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Photodisintegration of Calcium-40 David Walter Anderson Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1965 Photodisintegration of Calcium-40 David Walter Anderson Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Nuclear Commons Recommended Citation Anderson, David Walter, "Photodisintegration of Calcium-40 " (1965). Retrospective Theses and Dissertations. 4075. https://lib.dr.iastate.edu/rtd/4075 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. This dlsseriatton has been microfilmed exactty as received "* ANDERSON, David Walter, 1937- PHOTODISINTEGRATION OF CALCIUM-40. Iowa State University of Science and Technology Ph.D., 1965 Physics, nuclear University Microfilms, Inc., Ann Arbor, Michigan PHOTODISINTEGRATION OP CALCIUM-40 David Walter Anderson A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Physics Approved: Signature was redacted for privacy. Major Work Signature was redacted for privacy. Signature was redacted for privacy. Iowa State University Of Science and Technology Ames, Iowa 1965 il TABLE OP CONTENTS Page I. INTRODUCTION 1 A. Historical Background 1 Ilq B. Motivation for a Ca Experiment 3 C. Outline of the Experimental Technique 5 II. THEORETICAL CONCEPTS 7 A; Outline of Multipole Radiation 7 1. Definitions 7 2. Expansions 8 3. Transition probabilities - nuclear emission and absorption 9 4. Estimation of transition strength 10 B. Sum Rules 11 1. Integrated cross section - zero exchange mixture 11 2. Exchange forces - brems strahlung weighted integrated cross section 15 C. Hydrodynamical Model l6 1. Formulation of the problem l6 2. Solutions 17 3. Energy relationships 21 D. Shell Model 23 1. General review 23 2. Giant resonance 24 3. Residual interactions 24 4. El overtones - Ml and E2 transitions 25 Ill Page III. APPARATUS 27 A. Synchrotron 27 B. Detectors and Shielding 29 C. Experimental Timing 34 D. Delay and Gating 37 E. Discriminators and Coincidence Circuit 37 P. Analyzer and Staircase Generator 4l G. Dosage Monitor 43 H. Sample 45 ' IV. PEOCEDUEE 4$ A. Modes of Operation 49 1. Equations 49 2. Production 54 3. Counting 55 B. Pre-ezperimental Checks 59 C. A Typical Run _ 62 D. Post-experimental Checks 65 V. ANALYSIS OP DATA 68 A. Activation Method - Yield Function 68 B. Computer Techniques - Corrections 70 C. Effective Decay Constant 74 D. Yields 77 E. Data Treatment and Errors 79 P. Least Structure Analysis 83 17 Page VI. SYSTEMATIC EHEOES AND TESTS 90 A. Beam Swing 90 B. Beam Size - Dead Time - Bandom Coincidences 93 C. Gain Shifts - Discriminator Level Shifts 99 D. Extraneous Eeactlons 101 E. Integrator and Electrometer 103 P. Analysis 104 VII. HESULTS AND DISCUSSION 118 A. Experimental Besuits 118 B. Theoretical Predictions 126 VIII. CONCLUSION 132 IX. LITEBATUBE CITED 134 X. ACKNOWLEDGMENTS 139 V LIST OP PIGUBES ige Experimental set-up 30 Circuit for photomultiplier and White follower 32 Block diagram of electronic apparatus 33 Experimental timing 35 Circuits for programmer and gate 36 Circuit for delayed pulse generator 38 Gain shift of detectors after bombardment period 39 Circuit for discriminators and coincidence system 40 Photographs of the display of the analyzer memory 42 Circuit for staircase generator and reset unit 44 Circuit for dosage discriminator 46 Circuit for control unit 47 4o Decay scheme for major Ca photoproducts 50 4o Effective decay constant for Ca photoproducts 76 Distribution of chi-squared from background subtraction 78 Yield curves for 0.6z2.4 mode and average of all data 80 Distributions of chi-squared for yield and cross section 82 Reduced yield for average of all data 84 Beam swing comparison and intensity profile 92 Cross section solutions for distorted yields - I 94 Cross section solutions for average yield curves Cross section solutions for individual yield curves vi Page 23. Cross section solution for = 65, 104 and 125 108 24. Cross section solutions for distorted yields - II 110 25* Cross section solutions for distorted yields - Ill 111 26. Reduced yield recalculated from least structure solutions 112 27. Cross section solutions for distorted yields - IV 115-116 28. Resolution function 11? 29. Display of the results of previous ezperiments on Ca^° 125 hn 30. El Single particle transitions for the Ca nucleus 129 Ilq 31. E2-M1 single particle transitions for the Ca nucleus 130 vli LIST OF TABLES Page 1. Batio of transition probabilities for several multipoles 11 2. Solutions to the hydrodyziauioal problem 22 3. Energy ratios for solutions to the hydrodynamical problem 22 4. Overlap integrals for the shell model 25 5. Known photoreaotions in Ca^® 4-9 6. Fractional deviations caused by oversmoothing il4 7. Summary of resonance energies for the giant resonance region 119 8. Summary of resonance energies and strengths 121 1 I. INTRODUCTION A. Historical Background The interaction of high energy photons with the atomic nucleus has been a subject of interest to physicists for more than thirty years. The first study of a photpnuclear reaction was done by Chadwick and Goldhaber in 1934 (1). They used ThC gamma radiation to bombard deuterium. Investigation of the nuclear photo- effect using machine generated electromagnetic radiation did not begin until after 1940 (2). Since then a good deal of work has been done on the nuclear photoeffect in the energy region extending to 30 Mev. This region includes the giant dipole resonance which dominates the photonuclear cross section curves. In recent years the experimental resolution has improved and struc­ ture in the giant resonance has often been observed. Publications by research groups in Canada (3)» England (4), Prance'(.5) and Australia (6) indicate the chronological development of knowledge about the giant resonance region of Ca^®. Articles by Bishop and Wilson (7)» Berman (8) and Levinger (9) present excellent general reviews of the nuclear photoeffect. In 1948 Goldhaber and Teller (10) presented three models for nuclear dipole absorption of electromagnetic 2 radiation. Later papers (11, 12, 13, l4) developed their second model. The nucleus was considered to be composed of neutron and proton fluids which were caused to oscil­ late by incident electromagnetic radiation. The funda­ mental mode of oscillation corresponded to the giant resonance. This interpretation was called the hydrodynami- cal model. After development of the shell model of the nucleus (15) several articles offering a shell model interpretation of the giant resonance were published (l6, 17). In 1959 the residual or particle hole Interaction was proposed to explain the energy of the giant resonance (18). Specific. 40 calculations for the Ca nucleus have been made (19, 20, 21). Studies of photoreaction cross sections in the region beyond the giant resonance have been sparse. Possibly this can be attributed to the limited energy range of the beta­ trons and linacs commonly involved in photonuclear research and to difficulties encountered in the analysis of high energy data. Nevertheless several experiments have been reported which indicate that a good deal of cross section remains to be examined in the energy region above 30 Mev (22, 23). In light of several theoretical papers which predict resonances at energies above 30 Mev (14, 24), a more thorough investigation of this region is indicated. 3 Until recently the techniques available for conversion of the experimental yield into cross section (25» 26) were such that errors in the data often produced oscillating errors in the cross sections. In fact wild oscillations occurred In the cross section when analysis was extended to regions above the giant resonance and when many data points were considered. The least structure technique for conversion of the experimental yield into cross section (27, 28) was developed in 1902 and has been used since then with good results (29). This method enables one to Investigate the region above the giant resonance because the cross section solutions are smoothed, but at the expense of experimental resolution. Lq B. Motivation for a Ca Experiment Sum rule calculations by Levlnger and Bethe (30) give a value for the Integrated cross section for El absorption as, /OG (XgldE = 6o ^ (l+0.8x) Mev-mlllibams. X is the exchange fraction in the nuclear potential (xùil/2). Dispersion theory calculations (31) give, 4 150 Mev CT dE = 60 f(1-^) Mev-millibams * This Integral includes absorption by all multipoles but the additive term is considered to be good to only about 30 per cent» The disadvantage of the first expression is the indefinite upper limit. The disadvantage of the second is that experimental evaluation of the difference between the high energy photon absorption cross section for free nucléons and bound nucléons is necessary. Both of these Ilq calculations give values of 840 Mev-millibarns for Ca . Experimental determinations of the integrated cross J[lQ section for several photoreactions in Ca have been made. Johansson (32) estimates that, '28 Mev Gp dE = 440 Mev-millibams . Lindenberger and Scheer (33) give, '33 Mev (an + gpy, + ^pn^^ ~ ± 1? Mev-millibams. 0 The sum of about $60 Mev-milllbams is far short of the theoretical predictions. One would expect that a signifi­ cant amount of cross section has not been measured when the energy range extends only to about 30 Mev, Recent measurements (23) for Ca^^ give, 30 Mev aE = .27 .^60 , '80 Mev Cm-'Tn dE = .35 (60 f). 30 Mev The cross sections are defined by + 3or^^ + ... This is good experimental evidence for a large amount of cross section in the 30 to 60 Mev region in Ca^®. C. Outline of the Experimental Technique In the main body of this dissertation a thorough dis­ cussion of the techniques involved in the experiment con- 40 ducted at the Iowa State synchrotron on Ca will be given.
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