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Average Beta and Gamma Decay Energies of the Fission Products

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Average Beta and Gamma Decay Energies of the Fission Products AN ABSTRACT OF THE THESIS OE Chi Hung Wu for the degree of Doctor of Philosophy in Nuclear Engineering presented onAugust 10, 1978 Title: Avera e Beta and Gamma DecaEner ies of the Fission Products Abstract approved: Redacted for privacy Bernal& I. Spinrad One method of predicting the decay-heat is the "SummationMethod" in which the power produced by decay of each fission product at time t after shut-down is calculated. The reactor shut-down power produced at time t is then obtained by summing over all of the fissionproducts. An accurate determination of the average beta and gamma decayenergies is essential for the success of this method. Out of approximately 850 fission products, there are only about 150 whose beta and gamma decay energies have been measured. The rest were predicted by a fitting formula in whichthe ratio of decay energy to beta-decay Q value is taken as a linear sumof terms in mass number, charge number, and nuclear pairing energy; the coefficients weredeter- mined by a least-squares fit to known data. Instead of fitting, the average beta and gamma decay energies can be calculated theoretically. Nuclear models, such as the shell model and the collective model, can predict the first fewlow-lying excited states quite well on the average. On the other hand, the statistical model can be used for higher excited states, which we can approxi- mate by assuming that the states form a continuum. The probability of beta decay can be taken as proportional to E5p, where E is the beta end-point energy and p is the angular- momentum-dependent level density. If the parent nuclide's ground state spin and parity are known, then for allowed beta transitions (AJ = 0, ±1, no parity change) in the continuum, the average beta end-point energy and level density (at that end-point energy) for each LJ can be calculated, In the continuum, first forbidden tran- sitions (AJ = 0, ±1, ±2, yes parity change) are negligible compare to allowed transitions. However, for the discrete region (low- lying states), first forbidden transitions may be competitive, and they must be taken into consideration when necessary. By the above procedure, a fictitious beta decay level diagram for each nuclide was constructed and its average beta and gamma decay energies per disintegration could be computed. One hundred and thirty-six nuclei, which have experimental measurements, were subjected to this theoretical calculation. When calculated values (E + E ) were compared to experimental values for those nuclei, the differences between calculated E+ E and experimental E+ E divided by their Q values are found to be a normal distribution with one standard deviation (o) of 0.1567 (for E + E , then a = 0.1567Q). By this method, beta and gamma decay energies and their uncertainties can therefore be determined without bias and fairly precisely. Two summation method calculations were performed using ROPEY, a summation method code which was developed and used at Oregon State University. Treating other input parameters, namely, half- lives, branching ratios, and independent nuclear fission product yields as fixed, decay-heat calculated by using results of this study (E+ E ) compared better than a calculation using the exist- ing Evaluated Nuclear Data File B-IV (ENDF/B-IV) did with the American Nuclear Society (ANS) Decay-Heat Standard for the decay time between 1 and 60 seconds. Between 60 and 10,000 seconds of decay time, experimental data dominate the results, which are virtually identical. Average Beta and Gamma Decay Energies of the Fission Products by Chi Hung Wu A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Completed August 10, 1978 Commencement June 1979 APPROVED: Redacted for privacy Professor of Nucleir Engineering in charge of major Redacted for privacy Head of Department of Nnkear Engineering Redacted for privacy Bean of Graduate School Date thesis is presented August 10, 1978 Typed by Sue Wu for Chi Hung Wu ACKNOWLEDGEMENT I would like to take this opportunity to thank my major professor, Dr. B. I. Spinrad, for his guidance and encouragement for the last two years. I feel very fortunate to have him as my advisor; he demands hard work as well as creative thinking, which had made my learning experience very rewarding, even though at times I felt frustrated. I would also like to thank my committee members Dr. E. J. Dasch, Dr. K. Hornyik, Dr. V. A. Madsen, and Dr. J. C. Ringle for helping me set up the proper study program. Finally, my wife's effort in supporting my studies and typing the thesis is greatly appreciated. This work was performed as part of USNRC contract 11 AT(49-24)-0157 through a research assistantship which made it possible to complete my program. TABLE OF CONTENTS Chapter Page INTRODUCTION 1 1.1 Decay-Heat of a Fission Reactor 1 1.2 Decay-Heat Summation Methods 4 1.3 Goal of this Dissertation 5 II. BETA DECAY THEORY 10 II.1 Introduction 10 11.2 Beta Decay Q Values 10 11.3 ft Values 11 11.4 Selection Rules 13 III. NUCLEAR MODELS 15 III.1 Introduction 15 111.2 The Deformed Shell Model 15 111.3 The Collective Model 18 IV. NUCLEAR LEVEL DENSITIES 23 IV.1 Introduction 23 1V.2 Theoretical Considerations 23 1V.3 Determination of Parameters 25 1V.4 Discussion of the Parameter a 29 V. ALGORITHM DEVELOPMENT 32 V.1 Introduction 32 V.2 Ground State Spin and Parity 34 V.3 Metastable States 35 Chapter page V.4 Beta Decay Q Value 36 V.5 Departure Energy (Ed) from Discrete Region to Continuum 36 V.6 Discrete States Region 38 V.6.1 Even-Even Nuclei 39 V.6.2 Odd-A Nuclei 39 V.6.3 Odd-Odd Nuclei 39 V.7 Continuum Region 40 V.8 Average Beta and Gamma Decay Energies per Disintegration Calculation 42 V.9 Procedures 46 VI. COMPARISON WITH EXPERIMENT 49 VI.l Introduction 49 VI.2 Normal Distribution of xn 58 VII. COMPARISONS OF SUMMATION CALCULATION RESULTS 62 VII.1 Introduction 62 VII.2 Comparisons of Decay Power Predictions 63 VII.3 Uncertainties 75 VIII. CONCLUSIONS 77 REFERENCES 79 APPENDICES 84 LIST OF FIGURES Figure Page 1-1 Binding energy per nucleon as a function of mass number 2 1-2 Uncertainties in summation calculations of decay power 3-1 Level diagram derived from Nilsson's spherical Hamiltonian 17 3-2 Schematic vibrational energy-level diagram of even-even nuclei 20 3-3 The energy E2+ of the first excited 2+ states in even-even nuclei 21 3-4 The energy E3_ of the 3- collective vibrational states in even-even nuclei 22 4-1 a/A vs. the total shell corrections 30 235 5-1 Post-neutron-emission mass distribution of U fission 33 5-2 A typical fictitious beta-decay level diagram 48 6-1 Cumulative normal curve for ET 53 6-2 Cumulative normal curve for E 54 6-3 Cumulative normal curve for 0 55 6-4 Calculation of probabilities 1( 60 7-1 Ratio of ORNL corrected decay energies (beta or gamma) to ENDF/B-IV decay energies expressed in terms of Ho(t)(pulse irradiation 235U decay power) 64 7-2 Ratio of ORNL corrected decay energies (beta or gamma) to THIS STUDY decay energies expressed in terms of Ho(t) 66 7-3 Ratio of ENDF/B-IV decay energies (beta or gamma or sum) to THIS STUDY decay energies expressed in terms of Ho(t) 68 7-4 Ratio of ENDF/B-IV decay energies (beta or gamma or sum) to THIS STUDY decay energies expressed in terms of H1(t,e0)(infinite irradiation 235U decay power) 70 7-5 Ratio of Summation Method to ANS Standard expressed in terms of H1(t,co) 72 LIST OF TABLES Table Page 2-1 Beta decay selection rules for allowed and first forbidden transitions 14 4-1Pairing energies and shell corrections for protons .. 27 4-2 Pairing energies and shell corrections for neutrons . 28 6-1 Theoretical and experimental decay energies 50 6-2 Calculation of standard deviations 56 6-3 Calculation of the x2 59 7-1 Beta and gamma decay energies from ORNL and ENDF/B-IV expressed in terms of Ho(t)(pulse irradiation I35U decay power) 65 7-2 Beta and gamma decay energies from ORNL and THIS STUDY expressed in tetms of Ho(t) 67 7-3 Beta and gamma and total decay energies from ENDF/B-IV and THIS STUDY expressed in terms of Ho(t) 69 7-4 Beta and gamma and total decay energies from ENDF/B-IV and THIS STUDY expressed in terms of Hi(t,co)(infinite irradiation 235U decay power) 71 7-5 Total decay energies from ANS, THIS STUDY and ENDF/B-IV expressed in terms of Hi(t,c.) 73 7-6 Uncorrelated energy uncertainties in Ho(t) and H1(t,e0) functions 76 APPENDICES Appendix page I. Parameter Sc 84 II. Ao, Al, A2 Values 86 III. A Tabulation of Fission Product Decay Energies 88 IV. Computer Programs 106 AVERAGE BETA AND GAMMA DECAY ENERGIESOF THE FISSION PRODUCTS I. INTRODUCTION I.1 Decay-Heat of a Fission Reactor (1) Hahn and Strassmann were the first to establish that uranium, when bombarded with neutrons, splits into lighterelements with about half the atomic number of uranium. The phenomenon of a nucleus undergoing a division into twomore or less equal fragments, either spontaneously or induced bysome projectile, is termed binary fission. Less frequently, division into three fragments has also been observed; this is calledternary fission.
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