclei formed by removal of one or several a-particles or the equivalent nucleons, while transitions following one-to-three-nucleon removal are relatively stronger in the spectra from 19F, 27A1, and 51v target nuclei. Weaker transitions following reactions that involve charge exchange have also been identified and analyzed. The spectra following stopped ir~ absorption on 32s and 40ca show strong transitions in residual nuclei formed by removal of one to four nucleons. .. , Doppler broadening of the observed lines, branching ratios of the transitions, and cross sections for the formation of the corresponding residual nucleus states were determined where possible tc obtain evidence for the reaction..-and absorption mechanisms. The results shed new light on previous prompt Y~ray work on I'^C and ^0 [2,3] and on other pion-nucleus reaction and absorption studies.

*Supported in part by NSF (grants NSF-GP-25974 and GU-2612). ***Supported in part by NASA. Supported in part by NSF (grant NSF-GP-8602). [1JSREL is supported by NASA, NSF, and Commonwealth of Virginia. [2]J. Lieb and H. 0. Funsten, .Proq.. Third Int. Conf. on High Energy Physics and Nuci. Struct., Columbia (Plenum Press, 1970) [3]W. J. Kossler, H. 0. Funsten, B. A. MacDonald, and W. F. Lankford, Phys. Rev. C£, 1551 (1971).

~~-155- V.26 Nuclear Gamma Rays following ir" Absorption in light nuclei~~

H. Ullrich, E. T. Boschitz, D. Engelhardt and C. W. Lewis duster Effects in K: Institut ftlr Experimentelle Kernphysik Karlsruhe, CERN by K.O.H. Ziock, Uhr In 1951 Brueckni In a systematic research negative pions from the CERN synchro- negative pions takes cyclotron were stopped in targets containing 9^Be , 10B , 12C , 160, constituents of the i •^F, Mg, P, Ca and Nb. Nuclear gamma rays in coincidence back, sharing most o: the remaining nuclei* with stopped pion logic were measured with Ge(Li) detectors of tnat this capture mo< 3 30 - 45 cm sensitive volume. A Large number of gamma transitions qualitative features, from various residual nuclei could be identified and absolute of deuterons and trii yields per stopped pion of these transitions could be determined. also be accounted foi The qualitative feati although there remaii The method used has the advantage, that different nuclear shape of the deuteroi reactions, corresponding to the emission of different particles, deuterons and tritons can be compared directly and also final states from unexpected the case of He when reaction channels can be observed in the same measurement. Thus, shown by Eckstein to besides the expected deexcitation gamma rays from (A-np) and less implies the sim pair. The discovery (A-pp) residual nuclei, unexpected high yields from (A-2n 2p) emitted by complex ni have been observed. This suggests that,besides the pion ab- vided strong evidence sorption on correlated nucleon pairs, absorption mechanisms frequently incorporai involving substructures of 4 nucleons are of importance. a-cluster. This idee Kolybasov •* who calci for pion capti:re in In some cases also the momentum distribution of the absorbing actions. His result; nucleon pair or M N substructure, respectively, could be getic deuterons and determined. Such cases occured, when the lifetime of the final this simple a-cluste state produced, was short enough to allow the recoiling residual defined energy of thi nucleus to produce a Doppler broadened gamma line, the shape momentum, the 180° a of which could be observed. deuterons and triton was confirmed by Lee angular correlations The measurements showed, that the absorption process is selective, in 12C. (see Fig. 2 leading to specific final states of the various residual nuclei. B>.A. aruscjener. The results, therefore, contain also important information about 2} D. Cheshire and the configuration of these states as expressed in terms of work in this paj 3) S. Eckstein, Phy 2-hole and 4-hole strengths. 4) K.O.H. Ziock, C. 5> A.O. Vaisenberg, 6) P.J.Cas tleberry, 7) V.H. Koj.ybasov, 6) D.M. Lee. R.C. >

~~-156-~~

~~Ssl V.27~~

Cluster Effects in Nuclear Pion Capture by K.O.H. Ziock, University of Virginia, Charlottesville, Va. 22901, U.S.A. Li 1951 Brueckner, Serber, and Watson (B.S.W.)1' suggested that nuclear capture of negative pions takes place on closely correlated nucleon pairs. As a result the constituents of the capturing pair should be emitted back to Corba. back, sharing most of the rest energy of the pion and leaving the remaining nucleus as a spectator. Experiments ^ showed •*- TriKxM that this capture mode indeed exists and has the predicted qualitative features. Eckstein ' showed that the emission of deuterons and tritons that follows ir~ -capture in He can also be accounted for within the framework of the B.S.W. model. The qualitative features of her calculations were verified ' although there remained a quantitative discrepancy in the shape of the deuteron spectrum. The emission of energetic deuterons and tritons follows from the B.S.W. model only in the case of He where the emission of an energetic neutron, shown by Eckstein to be possible within the model, more or less implies the simultaneous emission of a triton or n-d pair. The discovery that energetic deuterons and tritons are emitted by complex nuclei as well,il ;,-'•= (see Fig. 1) thus provided strong evidence that the captiaririg pair itself is frequently incorporated in a closely correlated nuclear * (n.i) (n.d) a-cluster. This idea was put into quantitative form by — KOLYBASOV —KQLYBASOV Kolybasov •* who calculated the a-particle pole diagram o.io for pion capti:re in C, neglecting final state inter- 0.08 actions. His results showed that the emission of energetic deuterons and tritoiis is indeed to be expected in this simple o-duster model and that, although the well 0.04 defined energy of the tritons is washed out by the Fermi 0.02 momentum, the 180° angular correlation of neutrons with deuterons and tritons should be strongly maintained. This wo iso wo i?,o wo iso was confirmed by Lee et al. •* who measured the energy and OPENINFigurG ANGLe E2 (DEGREES) angular correlations of protons, deuterons, and tritons with neutrons following ir" -capture 12,, in (see Fig. 2). ii Bt.A. brusckner, K. i>erber, and K.ti. Watson, rhys.fttv. 34 (1951) , 256 2) D. Cheshire and S. Sobottka, Nucl.Phys. A146 (1970), 854; (references to earlier work in this paper) 3) S. Eckstein, Phys.Rev. 129 (1963) , 413 4) K.O.H. Ziock, C. Cernigoi, and G. Gorini, Phys.Letters 33B (1970) , 471 5) A.O. Vaisenberg, E.D. Kolganova, and N.V. Rabin, Sov.Phys. JETP 20 (1965), 854 6) P.J.Castleberry, L. CouJson, R.C. Minehart and K.O.H. Ziock, Phys.Letters 34B (1971) , 57 7) V.H. Koj.ybasov, Yadernaya Fiz. 3 (1966) , 535 6) D.M. Lee, R.C. Minehart, S.E. Sobottka, and K.O.H. Ziock, Nucl.Phys. A1979 (1S72), 106

-157- V.28 SOME PHOTON ENERGIES Pion absorption in lie. A.C. Phillips and F. Foig G G Jonsson Department of Physics, University of Manchester. Department < The tejo-nucleonabsorptio n model is submitted to a quantitative test Lund, Swede: by considerincr pion absorption in "^le. Wie usefulness of this PKxlel is based A photon wi on the premise that pion absorption rates may be calculated without a detailed form an exc .knowledqe of the absorption interaction or the short ranoe correlations in nucleon. In nuclei. Vfe consider several prescriptions for the ranqe dependence of the nucleons in absorption interaction and use Tfe wave functions which are e^>licitly develop. To constructed in terms of wave functions for the s-*ave two-nucleon systems. sections, ai •Bie effective coupling constants of the absorption interaction are determined particles, from the analysis of pion production data in nucleon-nucleon collisions. ratios, whii As the calculated absorption rates in He are model dependent we since isome: conclude that the effective coupling constants cannot include all the compli- of highly e: cations of the absorption interaction and of the short ranqe correlations. and they al: Thus the model cannot be fully implemented without specifying these properties. The most realistic cases correspond to a pion absorption range of O.6F and In Lund we 1 wave functions with sof fr-corean d hard-core repulsion. Agreement with the the product: experimental ratio for the imp and nd production rates is obtained only in energy regi< these cases. lfte theoretical absorption rates for s-wave pions are It is found us(nd) (.9 + .4) 1O16 sec"1 and us(nnp) • (3.2 + .P) 1O16 sec"1 of the reac increases w These results agree with experiment if a radiative absorption rate of dence on en 4.43 x 10 sec" is assumed and if the ratio for absorption in a 2p and in 200 - 800 M Is state is .65 x 10 . Calculation Gabriel and (1969)) hav calculation tical forma are found t isomeric ra

~~-158- V.29 SOME PHOTONUCLEAR REACTIONS LEADING TO 44Sc AT INTERMEDIATE ENERGIES~~

~~G G Jonsson and M Eriksson Department of Nuclear Physics, Lund Institute of Technology, Lund, Sweden~~

A photon with energy above the pion threshold will most probably form an excited nucleon, which decays into a pion and a stable nucleon. In the interaction of these particles with other nucleons in the same nucleus, a cascade-evaporation process will develop. To study this reaction model one usually measures cross sections, angular distributions and energy spectra of the emitted particles. In some cases one can also measure isomeric yield ratios, which are an important complement to these quantities since isomeric ratios give valuable information about the nature of highly excited nuclei, their spin- and energy-distributions and they also give information about the deexcitation process.

~~In Lund we have measured the yields and isomeric yield ratios in the production of Sc fronuheavier nuclei ( Sc - As) in the energy region 100 - 800~~

It is found that the cross section decreases with the complexity A Ajn 4-4- P of the reaction, but that the isomeric ratio a( Sc)/a( sSc) increases with increasing complexity of the reaction. The dependence on energy of these quantities is weak in the energy region 200 - 800 MeV. Calculations based on the cascade-evaporation model using the Gabriel and Alsmiller Monte Carlo program (Phys Rev 182, 1035 (1969)) have been carried out. With appropriate parameters these calculations together with the Huizenga and Vandenbosch statistical formalism for spin distributions (Phys Rev 12J3, 1305 (I960)) are found to reproduce very well booth the cross sections and the isomeric ratios.

~~-159- VI~~

NUCLEAR STRUCTURE VI. 1 Nucleon Distribution Dependence of p - Nucleus Scattering by R.J. LOMBARD Institut de Physique Nucleaire, Division de Physique Theorique, 91406 ORSAY, France and J.P. AUGER Laboratoire de Physique, Faculte'des Sciences d'Orleans, 45045 Orleans-Cedex, France

Proton-nucleus scattering at high energy has often be claimed to be sensitive to nuclear distributions. In practice, however, it is rather difficult to extract density parameters directly from experiments. On the other hand, progresses made in the nuclear many body problem make possible to calculate nuclear densities withconfidenoa Therefore, it seems worth to check how far theoretical densities can be used to fit experimental data. The sensitivity of high energy p - nucleus scattering to nuclear densities has been studied within the framework of the multiple scattering theory. Various kinds of nucleon distributions arising from different self-consistent approaches have been used. It allows us to discuss the nuclear surface shape dependence of elastic and inelastic differential cross sections. Comparisonswith available experimental data on differential cross sections are also of interest. As far as the total cross sections are concerned, they are not found to be sensitive to details of the nucleon distributions ; they may be a place to look for correlations.

-163- VI.2 HEPL Report 708 RESOLUTION OF THE APPARENT DISCREPANCY IN THE MAGNETIC FORM FACTOR OF THE DEUTERON* ME R.E.Rand and M.R-Yearian,High Energy Physics Lab. and Phys ics Dept., Stanford Univ. and C.D.Buchanan, Physics Dept., Univ. of California at Los Angeles I Summary: A long-standing discrepancy between theory and the highest momentum- transfer data,3?2 on the magnetic form factor of the deuteron has been resolved following a suggestion of Prof. H. Bethe3. We have re-examined the data presented in refs 1 and 2 and conclude that the experimental data are essentially correct. The source of the discrepancy is found in the original phenomenologi- eal fit to the neutron magnetic form factor data available at that time. This fit showed GMN/MN greater than Gj^p/np by about 12$ in the momentum-transfer 4 region of interest. Data from C-E-A. now show good evidence for the scaling A long of nucleon form factors in this region, i.e.: Ggp = GMP/MP = GMN/HW* There is also evidence now that Ggu 5/ 0 as was originally assumed. cross-seci The theoretical deuteron magnetic form factor has been recalculated using by conside scaling with the dipole4 nucleon form factor, GJ;N = -05 and the Hamada-Johnson5 model of the deuteron with % D-state. The result agrees exceedingly well with currents ti all the data up to q2 = lUfm"2, without the necessity of postulating scattering from meson exchange currents. This is a very satisfactory situation since the 0.6 +0.0 electric form factor is equally well described by essentially the same assump- tions6. However the static magnetic moment anomaly is still not resolved. omitted, 1 Reference 2 also reported data on inelastic scattering from the deuteron in the currents i: region where the cross section is dominated by the unbound ^-S state. The ex- S and S' st perimental data are still valid, but the impulse approximation theory with which they were compared is now thought to be incorrect. Riska7 has shown that in the cros the impulse approximation contribution is essentially negligible for q2>8fm~2. Moreover he has calculated the simplest exchange current contributions to the simulated process and has demonstrated that they dominate the theoretical cross section which now agrees extremely well with the highest q2 data (10 fm~2). initial n - Hence backward electron-deuteron scattering is not only sensitive to the magnetic form factor of the neutron, but also provides a powerful tool for Simila examining transition meson exchange currents. stantially * Supported in part by NSF Grant GP 28299 transfer, REFERENCES: explored 1. C- D. Buchanan and M. R. Yearian, Phys. Rev. Letts- 15, 303, 1965. 2. R. E- Rand, R. F. Frosch, C E- Littig and M. R. Yearian, Phys. Rev. Letts. 18, k69, 1967- Ontht 3. H- A. Bethe, private communication. drastic r< h. R. Wilson, Cornell conference on Electron and Photon Interactions at High When this Energies, 197I. structure 5- T- Hamada and I- D. Johnston, Kucl. Phys. 3h, 382, 1962. 6. J. E. Elias, et al., Phys. Rev. I77, 2075, 1969. 7- D. 0. Riska, Talk given at Asilomar Conference on Photonuclear Reactions, March, 1973.

~~-164- VI.3~~

~~MESON-EXCHANGE CORRECTIONS TOn + d-*t + y AND TO THE MAGNETIC FORM FACTORS OF THE THREE-BODY SYSTEM~~

~~E. Hadjimichael and A. Barroso University of Sussex U.K.~~

A long-standing discrepancy between theory and experiment regarding the cross-section for radiative capture of thermal neutrons by deuterons, is resolved by considering corrections to the nuclear magnetization density due to the mesonic currents that mediate the strong nuclear force. The experimental cross-section is 0. 6 + 0.05 mb. whereas the theoretical value when meson exchange effects are omitted, is found to be 0.20 mb. Taking into account the presence of mesonic currents in the nuclear system raised the cross-section to 0.43 mb. when only S and S' states of the initial and final nuclear systems were kept. A further increase in the cross-section to 0. 67 mb. was achieved by including a triton D-state with simulated short-range correlations. A D-state with scattering effects for the initial n - d system, is not presently available.

Similar considerations regarding meson-exchange currents, changed substantially the magnetic form factors of H.-arid He at high values of momentum transfer, especially near the dip in;ttf^f|>rm/factors. This region is still not explored experimentally. :"W0'^'*"

On the basis of these results, it is felt that meson-exchange currents play a drastic role in the determination of the electromagnetic properties of the trinucleoft When this role is fully understood it will yield valuable information regarding the structure of the three-body system.

-165- VI.4 Eikonal Approximation for Magnetic Electron Scattering J. Diarmuid Murphy and H. Uberall* Catholic University of America, Washington, D.C. 20017 Coulomb corrections for electron scattering cross sections are usually obtained from phase shift calculations as employed e.g. in the DUELS or GBROW Codes1; they have mostly been used for charge scattering, although applications to elastic and inelastic magnetic scattering have been made. Phase shift methods become inaccurate for electron energies above 500 MeV, where the high- energy approximation2 ("eikonal method") may be used to advantage. We have formulated and programmed the eikonal approach for transverse electron scattering of arbitrary tnultipolarity, in order to complete the cross section calculation of Ref. 2 in the highenergy approximation; in this way, magnetic elastic and inelastic scattering can be analyzed beyond the Born approximation. We start from the multipole transition matrix element of Reference 1, containing l transition densities for the nucleus (p ,ji!"T,) and for the electron (p ,jf ); the latter are evaluated using the distorted waves of Yennie et al2. As an example, we have calculated the squared elastic form factors Ml, M5,....M9 for elastic scattering from 2O9Bi, with the nuclear densities obtained from the single-particle shell model, see Fig. 1. The Born approximation results (light curves) agree with those of Li et al3; the eikonal approximation in the q-scale (heavy curves) fills in the diffraction minima. The deviation of the lone experimental point (obtained at 500 MeV) at q = 2.25 F"1 from the theory is seen to be made worse by the Coulomb correction, suggesting that the simple shell model may have to be improved by configuration mixing. xSee, e.g., H. Uberall, "Electron Scat- tering from Complex Nuclei," Academic Press, New York, I97I. 2D.R. Yennie et al, Phys.Rev. 137, B 882 (1965). 3G.C. Li et al, Phys. Letters 317 (1970).

~~Fig. 1 *Also at U.S. Naval Research Laboratory, Washington, D.C.2O375 tSupported in part by the National Science Foundation~~

~~-166- VI.4 VI.5~~

Threshold Dependence of Moment of Inertia on Nuclear Quadrupole Momen*

Alfred S. Goldhaber** lly University of California Los Alamos Scientific Laboratory r GBROW Los Alamos, New Mexico 87544 lications shift An empirical relation, valid over a wide range of even-even nuclei, he high- states that the nuclear moment of inertia is proportional to the square of the have electric quadrupole moment, with a proportionality constant independent of the . scatter- nucleus. It is possible to derive such a relation from the assumption that a i calcu- fixed fraction, f, of the mass density at each point in the nucleus is c elastic "normal," that is, contributes to the moment of inertia, while the remainder is L. We "superfluid" and does not rotate. The fraction f is proportional to a volume itaining integral over the nucleus of a positive definite measure of the departure of the nuclear density from azimuthal symmetry about the axis of rotation. This

As an assumption has several attractive features, of which the most obvious is the •. • • • • . . - - - 2 ..M9 for analytic vanishing of the moment of inertia when the deformation goes to zero. >m the The only apparent macroscopic analogue system is a rotating bucket of 4 ...... • . .. 4 .."'-• Lts (light superfluid He . Directly comparable data for He have yet to be reported, but \e q-scale the hypothesis that a threshold region exists, in which moment of inertia lone increases gradually with deformation, is consistent with extant results•"" it 500 theory Work supported by the U. S.-Atomic Energy Commission ^address after September!; 1973: I.T.Pi, SUNY, Stony Brook, NY 11790. .'--:-< Coulomb simple 1. G. Scharff-Goldhaber and A. S.i;goldhaber, Phys. Rev. Letters 24, 1349 (1970). oved by 2. A feature shared with the superconductor-crankingvmodel (J. J. Griffin and M. Rich, Phys. Rev> 118, .850 (I960), but not with the original cranking model (D. R. Inglis, Phys.; Rev. £6, 1059 ([1954)', 103, 1786 (1956).

on Scat- 3. J. D. Reppy and C. T,; Lane* Phys. Rev, 140, A106 (1965).= R. S. Packard, :adetnic Phys. Rev. Letters 28^, 1080 (1972). However, the possibility of formation of metastable states in Hell may preclude.- a successful comparison with the nuclear case. •_. . : . ;.

~~•2B, 317~~

-167- VI.6 Exchange Contributions to Inelastic Scattering from Collective Nuclei V. R.W.Edwards V.R.W.Edwards, B.C.Sinhaand P.W.Tedder Wheatstone Laboratory, King's College, Strand, London W.C.2, England. The anisotropic Several recent papers cast doubts on the presently accepted formalism for inelastic a deformed nucleu scattering from collective nuclei 1#2) and suggest that it is desirable to calculate the poles inelastic scattering formfactors from a deformed nuclear density rather than from a ftflO*-I deformed optical potential. It is important to include exchange contributions in such where k is the ang calculations because they play a dominant role in high spin transfer transitions. vector k and the r The exchange contribution to the 0^ are the col lee optical potential is of the form of the nucleus, ft 1st order density r J 7 0 relation . • where 5(0,5.) is the first order Nc|lt-Vautv«ri->v density matrix of the target nucleus, v> rUK) = j tyy is the solution of the Schrodinger SljUr ekj»r*> for a def So C3 (40 Mtv) scattering equation with the full opt- using the Dirac af ical potential acting as interaction, Jo ^^ •v(i) is the two body interaction and S= llj -T*l • Taking account of the 30 by assuming that i short range of v(s) we can reduce v^fr,) 1uh|fl|t Pot. wavefunctions fa to an equivalent local potential -I are related to rho: io spherical nucleus using the approximate relation ». Hut). R* ItO 110 wherefeMis the local wave-number The factor \ is ret of the scattered particle and was calculated from the W.K.B. approximation expression for the

ty.is the total optical potential including direct,exchange and Coulomb contributions. where ^ fo) and therefore fe are not spherically symmetric and this produces a deformed term (4) into (3) we se< int^d-,). Other deformed contributions arise from the mixed density, which was calculated from tne relation derived in another contribution to this conference Thus using a nucl< = (1- ir, f^ spherical nucleus For QJTI/C), .vhich is the first order density matrix of the corresponding undeformed nucleus, into (2) and expai we used the local expansion of Negele and Vauterin3). This includes terms arising from the been applied to tl diffuseness of the nuclear boundary as well as the usual Slater contribution. simple Fermi Gas The diagram compares the exchange contributions to the \-o, elastic, component of the will be seen that 40 MeV proton optical potential of Ca4^) obtained using the Negele-Vauterin and Slater fe. = 0.5fm-l in I approximations for $(£,&). The more accurate treatment of $,<5,0 pushes the formfactor The fwhm of this outwards and gives rise to a slight surface peaking. Calculations of inelastic formfactors U238. Medium w are being made as a function of incident energy for a number of targets and preliminary numbers. These < results confirm Satchler's conclusion2) that the exchange contributions help to justify the result for fc3 ;n < conventional treatment of inelastic scattering at low energies, while at high energies The results prc the original criticisms continue to be validl). tions into many n mine the deforme 1) V.R.W. Edwards and B.C. Sinha, Phys. Lett. 37B (71) 225. to calculate the I 2) G.R.Satchler, Phys. Lett. 39B (72) 495. 3) J.W. Negele and D. Vauterin, Phys. Rev. C5 (72) 1472.

~~-168- VI.7 Anisotropic Momentum Distributions in Deformed Nuclei~~

~~V.R.W. Edwards Wheatstone Laboratory, King's College, Strand, London WC2, England.~~

The anisotropic momentum spectrum fl(W of a deformed nucleus may be expanded in multipoles Co* 2+ ftflO* -£. where k is the angle between the momentum vector k and the nuclsar symmetry axis, and the <*>**. are the collective deformation parameters of the nucleus. ft(fe) can be obtained from the 1st order density matrix £(3,1*) using the relation - p :fe.(r. -r>^

for a deformed nucleus was calculated using the Dirac approximation by assuming that to 1st order the single particle wavefunctions falri) of a deformed nucleus are related to those of the corresponding spherical nucleus ^° CjO according to i The factor \ is required to reproduce the usual expression for the density where p°(l) = gtTjt') is the density of the corresponding spherical nucleus. Substituting (4) into (3) we see that to first order

Thus using a nuclear model to calculate the 1st order density matrix C°*-li »1*^ f°r a spherical nucleus, we may obtain c£r,,iv) for the deformed nucleus from (6), substitute it into (2) and expand ftCfe) in multipoles to obtain the functions A»dd • This method has been applied to the neutron momentum spectra in a wide range of nuclei employing the simple Fermi Gas Model to calculate Av'lO ana> *ne results are shown in the figure. It will be seen that for ^=2 we can approximately represent A2Ct0 by a Gaussian centred at fe = 0.5 fm"l in light nuclei which moves out to k= 1.1 fm"' as the nuclear mass increases. The fwhm of this Gaussian decreases from about 0.6 fm"' for C'^ to about 0.4 fin"' for 1)238. Mec|ium weight and heavy nuclei also show some additional structure at low wave numbers. These calculations are presently being extended to higher multipoles (a typical result for V^ in C'2 is shown in the lower left hand graph) and to proton momentum spectra.

The results provide a simple method of incorporating the effects of long range correlations into many nuclear structure calculations. They are currently being applied to determine the deformed imaginary component of the optical potential of a collective nucleus and to calculate the kinetic energy of the nucfeons in such a nucleus.

~~-169- VI.8~~

(e, e'p) REACTIONS AT 500 MEV WITH IMPROVED J. Julien, ENERGY AND MOMENTUM RESOLUTIONS Mougeot and 91190, Gif- A.Bussiere, A.Gillebert, J.Mougey, Phan Xuan Ho, M. Priou, D.Royer and I. Sick Coincidei Commissariat a I1 Energie atomique, C.E.N. Saclay, BP 2 have been pi 91190-Gif-sur-Yvette, France The two i coincidence tion 10"3, 1 Differential cross sections are measured for the (e, e'p) reaction on 12 2 40 58 trons, a co C,, %i, Ca and Ni as a function of the missing energy Eg and the ini- another of tial momentum of the knocked-out proton (1). The overall resolutions 2.10-3 sr) cal plane. I (fwhm) are 1.2 MeV for the energy and 6 MeV/c for the momentum. The and the ace: range of measurement is 0-80 MeV and 0-320 MeV/c in_1jhe energy, mermen Figures . turn plane^ Typical momentum distributions for (ld3/2) and (2sl/2) (e,e'?He) it peaks of K are shown in the figure. In the framework of the impulse against the distributioi approximation, the spectral function P(Es , k) is extracted. It represents Table I i the probability for a proton in the nucleus to have a binding energy Eg lar distribi and a momentum k. No isolated Is strength are detected in the missing of the momei bution widtt energy spectra of Si, Ca and Ni.; this is in contradiction with the results of previous high energy (p, 2p) experiments (2, 3). The model independent sum rule of Koltun (4) is checked.

~~l).A.Bussiere et al.Lett. Nuovo Cim. 2(1972)1149 2) A.N.James et al, Nucl, Phys. A138(1969)145 3) G.Landaud et al, Nucl. Phys. A173(1971)337 4) D.S. Koltun, Phys. Rev. Lett. 28(1972)182~~

•f

~~39, -40 -20 Oi CQ (e;e p ) K Ee=497MeV Ep = 86 MeV no radiarion correction 0.16 501 Nucleus target °- ^ ' ' thicto r Es=10_12.5MeV~~

~~£ 0.08r -0.25 hi 4.5 if u UJ 0.04. - 60 m t m .••••••••*•. *•%..-.. 9 10 Be 9 O 0 40 80 120 160 200 240 280 0 40 SO 120 160 200 240 260 u MOMENTUM (MeV/c) 24 «8 5~~

-170- VI.9 (e,e'x) COINCIDENCE EXPERIMENTS ON 6Li, 9Be and 2l*Mg J. Julien, C. Samour, G. Bianchi, P. Duval, J.P. Genin, R. Letourneau, A. Mougeot and M. Rambaut, Departement de Physique Nucleaire, CEN Saclay, BP 2, 91190, Gif-sur-Yvette, France and A.Palmeri and D. Vinciguerra, Istituto di Fisica Nucleare, Catania, Italy Coincidence experiments between scattered electrons and charged particles have been performed around the 600 MeV Saclay linear accelerator. The two outgoing particles, electron and charged particle, were detected in coincidence using two spectrometers: one of 700 MeV/c for electrons (resolution 10"3, momentum acceptance 10%, solid angle 2.10~3 sr). For detecting electrons, a conventional plastic ladder counter and a Cerenkov detector were used; another of 400 MeV/c (resolution 10~3, momentum acceptance 6%, solid angle 2.10"3. sr) for charged particles. Solid state detectors were used along the focal plane. With such detectors, there was no problem for identifying particles and the accidental rate was small. The total resolution was i 1.2 MeV. Figures 1 and 2 show the variations of the cross sections (e.e'd) and lZ (e,e »He) in function of the angle 82 of the charged particle spectrometer or against the K3 value of the recoil nucleus momentum. For such a q value, the distribution widths are about equal to 60 MeV/c. Table I gives the experimental cross sections for the studied nuclei. Angu- lar distributions for (e,e'd) on °Li will be presented for different values of the momentum transfer q. Variations of the cross section and of the distribution width against the q value will be discussed.

~~515MeV qslSJIm1 ie-- [T. kS2SMeV qstttftri4 S.h (V~~

~~4. 40 3. I 30 2. 20~~

~~1 I 10~~

~~0 70 eo 9, . . —J 4> 70 tO 6f -40 -20 0M«V/e 20 <0 Fig.l SO-30-20 0M,V/c 20 30 M kf Fi.J.2~~

~~Table I. Experimental 'cross sections (To « 520 MeV).~~

Nucleus taigaC reaction kinetic , residual oissing nunber intcgraceJ cress section ranentua t'nickr.nss energy nucleus energy of charge Q . 10-32 transfer Big/cm2 of heavy coscntua S counts (wCb) (csrhcV-lsr-2) 1 particle ks (KaV/c) (HeV) (fa" ) T2 OW)

~~6ti 4.5 (e.e'a) 11.4 0 1.5 205114 24 33.12.4 1.48 3 11 (c.e' Hc) 14.5 17 16 813 n 1.10.4 1.46 60 (e.e'd) 18.6 0 1.5 83110 3.6 4.10.4 1.34~~

~~9Be 9 (e.e'a) 11.4 0 2.5 60110 23 8.£1.5 1.48~~

~~24 «8 5 (e.e'a) 11.4 0 9. 6.13.5 116 0.810.5 1.48~~

~~-171- VI. 10~~

The Reactionsl2C(Tr+^ pn)10C and l2C(>-,TrN) C from 30 to 90 MeV J.Alster, D.Ashery, S.Cochavi, M.A.Moinester, Y.Shamai, A.I.Yavin and M.Zaider Department of Physics, Tel-Aviv University, Ramat-Aviv, Israel. The pion absorption and knockout reactions in nuclei are major components of the total pion-nucleus reaction cresr section. We bombarded C targets with ir+ and ir~ from the secondary pion beam of Saclay Electron Linac. The summed cross section of all the reactions leading to the bound states of1J -C (knockout) and the bound states of Ity] (absorption) were measured for E^ from 30 to 90 MeV. Chivers et al.1) studied these reactions from 80 to 300 MeV, by observing the B+-activity of the We u final nuclei. We used a 40 cc GeLi counter to measure turn space the 717 keV y-ray, following the l0C decay (see Fig.l); ized form this is more sensitive technique for small cross sections than the 3+-activity. For ^C, where no other + CHANNEL y-rays than the 511 keV are involved, we used the f$ dEl Fig. 1 activity. From the very small cross sections obtained for the where (a-o IT- induced reactions leading to l^C, we conclude that scattering "C(», + *' 1 the main contributor to the ir induced reactions is the I I (ir+,pn) reaction rather than the reactions (ir+,ir+2n) the standa + o I and (ir ,ir pn) which lead to the same final states. The bles speci: tab) excitation function for the absorption reaction is 2 _ I1 shown in Fig. 2. Ef = Pf /2] 1 1 ••.Pmtnt data : In Fig. 3 we show the ratio of the ir~ to induced WKB approx: | **,Chh«rt •« al. ; knockout reactions, defined by I r-,Pm«it data culated fr< 1 tion. j i , . . • . . . . IOO 1*0 One I .2 E»(H«V) deduced from our data and those of Chivers et al. We also show the ratio deduced from a theoretical calculation of th tion of Bertini2) and the ratio R(N), which is the ra- the differ< tio for the corresponding pion nucleon cross sections. arises lar| It was already known that at 180 MeV the experimental is clear tl ratio was equal to one instead of the expected value angles. of three. Our data^show that this ratio is lower by approximately the same factor at the low energies as Const well. shell t-ma known long- 1) D.T.Chivers et al., Nucl.Phys. A126, 129 (1969). tering wav< rect on-sh< 0.2 2) H.W.Bertini, Phys. Rev. 131^, 1801 (1963). tainties ii 100 20CT ate to co-i PION ENERGY (MtV) Fig-3 3) J.Alster et al., submitted to publication J. Work £ John Sir 1. Edward 2. Gerhard 3. G. J. Si Phys. R< 4- H. S. P: 287 (19; Am. Phys

~~-172- VI.11~~

~~Off-Shell p-p Cross Sections Appropriate to (p,2p) Reactions~~

~~Edward F. Redish University of Maryland, College Park, Maryland, USA~~

~~G. J. Stephenson, Jr. Los A?amos Scientific Laboratory, University of California Los Alamos, New Mexico, USA~~

~~We use a recent formulation of the (p,2p) reaction in which the momentum space representation of the DWIA integral is employed to obtain a factorized form of the cross section~~

dE dfl dfl = (a~off) _ x (kinematic factors) * Hdistorted waves) where (G-off) is a fully off-shell p-p cross section calculated from a scattering amplitude t(p. + Ap., p + Apf; Ef - AEf) and the last term is the standard distorted momentum distribution. The differences of the variables specifying the t-matrix from the half-off-shell values p., p.., and 2 x E- = P, /2M are easily calculated from a given set of distorted waves in the WKB approximation. Since these differences will be small, cross sections calculated from the half-off-shell t-matrices should give a very good approximation. One may well be concerned about possible model dependence in the calculation of the off-shell cross section. In fact, it has recently been shown^ that the differences in the predictions of this quantity among divers potentials arises largely from the differences in their on-shell predictions. However, it is clear that no on-shell approximation suffices over a reasonable range of angles.

Consequently, we have utilized a wave-function model for the half-off- shell t-matrix^ which uses the experimentally determined phase shifts and the known long-range part of the interaction as input and parameterizes the scattering wave function at short distances. This enables us to guarantee the correct on-shell behavior and to study explicitly the effects of reasonable uncertainties in the off-shell extrapolation. Curves have been calculated appropriate to co-planar experiments at incident energies of 155 and 185 MeV.

, Work supported in part by the United States Atomic Energy Commission. John Simon Guggenheim Fellow on leave from the University of Maryland. 1. Edward F. Redish, University of Maryland Technical Report No. 73-111. 2. Gerhard Jacob and Th. A. J. Maris, Rev. Mod. Phys. 45, 6 (1973). 3. G. J. Stephenson, Jr., Edward F. Redish, Gerald M. Lerner and M. I. Haftel, Phys. Rev. C 6^, 1559 (1972). 4. H. S. Picker, Edward F. Redish and G. J. Stephenson, Jr., Phys. Rev. C 5_, 287 (1971); G. J. Stephenson, Jr., H. S. Picker and Edward F. Redish, Bull. Am. Phys. Soc. 18, 548 (1973).

~~-173- VI.12 DWIA analysis of quasi-free scattering in Ca~~

~~R. Bengtsson, T. Berggren and C. Gustafsson Dept. of Math. Physics, Lund Inst. of Technology, S-220 07 Lund 7, Sweden~~

.n Using an eikonal approximation we have performed a DWIA analysis of the Ca(p, 2p)39K reaction studied experimentally at h60 MeV /1/ and 600 MeV /2/. The optical potentials were calculated using the KMT theory /3/ from nucleon- nucleon amplitudes fitting existing data and using a Saxon-Woods density shape with parameters fitting electron scattering data. Neglecting two-step processes, which should contribute only little at these energies, the reaction cross sec- De tion can be calculated from the overlap integral between the initial target state and the final residual state. This function was approximated by a single- proton wave function generated in a Saxon-Woods well with binding energy calculated from the proton separation energy and the appropriate excitation energy of the final state. The parameters of the well were determined suclji that the 1d3/2, 2s1/2 and 1d5/2+energies correspond to the lowest 3/2 , 1/2 and (estimated centroid of) 5/2 states of 39K. (Approximate positions and weights for the 5/2+ states were taken from ref. /h/ assuming charge invariance.) According to KMT a satisfactory approximation for the optical potential at -M co' high energies is given by U(q) = CA(q)F(q), where q = momentum transfer, A(q) if is the nucleon-nucleon scattering amplitude, and F(q) is the formfactor of the a mec (target) nucleus. The Fourier transform of F(q) is the nucleon density of the lO£ nucleus, and that of U(q) is the optical potential (C is a constant). In the 1 see lowest-order approximation the q dependence of A(q) is neglected; KMT show that a better approximation is obtained by modifying the density p(r) such that the 1 anc r.m.s. radius is increased by - 3d2A(0)/dq2/A(0). We have used this prescriptiai in some calculations but have also tried the improved formula 1 ser 2 2 cle U(r) = C|(A(0)p(r) - (d A(0)/dq )(2p-(r)/r + p"(r))) 1 where primes denote differentiation with respect to r. Here p(r) is the unmodi- lev fied nucleon density. This formula is theoretically better approximation of the Fourier transform of U(q). Taken as a modification of the density it yields the (1/ 1 16 same modified r.m.s. radius as the KMT prescription. However, this corresponds 1 to a change of the diffuseness parameter rather than the half-depth radius (the thE derivative term changes sign in the nuclear surface region). We have accordingly performed the ordinary calculations with two different values (0.55 fm and 0.75 see fm) of the diffuseness parameter in the optical potentials. 1 the Apart from the modifications described above the calculations were performed 1 as described in refs. /I,2/. As in all earlier calculations we found that the ri£ results are very sensitive in shape as well as in magnitude to the properties an of the overlap integral. But also the optical model parameters can change the shape and magnitude of the calculated cross sections by large amounts. Within the limited budget available to us we have not been able to search systematical- 1 ly for consistent values of those parameters which are not fixed by the pheno- ang menological restrictions we have imposed. It seems, however, that the variations knc in the results obtained permit the existence of such a set of parameters for 1 this target nucleus. /1/ H. Tyren et al., Nucl. Phys. J_9_ (1966) 321 12/ S. Kullander et al., Nucl. Phys. A173 (1971) 357 /3/ A.K. Kerraan, H. McManus and R.M. Thaler, Ann. of Phys. J3 (1959) 5*H A/ J. Kallne, B. Fagerstrom and E. Hagberg, preprint Gustaf Werner Institute, Uppsala 1972

~~++ Work supported by the Swedish Atomic Research Council On leave of absence at C.E.N. Saclay, France.~~

~~-174- VI. 13~~

~~MULTIPLE SCATTERING EFFECTS IN (p,2p) COLLISIONS ON 12C-~~

~~R.Guardiola and P.Pascual Department of Theoretical Physics. University of Barcelona. Spain~~

From the study of Glauber's multiple scattering series in (p,2p) 12 collisions on C one is able to obtain an information on the reaction 11 mechanism. When using closure for the residual X nucleus, the energy- loss spectrum is written as a sum of single, double ...... incoherent scattering terms. The single scattering term corresponds to the D.W.I.A., and the fact that the double scattering term is very important puts serious limitations on the validity of the D.W.I.A. This is shown clearly when analyzing the contribution to the spectrum of the "allowed" 11 levels, in the D.W.I.A. theory, of the residual nucleus, namely B (i/2+, 35 MeV), 11Be (i/2+, 35 MeV), 11B (3/2~, 16 MeV) andU B (3/2~, 16 MeV): the summed spectrum appears to be significantly lower than the spectrum obtained fro the closure approximation (all multiple scattering terms included), but has the correct shape. This indicates that the ecitation of (2p,2h), (3p,3h) levels of X gives rise to non negligible contributions, and that all them contribute as an almost constant background to the differential cross section. The theory, however, is only applicable to high energy and small angle scattering, and is not able to account for the distortion of the knocked-out nuclean.

~~-175- VI.14~~

Momentum Distributions for Neutrons in H, He and He from Quasi- elastic Scattering of 1.3 GeV/c Protons P. Kirkby, J.M. Daniels, T. Gajdicar, S. Friedlander, G.F.Krebs, H. Coombes, E. Dennig and K. Kairies. University of Toronto, Toronto, Ontario, Canada. Measurements have been made of quasi-elastic scattering of 1.3 GeV/c protons using the (p,pn) reaction, in the three light nuclei %, %e and ^He. The experiment consisted of a proton spectrometer, to momentum analyse the outgoing proton, and a bank of 30 neutron counters, to determine the momentum of the outgoing neutron. From these measurements, the momentum of the neutron in the initial state (k., k^, k ) was calculated for each event. These are the components of momentum along The beam, perpendicular to the beam in both the horizontal and the vertical directions. The distribution for measured values of k for ^H and %e are shown in Fig. 1. In addition, there is a distribution of k measured from a hydrogen target to determine the resolution of the apparatus. For this target the neutron counters were used to detect protons. From these distributions the momentum distributions will be determined by dividing the measured cross sections by the free scattering cross section for p-n elastic scattering and a kinematic factor.

~~Gaussian distributions have been fitted to the measured distributions for , and k and the results are:-~~

~~Target Standard Deviation to fit Gaussian Distribution~~

18 23 13 Mev/c. 57 60 37 et -al. JHe 65 112 58 gaussian as has 75 116 6k motion 1) J.C. The hydrogen data demonstrates that the experimental resolution is a small component of the values measured for the other nuclei. There are 2) A unexpectedly large values of ^ for both ^He and %e. At present, it is not 3) I.V. h known if this originates from the events selected by the experiment or if 4) Y.C. it is actually an aspect inherent in the scattering process. *Nuclear 0 Mi ami sPennane

~~c -5,0 -in o 40 1M. Riou, Rev. Mod. Phys, 37, 375-387 (1965).~~

~~-176- VI.15~~

~~The 6Li(p,pd)*He. Reaction at High Recoil Momenta~~

p. Kitching*, W.c. Olsen*, W. Dollhopf , C. Lunke+S, c.F. Perdrisat+, J.R. Priest0., W.K. Roberts s The cross section for the reaction Li(p,pd) *He(g_s>j has been measured with S90 MeV protons. Recoil momenta of the residual "He nucleus up to 240 Me%vere observed. This work is an extension of our previous measurements1' at lower recoil momenta, and uses the same apparatus. The angles of the observed proton and deuteron were kept fixed, at those corresponding to 90° cms angle for free pd scattering, and the energies varied.

~~6 l The Li(p,pd) *He(g,s,) reaction was selected in the analysis.by applying cuts to the E missing energy Emiag = Eo - (E + Ea + recoii' where Eo is the incident energy, E and~~

~~E. the scattered proton and deuteron energies, respectively, and Erecoil the recoil energy. Figures (a) and (b) show the observed missing energy spectra for the two measurements, with~~

~~the kinematics appropriate to different values of qT, the average transverse recoil momenta.~~

The main peak around E^ss = 0 was interpreted as originating from the quasi-elastic reac- 6 I> tion Li(p,pd) He^_ s ). For each event within the cuts on Emiss, the total recoil momentum, q, was calculated from the measured angles and momenta. The cross section d a. was then calculated as a function of q. dfi dfi^dE

Assuming that the Plane Wave Impulse Approximation is valid, the cross section can be written as ds0 , , do , , , where k is a kinematic factor, ' _ .u ^_— = k ( TFT ) n_,. P(q) *t •> • ^p^d^p dfi ^ ad ( ^ ) 2) is the 90° CM

6 elastic pd cross section, nad is the number of a-d clusters in the ground state of Li and p(q) is the internal momentum distribution of the deuteron relative to the ''He spectator .The values of p (q) calculated from this formula are shown in Figure 2, together with the results of our previous experiment1) . The value of n^j was obtained by calculating f p (q)d3q using the trapezoidal method to give n^ = 0.78 +_ 0.07. A gaussian fit, of the

2 form exp(-(q/q0) ), to the experimental points gives a width parameter qo = 73 + 1& Hev/c. Also shown in Figure 2 are fits using a theoretical distribution due to Kurdyumov et -al.3) and a 2S harmonic oscillator wave function. Both give much worse fits than the gaussian, which corresponds to a IS state for the relative motion of the a-d system. However, as has been pointed out4), the exclusion principle requires that the lowest state of relative motion be 2S. 1) J.C. Alder et al., Phys. Rev. C£, 2023, (1972) 2) A value of ( ^ ) = 0.0485 pb/sr was used; see J.C. Alder et al., Phys. Rev. C, 6, 2010, d" pd <1972> 3) I.V. Kurdyumov et al., Phys. Lett. 40B, 607, (1972) 4) y.C. Vang et al., Phys. Rev. 123, 548, (1971) *Nuclear Research Centre, university of Alberta; +College of William and Mary, WiUiamsburg.Vat °Miami University, Oxford, Ohio; *N.A.S.A. Lewis Research Centre, Cleveland, Ohio? Spermanent address: physics Institute, University of Neuchatel, Switzerland.

~~-» -JO 0 M «0 « » MISSING ENEKGT (M.VI~~

~~ISO 300 SO -» -JO 0 10 40 W «0 q(M«V/c) MISSING ENSKST («.V) I -127- VI. 16~~

~~Quasi-Free Scattering on Clustering Particles and Q Values P. Ciier Laboratoire de Physique Corpusculaire, C.R.N., Strasbourg and Y. Sakamoto Institut fur Kernphysik der UniversitMt, Frankfurt/Main~~

The cross section for the quasi-free scattering (QFS) on clustering particles is explained in terms of the binding energy of the particles in the nucleus. For the most case the cm. wave function of the clustering particles relative to remaining ones has nodes. This is seen by imposing the energy conservation of the particles, when the internal states of the clustering and remaining particles are restricted to the ground or lower excited ones. The number of nodes is the same as that appeared in the antisymmetrized cluster model wave function. The nodes are well localized in the interior region. The oscillatory structure of the nodes acts to cancel the contribution of the wave function to the overlap integral in the interior region. The situation is completely different for the form factor, where the square of the wave function cannot give are k rise to any cancellation. In the region of small momentum transfer the form factor does not sensiti- angle vely depend on the detailed form of the wave function. It depends only on the r.m.s. radius. measu The QFS is dominated by the low momentum components of the wave function. Such low momentum components are correctly given by the asymptotic form of the wave function which essentially depends only on the binding energy. out o With the asymptotic function and the nuclear radius the parameter-free calculation is possible for the cross section. The detailed form of the wave func- of el tion in the interior region is not important for the calculation because of the cancellation occurred on the overlap integral. The asymptotic part of the wave ation function largely accounts for the cross section. The calculated results are compared with available data and found to be in cuss good agreement. Many interesting results are obtained. Some of them are given as follows: For a small binding energy there is only very small difference bet- Glaub ween the cross section calculated by the asymptotic function with a reasonable cut-off radius and that calculated by taking account of the interior function. teron This means that the cross section does not sensitively depend on whether the target nucleus is completely black or not. If this is the case, the antisymme- commo trizatxon effects of particles in the target nucleus is not important. The absorption effects for the incident and outgoing particles are largely diminished by the oscillatory structure of the wave function. The particles which easily elast loses its structure by nuclear interactions can be used as a projectile particle for the QFS. In this case the cut-off approximation is valid and the anti- large symmetrization effects do not bother the calculation. However, before conclu- ding that the clustering structure is a surface phenomenon, on the basis of ap- depen parent agreement between data and results calculated by the asymptotic function with the cut-off approximation, attention should be paid to the cancellation kinem occurred on the overlap integral in the interior region. The large difference between the cross section for the break-up of 6Li into ^He and 2g and into 3Re on ta and 3H does not indicate the small possibility of the T - t configuration in the &Li nucleus. This difference is simply the reflection of their reaction Q values. The break-up into 3ne and 3H is strongly hindered by its large Q value, the p even if the internal wave functions of x and t clustering particles are assumed to be respectively identical to those of free 3He and 3H nuclei. The Q value gives tne indication for the facility of the removal of the particles from the nucleus, and takes an essential part to determine the absolute magnitude of the cross section for the QFS. The Q value determines the width of the correlation cross section for the QFS in good agreement with data. Data for the pion absorption by clustering particles in nuclei are also consistently explained.

~~-178- VI.17~~

~~ENERGY DEPENDENCE OF THE CROSS SECTION OF FIST DEUTERON KNOCK OUT FROM Li, Be, C BT 380-670 MEV PROTONS~~

7 .1 .Komarov, G.E.Kosarev, G.P.Reshe tnikov,O.Savchenko f S .Teach. Joint Institute for Nuclear Research,Dubna,USSR ABSTRACT The high energy parts of spectra of fast deuterons,which are knocked-out from Li,Be,and C targets by protons at 5.5°iab. I angle with proton energies 666,578,484 and 383 Me? have been measured. The cross sections of quasi-elastic deuteron knockout obtained are compared with the corresponding cross sections of elastic pd-scattering at energies mentioned above. The evalu- ations of the effective number of two-nucleon clusters are discussed, which have been obtained taking into account (in the Glauber approximation) the incident proton and knocked-out deuteron interactions with nuclear nucleons. The results show the common behaviour of the scattering mechanisms responsible for elastic pd- and quasi-elastic proton backward scattering with large momentum transfer to two nucleon clusters. The energy dependence of the deuteron production cross section at energy kinematically corresponding to the p + (N)-*d +3T process on target nucleons is close to that of the cross section for the p + p ->- d +3T+ process*

~~-179- VI.18 On Quasi-Elastic Reactions with Knock-Out of a Nucleon Group I. Rotter Zentralinstitut fur Kernforschung Rossendorf bei Dresden, GDR~~

The cross section of a quasi-elastic reaction with knock-out of a nucleon group may be written in the form 6" c£^). There is, however, no analogy for the quantum numbers n,l ^ 0,0 in the simple elastic scattering process (unlike spin, isospin and Young scheme), where all scattered particles The are observed (n = 0, 1 = 0). One has therefore to discuss the ttering 1 influence of contributions depending on the quantum numbers n,l ^ 0,0 in the intermediate state (CL^—* cj^1 ) like in some residual special multi-nucleon transfer reactions . some moi The cjj^ may be very different from the c?^ because of the obtained coherent sums appearing in the cj^. As an example, the reaction Li(p,pd) is considered with the assumption that the dynamical amplitudes dp not depend on the oscillator quantum numbers. As a result, the analysis of the reaction Li(p,pd) using the c£k would lead to a value of the reduced deuterbn widths which is smaller by one order of magnitude than that obtained with the

~~1. I. Rotter, Symposium on Heavy Ion Reactions and Many-Particle Excitation, Saclay 1971» Journal de Physique, Suppl., 32 (1971)0 6-113~~

~~-180- VI.19~~

~~ASYMNLHTBT IN QUASI-ELASTIC SCATTERING OF POLARIZED 635 MEV PROTONS BY 6Li NUCLEI V.S.Nade;jdin,N.I.Petrov,V.I.Satarov Joint Institute for Nuclear Research, Dubna, USSR~~

ABSTRACT The dependence of the asymmetry of quasi-elastic scattering by polarized 635 MeV protons by Id. nuclei from the residual nucleus has been studied* The asymmetry values for some momenta transferred to the residual nucleus have been obtained within 0 < Presid.

-181- VI. 20 A MICROSCOPIC CALCULATION OF REARRANGEMENT ENERGIES IN 16O A SELF-CO NUCLEAR M R. PADJEN & B. ROUBEN University of Montreal, Montreal, Quebec, Canada F.C. KHAN Atomic En F.C. KHANNA Chalk Riv Atomic Energy of Canada Limited, Chalk River Nuclear Laboratories, Q. HO-KIM Chalk River, Ontario, Canada Laval Uni The rearrangement energies in16 0 are computed microscopically. Starting from a realistic G-matrix (S. Kahana, H.C. Lee 6. C.K. The Scott, Phys. Rev. 180(1969)956 called KLS henceforth) the second 115(1959) and the third order contributions to the single particle energies particle in the Hartree-Fock basis (EJ.0) are calculated. frequency First the single particle energies are calculated by taking potential into account the third order contribution: e^ = e^0 + A i where nucleus ( 3 First the A3i = Ep££' with pfeP being the occupation probability of the state k. The total energy is expressed as E = E° + E', where is trunca E1 is an attractive contribution from the four-body cluster terms. (1966)778 The single particle energies e^ and the occupation probabilities self-cons p(l) are used to calculate the diagonal part of the second order nuclear n correction, which is the lowest order off-shell contribution to sets of t the mass-operator M(OJ) , to e^. the parti M(o>) is a smooth function for the p-states but for the s-state for the c M(u)) is a rapidly varying function of 0). We follow the suggestion probabili of Engelbrecht & Weidenmiiller (Nucl. Phys. A184U972) 385) and per- the optic form an energy averaging of M(oi) over an energy interval x>d where particle d is the average energy spacing between the 2h-lp configurations. be drawn The corrected single particle energies are solutions of the self- a) The sa consistency equation u = e^ + Re and the spreading widths very s for the s-state quasi-particle are 2 Im | u)=es. The results are shown in the table. For comparison we show similar numbers b) Three obtained by Padjen et al. (to be published) in the harmonic oscil- late t lator basis using the potential of de Tourreil & Sprung (Nucl. and A] Phys. A201(1973)193) . partic The Hartree-Fock calculation yields E = -105 MeV with an R.M.S. substc radius of 2.15 fm. The second order rearrangement energies are c) The or quite sizeable for both the forces. The s-state spreading width potent calculated in the same approximation is 14.4 MeV. The average shallc rearrangement energy is ^8 MeV compared to the experimental value imagii of ^8.5 MeV. The four particle cluster contribution to the energj rearrangement energies is quite small (< 1 MeV). with t

Os Op Op d) The sj 1/2 3/2 1/2 the F« dT-S KLS dT-S KLS dT-S KLS e) The oi smootl o -54.8 -70.3 -26.3 -33.0 -21.4 -26.7 the a partic P1 - 0.05 - 0.03 - 0.08 - 0.04 - 0.10 - 0.05 3 and 0 A 4.9 2.1 3.6 2 3.2 1.0 1. f) The pi Re 17.1 19.8 3.0 3. 2 3.8 3.1 relat: energj * -30.5 -45.7 -•16.1 -25.0 -10.8 -19.0 ei calcu' e±(expt.) -44 ± 5 -19.0 ± 1.0 -12.4 ± 1.0 low ii energy e + A + Re + A + A . imagii o 3 Coul. CM Interi

-182- .20 VI. 21 A SELF-CONSISTENT CALCULATION OF THE OPTICAL MODEL POTENTIAL FOR NUCLEAR MATTER F.C. KHANNA Atomic Energy of Canada Limited, Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada Q. HO-KIM Laval University, Quebec City, Quebec, Canada ..-.•'• The Green's function approach (Martin & Sohwinger, Phys. Rev. 115(1959)1342) is used to calculate I(k,to) , the self energy of a particle in the nuclear matter as a function of momentum k and frequency u). The on-shell part of E(k,u)) is related to the optical potential for scattering of a nucleon from a large (infinite) nucleus (J.S. Bell & E.J. Squires, Phys. Rev. Lett. 3(1959)96). of First the hierarchy of coupled equations for the Green's function e is truncated (R. Puff, A.S. Reiner & L. Wilets, Phys. Rev. 149 s . (1966)778) to obtain a closed set of equations that are solved self-consistently to obtain a minimum for the binding~energy: of nuclear matter for each value of fcf, the fermi momentum. Several sets of two-body separable interactions with two terms in each of the partial waves S, F and D have been employed. The potentials for the coupled channel 3S-3D are chosen such that the D-state e probability in the deuteron varies from 1-7%. For calculation of on the optical potential (u)>U)f, the fermi energy) also the quasi- r- particle approximation is used. Several definite conclusions can ire be drawn from our calculations. a) The saturation of the binding energy of nuclear matter depends very sensitively on.the strength of the tensor force. b) Three different A approximations for A have been used to calculate the T-matrix: (T = v+vAT) Aoo = iG G , Aio = Y(G G-G G ) .1- o o Q o and Aii = iGG where Go and G are the unperturbed and exact one particle Green's functions, respectively. The binding energy is substantially better iri^the Axi approximation. c) The on-shell part of E(k,u)) leads to a real part of the optical potential which is ./V40 :MeV deep at low energies^ and becomes shallow for high energy^jscattering. The strength of the imaginary part of the opltical potential varies smoothly with energy from 2 to ^4.2 MeV. These numbers compare quite well with the values used in heavy nuclei. d) The single particle spectrum does not appear to have any gap at the Fermi-surface. e) The off-shell part of £(k,0)) has been mapped out and is quite smooth as a function of k,ui. This information can be used in the calculation of the rearrangement effects for the single particle energies before comparing them to high energy (p,2p) and (e,e'p) experiments. f) The present calculation takes into account the short range correlations accurately and therefore.should be valid for high energy (p,p') and (p,2p) experiments. We stress that the above calculations were for nuclear matter. For finite nuclei and at low incident nucleon energies (S 50 MeV) the excitations of low energy collective, states will make a large contribution to the imaginary part of the optical model potential (N. Vinh Mau, International Course on Nuclear_Theory, Trieste (1969)).

-183- VI.22 Microscopic Description of the Spreading and Decay of Hole States W. Fritsch, R. Lipperheide and U. Wille Hahn-Meitner-Institut fUr Kernforschung Berlin and Freie Universitat Berlin, Berlin-West, Germany Nuclear hole states are formed in quasifree (p,2p) and (e,e'p) reactions and in pick-up processes like (p,d) and (d, He). The cross section for these reactions can be analyzed in terms of the 2 hole spectral functions 1» 'SV(E), which measure the strength of the single-hole state v as a function of the separation energy E:

e-(p.E) = SV.(E) , (p*, E: momentum, energy transfer) where 2 "*" is the (distorted) momentum distribution of state V. Calculations of Sy(E) in the single-particle model yield a single &-function peak at the energy of state v. Spreading and decay widths are due to correlations, and have been calculated phenomenologically3' and by nuclear-matter methods^'. The microscopic finite-nucleus description5* ' is based on 1the following picture (cf, figure): the coupling of the lh state v to the many bound lp-2h states <. leads to the spreading of v, and the coupling to the continuous lp-2h states c to the particle decay of v. With- out direct coupling between the lp-2h states i. and c , the state * is decoupled from v at the energy of state ^, and S^tE) vanishes at this point. The zeros of Sv-(E) corresponding to the various states *1 , force it to have an un- lp-2k realistically violent structure consisting of a succession of spikes 5 the zeros are removed by providing the states * with a width via a diagonalization in the space of states A. and c with interaction Vv, .

perturbation theory ( S^E) = (1/TT) Im Gy(E-i^) ) and (b) by diagonalization of V^ using the continuum shell model ap- proach8'' for 1^C(p,2p). Method (b) results in a smoother structure for Sy.CE) and hence for the (p,2p) cross section, and leads to an appreciable improvement over the results of method (a) in comparison with the experimental data.

1) D.H.E. Gross and R. Lipperheide, Nucl. Phys. A150 (1970) 2) G. Jacob and Th.A.J. Maris, Rev. Mod. Phys. _45_ (1973) 6 3) V.E. Herscovitz, Nucl. Phys. A161 (1971) 321 4) H.S. KShler, Nucl. Phys. 8£ (1966) 529 5) U. Wille and R. Lipperheide, Nucl. Phys. A189 (1972) 113 6) W. Fritsch et al., Nucl. Phys. A198 (1972) 515 7) A. Faessler et al., Nucl. Phys. A203 (1973) 513 8) W. Fritsch et al., to be published

-184- VI. 23 SLATER DETERMINANTS, JASTROW WAVE FUNCTIONS and HIGH MOMEN- TUM COMPONENTS in ELECTRON FORM FACTORS. C. Ciofi degli Atti, Physics Laboratory, Istituto Superiore di Sanita and INFN Sezione Sanita, Rome, Italy

Jastrow wave functions, unlike various type of single-particle orbitals (Harmonic oscillator, and Saxon-Woods),can give a very good phenomenological explanation of the high momentum part of the charge form factors of light and medium-weight nuclei. However, since the charge form factor is the expectation value of one-body operators, it is legitimate to ask whether the results obtained with Jastrow wave functions can equally well be obtained with a Slater determinant. Gqudin, Ripka and Gillespie , starting from the Jastrow function which fits the "*°Ca form factor and diagonalizing the one-body density matrix, were able to obtain a new Slater determinant whose single-particle density is similar to the Jastrow one. These results are sometimes quoted as the proof that the good Jastrow-type results for the form factor/equally well be obtained with a Slater determinant. Such a statement cannot be accepted for two different reasons. The first, very simple one, is that in Ref. 1 the calculation of the form factor with the new Slater determinant is not presented; on the other hand, it is well known that very similar densities can yield very different form factors at high momentum transfer (where F(q)<^ 10 ); the second, more fundamental reason ^ j is that using Jastrow functions the center-of-mass motion can be treated uniquely whereas using the new Slater determinant this cannot be done,for there are many methods to remove the center-of-mass motion coordinate. If the Slater-determinant form factors calculated using these methods do not differ each other appreciably and, at the same time, give results similar to the Jastrow case, only then one can state that a Slater determinant can be found which is equivalent to the Jastrow wave function. We are studying the problem by determining a Slater determinant having maximum overlap with Jastrow wave functions and then by calculating the form factor treating the center-of-mass motion in different ways. The single-particle orbitals are chosen to be expansions in a large harmonic oscillator basis. Prelimi- nary results for %e (0s, Is, 2s, 3s, 4s, states included) show that for such a light nucleus the Slater determinant having maximum overlap with Jastrow functions gives completely different form factors depending on the way the center-of-mass motion is treated. Calculations for heavier nuclei (*°O and 40ca) are in progress.

1 - M. Gaudin, J. Gillespie and G. Ripka, Nucl. Phys. , A176, 237 (1971) 2 - F. Palumbo, "The Many Body Problem". Proceedings of the Symposium on the Nuclear Many Body Problem* Rome, September 1972, F. Calogero and C. Ciofi degli Atti Editors (to be published) 3 - J. L. Friar, Nuci. Phys. , AjL73_, 257 (1971); C. Ciofi degli Atti, L. Lantto and P. Toropainen, Phys. Lett. , 42B, 27(1972)

~~-185- VI.24~~

~~THE BEST-ENERGY CRITERION FOR THE NUCLEAR INDEPENDENT PARTICLE MODEL~~

~~S. BOFFI and F.D. PACATI Istituto di Fisica Teorica dell'University, Pavia, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Pavia~~

In the definition of the Independent Particle Model (IPM) the best-energy criterion is, among others, the most widely used, leading to the Hartree-Fock (HF) equations. Tiro difficulties are met when applying it to finite nuclei: a correct separation of center of mass (cm.) motion and convergence problems arising from the short range repulsion of the interaction* The latter is usually overcome vith nonsingular effective forces, and a rather good value of the ground state (g.s.) binding is then reached. The discrepancies between theoretical and experimental charge form factor, however, indicate that the HF one-particle density matrix p is not realistic. This fact, supported by the available uncertain estimate of cm. spurious effects, has been interpreted simply as the failure of the IPM. Calculations are here reported for a self-consistent cm. correction to the He g.s. function, applying the HF method to the case where the cm. is placed in an external harmonic field (l). A fairly clean separation of cm. motion is obtained. The practical coincidence between the final solution and the one of the usual HF method applied to the intrinsic Hamiltonian suggests that also in the usual HF approximation the spurious cm. excitation is absent in practice. A simultaneous description of all g.s. properties seems then impossible in the frame of the best-energy criterion. It is suggested, also on the basis of previous works (2) on 0 and Ca, that such a task could be accomplished, however, in terms of a suitable p . In. tbis case the IPM should be built according to the best-density criterion.

~~(1) H.J.Lipkin, Phys. Rev. JL09. (1958) 2071; 110 (1958) 1395 (2) S.Boffi and F.D.Pacati, Nuclear Physics (to be published); Rend. 1st. Lombardo (Ace. Scienze e Lettere, Milano) (to be published)~~

-186- VI.25 VI. 24 Density fluctuations and nuclear structure F. Calogero , F. Palumbo*', 0. Eagniaco* **Istituto di Pisica dell* Universita di Roma, Borne, Italy •* Istituto Nazionale di Pisica Nucleare, Sezione di Roma + Centro Studi Nucleari della Gasaocia, CNEN, Roma + Center for Theoretical PhysicB, HIT, Cambridge, Mass., USA

Results will be reported of nuclear matter variational calculations performed with a trial many-nude on wave function displaying density fluctuations in the different spin-isospin states. These computations are motivated by the recent findings concerning the conditions nuclear forces must satisfy to be consistent with the asymptotic saturation property of nuclear binding energies•( ) Their purpose is to ascertain whether nuclear matter configurations other than the homogeneous and isotropic one might be energetically favored for some "realistio11 model of the nuoleon-nucleon interaction. Preliminary results for the One-P-ion-Exchange Potential had suggested that this is the case, but only at densities somewhat higher than the central density of ordinary nuclei•( ) This indication is supported by more recent computations with realistio One-Boson-Exchange Potentials.

(X) F. Calogero and Yu. A. Sinonov, Lett. Nuovo Cimento £, 219 (1970); F. Calogero, "Nuclear Forces and Saturation", in Problems of Modern Nuclear Physics, Proceedings of the "Second Problem Symposium on Nuclear Physics" (Novosibirsk, 1970), Nauka, Moscow, 1971, p. 102; F. Calogero and Yu. A. Simonov, "Rigorous constraints that nuclear forces must satisfy to be consistent with the saturation property of nuolear binding energies", in The Nuclear Many-Body Problem (F. Calogero and C. Ciofi degli Atti, editors), Proceedings of the Symposium on "Present Status and Novel Developments in the Nuclear Many-Body Problem" (Rome, 1972) (in press), Rome preprint n. 394 •

(2) F. Calogero and F. Palumbo, Lett. Nuovo Cimento (in press), Rome preprint n. 414 *

~~-187- VI I MISCELLANEOUS TOPICS VII.1~~

~~The geyser, a new detector for nuclear recoils~~

~~B. HAHN, H.W. REIST Department of High Energy Physics, University of Berne, Switzerland~~

With the aim of detecting very rare nuclear processes e.g. spontaneous nuclear fission (possibly from superheavy elements) , energy transfer to nuclei in high energy collisions and the detection of so far undiscovered heavy objects in cosmic rays or at high energy accelerators, a massive and continuously sensitive counter has been developed. Such a counter must be completely insensitive to all other radiations except for heavy recoils. We describe a new method with a liquid system of extreme simplicity. Since the liquid jumps up at each event, the detector might be named "geyser".

The detector is a glass vessel filled with a suitable liquid (e.g. alcohol). The liquid is superheated by cooling the vapor phase above the liquid surface (for the case of alcohol the liquid being near 60°C, the vapor near 10 C).Several kg of the desired substance can be dissolved in the alcohol. Bubble nucleation occurs for recoil particles with large ionizing power and with sharp threshold sensitivity. When the bubble arrives in the container neck, the vapor recondenses at the cold glass wall and the metastable state of the system is automatically re-established. The events can be recorded easily either electrically from a pressure pick-up or by photographing. A pure alcohol geyser of 20 1 showed no background events during several days, calibration curves for spontaneous fission will be shown.

~~•191- VII.2~~

~~HIGH RESOLUTION APPARATUS FOR 600 MeV ELECTRON SCATTERING PH. LECONTE J. BELLICARD. DPhN/HE, CENSaclay (France)~~

-4 A "zero count" resolution limit has been found at 2. 1 x 10 -4 -4 A wide opened system allows 3. 1 x 10 and 4. 0 x 10 for 400 MeV and 200 MeV electrons respectively. The corresponding transmission The tot rate of slit is then in the range of I. to 5. percent. _4 of 9.6 and 6 Analysis of the components of the resolution (FWHM) in 10 units: It is s parate nucle Monochromatic spot size on the slit ' 1. Distrib Slit aperture 1. angles are c Slit transparency 0. 3 Field stability of the analysing magnet 0. 2 A comps Spot size on the target 1. with nuclei. Spot stability on the target 0. 1 Straggling in the target 0. 7 Windows after target - straggling effect 0. 2 - multiple scattering 0. 5 Field stability in the spectrometer 0. 1 Spectrometer resolution 1. 5 • Detector on focal plane position 0. 5 •Detector size .^ ;*" J^^y;j«v 1.5 • Kinematic broadening ( U ) 0. 1

~~-192- VII.3~~

~~Total Decay of Ag and Br Nuclei Induced by 10 and 70 GeV/c Protons~~

~~R.A. Khoshmukhamedov and K.D. Tolstov Joint Institute for Nuclear Research, Dubna, USSR~~

The total decay of Ag and Br nuclei, induced by the protons with momenta of 9.6 and 69 GeV/c, is studied. It is shown that the decay without a residual nucleus and mainly into separate nucleons takes place. Distributions of secondary particles over charges, energy and emission angles are obtained. A comparison is made with the models of interaction of fast particles with nuclei.

~~-193- VII.4~~

~~A THEORY OF INELASTIC INTERACTIONS BETWEEN RELATI7ISTIC IONS AND NUCLEI~~

~~V.S.Barashenkov, K.K.Gudima, F.G.Gereghi, A.S.Iljlnov, V.D.Toneev Joint Institute for Nuclear Research Dubra, USSR~~

The model of intranuclear cascades is used to describe the inelastic collisions of deuterons, Q^-particles and the heavier nuclei with the nuclei of different targets in an energy range from several tens of MeV to several ten* of GeV per projectile nucleon. In the region of energies higher than several GeV/nucl. and at lower energies in the case of colliding heavy nuclei, one should take into account a decrease in the density of the number of nuclear nucleons in the course of the cascade development* In the collisions of heavy nuclei the simultaneous development of cascade takes place in both the target nucleus and m the projectiles. ims Though the calculations account for the space-time positions of each nucleon and all cascade particles inside the nucleus, they require a reasonable amount of computer time* The calculated results agree with the experimental data obtained in cosmic space and using accelerators.

~~-194- VII.4 VII.5~~

~~FISSION OP HEAVY NUCLEI BY HIGH-ENERGY PARTICLES V.S.Barashenkov, F.G.Gereghi, A.S.Iloinov, V.D.Toneev Joint Institute for Nuclear Research Dubna, USSR~~

•§f A statistical Monte-Carlo method is developed for calcula- be the ting the decay of excited nuclei produced by high-energy par- .eavier ticles during the competing processes of particle evaporation range i 1 and fission* The method is based on the semiphenomenological ctile M approximation of fission barriers which includes the smooth V/nucl. 1 liquid-drop part, shell corrections and pairing and other odd- .ei, even effects* ' the In spite of the general opinion, th« width ratio T^/fr la Levelop- shown to depend strongly upon the excitation energy* In experi- deve— ments with heavy-ion induced reactions some average quantity ( and Ir!\-\l3 usually measured which appears to be practically constant in both experiment and theory* The fission cross sections, the yields of different isoto- i the pes and the distributions of fissioning and evaporating nuclei over excitation energy and mass and charge numbers are calculated and compared with the experimental data for an energy range of 100 MeV+30 GeV* Though the calculation agrees well with experiment, at energies exceeding several GeV one should take into account a decrease in nucleon density in the target nucleus during the development of intranuclear cascade initiated by the projectile* -

~~-195- VII.6~~

~~FION DOUBLE CHARGE EXCHANGE ON H NUCLEI Yu.A.Batusov,G.Ganzerig,I.V.£>udova,B.F.Osipenko,V.M.Sidorov, V.A.Khalkin,D.Chultem~~

~~Joint Institute for Nuclear Research,DubnatUSSR~~

~~ABSTRACT~~

The pion double charge exchange reactions: dr -f 7Bc —*• ;.+ CT~ + xn, on BLnuclei have been studied. Astatine isotopes or a daughter FQ product have been identified by detecting oC -particles and by measuring their energies. The cross section of the at* + 2p9Bt.-^2o9~acAt+ Of" + 2.H reaction has been obtained to be (12 + 3)x 1O~29 cm2. The upper limit for the cross section of pion elastic double charge exchange on BL nuclei has been found to be equal to410"29 cm2. A possible mechanism of21&1 "Atproduction by the reaction

~~has been considered.~~

~~-196- VII.6 VII.7 TOTAL MIXING OP ROTATIONAL BANDS IN THE TRANSITIONAL REGION B. S. Nielsen and C. S0ndergaard Physics Laboratory Royal Veterinary and Agricultural University, Copenhagen~~

It has been shown ' that several levels in odd N isotopes of W and Os can be described in terms of strongly Coriolis mixed rotational bands built on the 2~[51°] and- 2~[512] orbitals. Energies, B(E2) values, and cross sections for neutron transfer reactions are all well reproduced. In the present study, it is pointed out that the B(E2) values imply quadrupole moments equal to those of the neighbouring even isotopes, while Coriolis matrix elements calculated using the even isotope value of the moment of inertia must be reduced considerably in order to obtain agreement with experimental results. 1 ClC A Q.*7 •! QQ In the case of W and ' Os the excitation energy sequence for the two bands shows a systematic behaviour which can be formulated as EL.(l) = EL (i-i). Such a pattern, also observed for other transitional isotopes, are theoretically reproduced when two AK = 1 bands are strongly Coriolis mixed due to a small energy difference between band heads, provided the following condition is fulfilled: K±1 PK±1,K~ A Here A is the rotational constant of the neighbouring even isotopes, the T| factors describe the Coriolis attenuation, P is the pairing factor, and A the unperturbed rotational constant for the two bands. For Os the approximate degeneracy is shown in Fig. 1. The calculated energy values are given in parantheses. For strong coupling the mixing amplitudes for the perturbed band members become almost equal to i\lo.5 (total mixing). The phenomenon is illustrated in Fig. 2, where calculated BIE2) Ratios . intra-band to inter-band 7»" •••(735.31 B(E2) ratios are shown. The 10 symbol 3111/3133 represents 1 I5u.ll

~~Experimental values are indi- J0 cated by heavy lines. The ° 1.0 limiting values for complete mixing are shown by arrows. -71.tl7G.tl 5 -75.U79.il~~

~~-9 817.11 1) C.Sendergaard, B. S. Nielsen, L 0.1 _L P. Kleinheinz and P. Morgen, 0.5 1.0 .1-5 to be published. Fig. 1 Fig. 2 VII.8~~

~~TITLE : Interaction of accelerated high energy heavy ions (0 at 2,1 GeV/nucleon) with nuclear emulsion nuclei~~

AUTHORS : R. PFOHL, R. KAISER, J.P. MASSUE, D. PRAMANOUKIAN, M. JUNG, J.N. SUREN, R. SCHMITT, P. CUER F. FERNANDEZ, J. MEDINA, A. DURA, J. SEQUEIROS, V. GANDIA, J.M. BOLTA, J.L. RAMON Lab. de Physique Corpusculaire - Universiti de Stras- m bourg (France) f Lab. de Fisica Corpuscular - Facultad de Ciencias - Univ. Autonama de Barcelona (Spain) Instituto de Fisica Corpuscular - Facultad de Ciencias de Valencia (Spain)

ABSTRACT : Since August 71 high energy heavy ion beams (C-N-O-Ne) are available at the Bevatron (Lawrence Berkeley Laboratory) . Several stacks of different kinds of nuclear emulsion have been exposed to carbon and oxygen beams. The stars observed in the nuclear emulsions correspond to the interactions of the incident ions with the target nuclei. From the study of the stars preliminary results are given such as mean free paths, fragments and evaporation products distributions, angular distributions, fragmentation parameters. The results are compared with those obtained by the study of the interactions of cosmic heavy ions in the same range of energy.

-198- VII.8 VII.9 A Study of Nucleus-Nucleus Interactions Produced by Heavy Nuclei (12 1 GeV/Nucleon. " B.Jakobsson, R.Kullberg and t.Otterlund. Department of Cosmic High Energy Physics, University of Lund, Lund, Sweden. :AN, This investigation is based on 82 interactions between heavy cosmic ray primaries and emulsion nuclei. In accordance with investigations of p-N interactions we have found that in N-N interactions target helium nuclei are often emitted with much higher energies than can be expected from any stras- evaporation model. Table 1 shows some characteristics of these fast helium nuclei (Ej, > 40 MeV). Obviously several fast heli- is - um nuclei can be emitTed'in the same collision when the target nucleus is completely disintegrated. Fig. 1 shows the angular '" distribution of the fast helium Lencias Table 1 nuclei for different incident energies. The anisotropy seems

to decrease with increasing prima- N He He (MeV/n) (DEGREES) ry energy. The emissi'on of heli- 1 um nuclei is also studied in in- 0 7 ± 1 _ teractions produced by heavy ions 1 15 ± 2 24 ± 4 78 ± 8 of 2.1 and 0.2 GeV/n from the N-O-Ne) 2-3 27 ± 2 27 + 4 61 ± 8 4- 33 ± 2 . 43 ± 8 62 ± 6 Berkeley Bevatron. ry) . The angular distribution of the e been shower particles is shown in Fig. 2. The ir-mesqn spectrum can be described by the relation N=a exp (bcos6)+c exp(dcosO). In the Table 2 the parameters obtained in some investigations are shown. ncident Table 2 • &kMSc • :. , . • . • • preli- Type of ; b d interaction F.nergyi 5p; - •; a c ts and N-N =5GeV/n O..6iO.l 1. 3+0.3 (2 .6 |jj10" 10.2?1 ,4

, frag- 2.3 Gel' 3.4±2.0 3. 4 + 0-6 9 jio 11. P-N -0.4 (2 - -!:l ~* 2*1is +0.S obtai- p-N- 20 GeV 1.3+0.6 1. R ,5±4jin 19. Sil .0 8-0.3 (S + 0.7 in 7T-X 60 GeV 0.9-M1.4 2. +0.8)10"' 21.4il .0 -0.3 fl

~~(MtOUUZED 10 THE 5AME NUWER OPfMTKLES M«E«100Mrt) t CBOaS HATCHED *KEAaH«-nuclri ' W1H E*J0O M* "~~

~~3D CO » 130 190 in Fig.l EWSSW WU (DEWCES) Fig. 2~~

~~-199- INDEX OF AUTHORS~~

Adamovic 0 37 Bergstrom I 146,148 Agassi D 99 Bernabeu J 21,133 Alberg M 151 Bernas M 126 Alberi G 40,41,42 Berovic N 147 Albu M 51,54 Besliu T 51,54 Alexander Y 89 Beusch W 29,34 Alladashvili B C 85 Beveridge J 5 Allardyce B W 65,66,67,68 Bianchi G 171 Alster J 76,172 Bingham H H 9 Amiet J P 74 Bird L 80 Amirkhanov IV 10 Bizard G 114 Anjos J C 120 Blecher M 61 Arlt R 141 Bleszynski M 119 Ascoli G 30 Boffi S 186 Ashery D 76,172 Bolta J M 198 Astbury P 29,34 Bonazzoia G C 122 Aswad A 137 Bongardt K 121 Auerbach N 76 Bonthonneau F 114 Auger J P 163 Boschitz E T 156 Auld EG 5 Boyard J L 126 Axen DA 5,47 Bressani T 122 Brody H 118 Bachelier D 126 Bruton PC 35 Backe H 140 Buchanan C D 164 Backenstoss G 136,146,148 Bunaciu T 148 Badetek B 13 Bunyatov S A 6,144 Baldini-Celio R 38 Bussiere A 170 Bamberger A 12,148 Banaigs J 39,113,116,117 Cage M E 65,66,67,68 Banerjee M K 63 Calogero F 187 Barashenkov V S 194,195 Camani M 135 Barnes P D 14 Cammarata J B 63 Bar-Nir I 115 Cannata F 133 Baroni G 37 Carlson P J 77 Barroso A 165 Carroll J B 20,145 Barton H R 30 Cester R 122 Barshay S 62 Charquet B 37 Bastien PL 9 Chemtob M 17 Batty C J 65,66,67,68 Cheon Il-T 112 Batusov Yu A 6,144,196 Chernev Ch 144 Baugh D J 65,66,67,68 Chiavassa E 122 Baumann G 37 Chirapatpimol N 20 Belli card J 192 Chultem D 196 Bellini G 29 Ciofi degli Atti C 86,185 Bellotti E 15 Clough A S 65,66,67,68 Bemporad C 29,34 Cochavi S 76,172 Bengtsson R 174 Comparat V 88 Bercaw R C 61 Coombes H 176 Berg R E 105 Cottereau M 39,113,114,116,117 Berger J 39,113,114,116,117 Cox C 75 Berggren T 174 Craig J N 105

-120- Cuonon J 112 Freschi D 122 Curran C S 35 Fretter W B 9 CUer P 37,178,198 Freudenreich K 29,34 Fried!ander S 176 Daniels J M 176 Fried lander EM 37 Davies J K 35 Fritsch W 184 Debrunner P 16 Fritz D 16 Dellacasa G 122 Fujii A 131 Deloff A 11 Funsten HO 155 Dennig E 176 Desplanques B 17 Gabathuier K 75 Devienne R 37 Gajdicar T 176 Dillig M 107 Gal A 99 di Corato M 29 Gandia V 198 Dixit M 20,139 Ganzerig G 196 Dollhopf W 109,177 Gardes J 87 Domingo J 75 Garfagnini R 51,54 Dubai L 80,108 Genin J P 171 Dubnicka S 48 Gentit F X 29,34 Dudova IV 196 Georgescu C 55 Duesdieker G 5,47 Gereghi F G 194,195 Dufey J P 34 Gennond J F 74 Duflo J 114 Giliebert A 170 Duggan F 94 Glagolev V V 85 Dumbrais 0 V 10,48,49,52 Goggi G 127 Dunn LA 9 Goldfarb L J B 91 Dura A 198 Goldhaber A S 27,70,96,167 Duval P 171 Goldzhal L 39,113,114,116,117 Golovin B M 84 Eckhause M 14,138 Goulard B 143 Edwards V R W 168,169 Gowfow K 61 Egger J 135,146,148 Graves W R 9 Eisenberg .J M 64,106 Green AM 3 Eisenstein R ,A 14 Gregorio M 42 Ekelof T 35 Gross F 81 Engelhardt D 156 Groves J L 58 Engfer R 140 Guardiola R 86,175 Eramzhi an R A 137 Gudima K K 194 Eriksson M 159 Gulkanian G R 6,144 Evseev V S 141,142 Gurtu A 43 Ezrow D 105 Gustafsson C 174 Fabbri F L 38,39,117,119 Haapakoski P 3 Faessler M A 12,123 Hadjimichael E 165 Fainberg A 122 Hagberg E 35 Faldt G 31, 32,71,92 Hagelberg R 136,146 Falomkin I V 51,54,55 Hahn 8 191 Felawka L 5,47 Halliwell C 80 Fernandez F 198 Hargrove C K 80,108,139 Feshbach H 95 Harris R 9 Fiorini E 15 Haupt H 141 Fisher S M1 35 Hebert J 37 Fox J D 14 Heinzelmann G 123 Frahn W E 97,98 Henley E M 151 Frascaria R 88 Herriander C J 136,146 Frauenfelder H 16 Herz A J 35

-121- eymann F F 35 Korenman G Ya 152 ,154 KTricks E P 80,108 Kosarev G E 179 Ho-Kim Q 183 Kossler W J 155 Holloway L E 30,58 Krebs G F 176 Holmgren H D 105 Kropf A 22 :Kruse~U ti 30•_ Hornstein 0 81 Kubodera K 19 Hsieh C S 145 Kujawski ..Es 100,101 Huang KN 135 Kullander S 35 Huang Haw 93 Kul1 berg R; 199 Huber M G 107 Kulyukin M 51,54,55 Hughes; V W 134,135 Kunselman A R 14 Hultberg S 148 Hwang C 16 Lai S 44 Lam W C 14 Iachello F 153 Lambiert E 100,101 Igo G J 20,78 Lamers B A 125 Iljinov A S 194,195 Lamers G B 125 Imrie DC 35 Landau R H 61 Ingram C H Q 5,47 Lande A 153 Larson D A 108 Laville J L 114 Jacobsson B 199 Lazard C 126 Jager H U 137 Lebedev R M 85 Jarlskog C 21 Le Brun C 39,113,114,116,117 Jamie N 16 Leconte Ph 192 Jenkins DA 14 Lee J G 29,34 Johnson R R 5,47,61 Lefebvres F 114 Jones G 5,47 Le Meilleur F 87 Jonsson G G 159 Leon M 149 Joseph J 143 Leonardi R 132 Jourdai n J C 126 LePatourel D 5,47 Julien J 171 Lesniak H 59,60 Jung M 198 Lesniak L 59,60 Juric M 37 Letheren M 29,34 Letourneau R 171 Kairies K 176 Levy D 120 Kaiser R 37,198 Lewis C U 156 Kalinina N A 23 Lewis M L 135 Kane J R 14,138,145 Lind V G 155 Kankeieit E 140 Lipperheide R 184 Karamanoukian D 198 Liu W K 58 Karapetyan V V 154 Lombard R J 163 Kessler D 108,139 Londergan J T 72 Khalkin V A 196 Lory J 37 Khamraev F Sh 84 Lovoi P 16 Khanna F C 182,183 Lubatti H J 8,9 Khoshmukhamedov R A 193 Lucas C W 125 Kilian K 123 Lunke C 109,177 Kirkby P 176 Lush G J 35 Kissener H R 137 Lykasov G I 84 Kitching P 109,177 Lynen U 12,123,148 Koch H 136,146,148 Lyashenko V J 51,54,55 Koester L J 30,58 Kohyama Y 131 Ma?ecki A 33 Komarov VI 179 Malherbe J C 114 Kopeliovich V Z 50,110 Mamedov T N 142

~~-122- Mantovani G C 127 Osipenko B P 196 Mari6 Z 126 Otterlund I 37,199 Marty N 88 Overseth 0 E 79~~

Massue J P 37,198 . Pacati F D 186 McCaslin_J 80; ._ Padjen R McDonald W" 0^65,66,67; 68 i Palmeri A>- McKee R J: f^6VlO8,l39 v Palumbo FV rl87 'J:?i, V : McKibben J ?•• Pascual P^ 175 McVoy K W: .73: > Paul H .:^'22 Medina J 198 fPauty J Fr "87 Merited! •87 iPedroni E- 75 Mes H;r 80,108,139 'Pelliceri 37 Meton C * 37 Perdrisat^CIF 109,177 Michaelsen R 140 Perez-Mendez V 20 MihuUA 51,54,55 PetroyN I 181 MillerGH 138 Peynet G 87 Miller J 14 PfohlR 198 Milder R A 81 Piazzoli A 127 Minehart R C 61 Picchi P 119 Mirfahk^ai N 122 Picdzza P. 38,39,117,119 Mirsalikbva F 144 Phillips A C 158 Mifchke R 16 Piekartz H 12,123 Moiriester MA 76,172 Piekartz J 11,12,123 Moniz E J 72 ; Pietrzyk B 123 Moriyasu K 8,9 Piketty C A 18 Morlet M 88 Pilkuhn H 92,121 Morrison R 80 : Piragino G 51,54,55 Mougeot A 171 Plendl H S 155 Mougey J 170 Plouin F 114 Mueller R 0 134 Pniewski J 12 Muhlemann P 29,34 Podolsky W J 9 Murphy J D 166 Pol gar E 29,34 Murtazaev Kh 10 Pontecorvo G 51,54,55 Musso A 122 Popov V P 154 Myhrer F 150 Poropat P 40 Myrianthopoulos L 108 Potashnikova IK 110 Potter J 16 Nadejdin V S 181 Povel H P 136,146 Nagl A 124,125 Povh 3 12,123 Nagle D 16 Price R H 146 Namysfowski J M 82,83,91 Priest J R 109,177 Nassalski J 85 Priou M 170 Nasser M 20,78 Pyle G J 65,66,67,68,147 Negri P 15 Nichitiu F 48,49,51,52,53,54,55,56 Querrou M 87 Nielsen B S 197 Nioradze MS 85 Radvanyi P 126 Noble J V 106 Ragnisco 0 187 Nodulman L J 30,58 Rambaut M 171 Nomofilov A A 57 Ramon J L 198 Rand R E 164 Ohlsen G 16 Ravenhaii D G 58 Olsen WC 109,177 Redish E F 173 Ortendahl D 20 Regimbart R 114 Orth R 5 Reist H W 191 Orthlepp G H 141 Remler E A 81

-123- Wenr Reshetnikov G P 179 Smith J H 30,58 Rey G 37 Soergei V 12,123 West Rho M 19 S0ndergaard C 197 Wetmi Riddle RAJ 65,66,67,68,147 Sorensen L 16 Wile Rinat AS 89 Spence C B 145 Wiik Rinaudo G 122 -,- s- iV= :*. Squier G T-A 65>66,67,68,147 WiU< RisserT Xn3,1l5;n6ni7 -•": StepaniakJ 13,85 -,-".•-*' r Will Ritteiv-H-G* 12,123,148 ^ iStephenson^JrrG 173 > •_>.. Will* Roberts BL ^14,138 ;• Sternheim--M M 111 Wojs' Roberts W K 109,177 i -Stets A" 20 > 7 Wu C! Robertson LP 5,47 Stevens R 16 Wu C Roganov V S 141 Streltsov V N 85 Rohlin J 75 Stronach CE 155 Yavii Roig F 158 Strunov L N 57 Year Rosa L 41 Stutte Lr;9 Yoko< Rosenthal H 134 Subramanian A 43,44 Yost Rostokin V. 62 -Sufen J N 198 Rotter I 180 Sutton^ R B 14 Oben Rouben B 182 Royer D 170 Tanner N 75 Zaid< Tauscher L 136,146,148 Zainir Sabirov B M 141 Tedder P W 168 Zehrii Saitov I S 85 Tesch S 179 Ziei- Sakamoto Y 178 Thome Z 42 , Ziocl Salomon M 5,47 Thompson AC 80,108,139 Zul'l Samour C 171 Timonina A A 23 Sandacz A 85 Toistov K D 193 Santoro A 120 Toneev V D 194,195 Sapp B 145 Tsai-Chli 37 Sararu A 55 Turchetti G 4 Satarov VI 181 Turner G K 65,66,67,68 Savchenko 0 179 Scannicchio D 127 Ullo J 95 Scherbakov Yu A 49,51,52,53,54,55 Ullrich H 156 Scheuwly H 140 Schiaile H G 92 Vagradov G 62 Schmitt R 198 van Oers W T H 93 Schroder W U 140 Vazeille F 87 Schueriein B 123 Vegni G 29 Schune D 37 Vincent J S 61 Schlirmann B 97,98 Vinciguerra D 171 Schwaiier P 75 Vizireva L 144 Schwitter A 136,146,148 von Egidy T 136 Seki R 69,149 Vu-Hai L 39,113,114,116,117 Sequeiros J 198 Vyas P 44 Shamai Y 172 Shahbazian B A 23 Wagner A 123 Shuster M D 115 Walenta AH 123 Sick I 170 Mall N S 105 Sidorov V M 6,144,196 Walter H K 140 Siebert H W 123 Walters J 80 Siemiarczuk T 85 Warszawski J 76 Silbar R R 111 Watsun L H 65,66,67,68 Sinha B 94,168 Weber H J 64,106 Sitnic I M 57 Websdale D 29,34 Slepetz LA 57 Weise W 90 Smith A 80 Welsh R E 14,138,147

-124- Werntz C 125 Westlund 1W 5,47 Wetmore R J 145 Wilets L 151 Wilkin C 75 Wilie U 184 Willis A •,88J ^.*-.-. -: WilTotvB 37 r Wbjslaw R 30 vr • : Wu Chao A 961 w " C S ;t Yavin'A I 76,172 Yean an M R 164 Yokosawa ;A 7 Yos^G- 9

~~Oberall H 124,125,166~~

~~Zal^er: M 76,172 ZaTinidorpga 0 34 Zehfider A 140 Zielinski P 13 Ziock K 0 H 157 Zul'kErneev R Ya 10~~

~~-125-~~