W&M ScholarWorks Dissertations, Theses, and Masters Projects Theses, Dissertations, & Master Projects 1972 Gamma rays following negative muon capture in medium Z nuclei George H. Miller College of William & Mary - Arts & Sciences Follow this and additional works at: https://scholarworks.wm.edu/etd Recommended Citation Miller, George H., "Gamma rays following negative muon capture in medium Z nuclei" (1972). Dissertations, Theses, and Masters Projects. Paper 1539623661. https://dx.doi.org/doi:10.21220/s2-g0de-9771 This Dissertation is brought to you for free and open access by the Theses, Dissertations, & Master Projects at W&M ScholarWorks. It has been accepted for inclusion in Dissertations, Theses, and Masters Projects by an authorized administrator of W&M ScholarWorks. For more information, please contact [email protected]. INFORMATION TO USERS This dissertation was produced from a microfilm copy of the original document. 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University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 A Xerox Education Company MILLER, George Hollis, 1945- G A M ^ RAYS FOLLOWING NEGATIVE MUON CAPTURE IN MEDIUM Z NUCLEI. The College of William and Mary in Virginia, Ph.D., 1972 Physics, nuclear University Microfilms, A XEROX Company, Ann Arbor, Michigan GAMMA RAYS FOLLOWING NEGATIVE MUON CAPTURE IN MEDIUM Z NUCLEI A Thesis Presented to The Faculty of the Department of Physics The College of William and Mary in Virginia In Partial Fulfillment Of the Requirements for the Degree of Doctor of Philosophy ■by George H. Miller June 1972 APPROVAL SHEET This dissertation is submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy 1^' M v A A a y Author Approved, May 1972 Robert E. Welsh M. Eckhause William J. KosaLer, Jr. Hans C. von Baeyer Garnett R. Brooks, Jr. 717 Department of Biology PLEASE NOTE: Some pages may have indistinct print. Filmed as received. University Microfilms, A Xerox Education Company GAMMA RAYS FOLLOWING NEGATIVE MUON CAPTURE IN MEDIUM Z NUCLEI TABLE OF CONTENTS Page ABSTRACT.............................. vii I. INTRODUCTION........................................ 1 II. THEORY.............................................. 3 A. Weak Interactions............................... 3 B. Muon Capture.................................... 7 C. TT“V Correlations............................... 16 III. EXPERIMENTAL PROCEDURE............................... 20 A. Introduction..................................... 20 B. Beam Characteristics, Geometry, Targets ........... 21 C. Gamma-Ray Detection ............................ 25 D. Electronic Logic................................. 27 E. Computer Controlled Data Acquisition System........ 31 F. Calibrations..................................... 32 G. Activation Experiments........................... 35 H. Targets........................................ 36 1. 28Si ............................................. 37 2. 29Si .............................................38 3. 2Vg ............................................. 38 H. 12c ............................................. 38 IV. DATA ANALYSIS...................................... 39 A. Yields - General................................. 39 i n 1. Gain shifting............................... 39 2. Least-squares fitting ....................... 4l 3. Efficiency measurements and the raw yields. kk U. Corrections to raw yields .................... 51 5. Energy measurements ......................... 53 6. Total muon capture rates...................... 55 B. Yields of Specific Nuclei ....................... 56 1. 28Si02...................................... 56 2. 29Si02...................................... 6o 3. 2V g O ...................................... 6o U. 12c ................................................................................................ 62 C. V -V Correlations ............................... 6k 1. Formulation in terms of a Doppler broadened V-ray 6k 2. Instrumental resolution ..................... 6? 3. Least squares fitting - analysis of states in 28„n „ 2 8 _ A1 from ft m SiC>2 ....................... 69 Effect of finite target size - analysis of data from }x in Si(nat)........................... 71 D. Neutron Energies................................. 73 1. Intrinsic lineshape for a two-step GDR process. 73 2. Instrumental resolution ...................... 7^ 3. Analysis.................................... 7k Intrinsic lineshape for a direct reaction process 75 V. DISCUSSION OF RESULTS ............................... 77 A. Yields.......................................... 77 iv 1. Specific yields 77 28,. 0 a. ®1®2* ' ’ 77 29 b. SiOg. • . 83 c. Si(natural) 83 2h d. MgO . 85 86 f. Summary of individual yields.............. 90 2. Comparison of n) yields with ( ^ ,p) and ( Tf ,n) experiments......................... 91 3. Comparison of ( JjT , V ) yields with (e,e’) experiments ................................ 93 B. Tf-V Correlations............................... 96 1. Interpretation of results . .............. 96 a. Allowed transitions ...................... 96 b. Second forbidden transitions.............. 100 2. Methods of improving subsequent experiments . 103 3. Problems associated with the observed Tf-Vcorrela­ tions .................... ................. 107 U. Significance of the experimental measurement. 109 C. Tf-ray Transitions Doppler Broadened by V and n Emission........................................ 110 VI. SUMMARY OF EXPERIMENTAL RESULTS AND CONCLUSIONS ....... llU VII. APPENDICES......................................... 116 A. Electronic Logic................................. 1 1 6 v B . Errors.......................................... 119 C. Finite Gate W i d t h ............................... 122 D. Correction for "Heal Valid Stops" in the Target Empty Runs........................................... 126 E. Correlation Function............................. 128 F. Slowing Down Effects in the Tf-V Correlation Function. 130 G. Numerical Derivatives of Correlation Function for Least-Squares Fitting Code....................... 13^ H. Doppler Broadening of I f -rays Which Follow n and V Emission in a two-step Giant Resonance Model........ 138 I. Doppler Broadened "X Rays Following Direct Emission of n and V .................................... lh 2 J . Combinations of Nuclear Matrix Elements Contained in the Tf-V Correlation Coefficients.................. ll+5 VIII. ACKNOWLEDGMENTS..................................... 151 IX. REFERENCES.......................................... I5 I+ X. TABLES.............................................. 162 XI. FIGURES............................................ 198 vi ABSTRACT 12 2^v 28 Muon capture in the medium Z nuclei C, Mg, and Si has been studied by the observation of y rays from specific final nuclear states. The measured yields of these transitions are compared to the results of (y » p )» (Yj n) and (e, e') experiments to obtain information on the nuclear structure of the elements involved. The energy distribution of some y rays in the (A-l, Z-l) nuclei are interpreted in terms of the pro­ duction mechanism. In all cases, there is good evidence for participation of giant resonance states in muon capture. Several Doppler broadened y ray transitions in (A,Z-l) nuclei have been observed which are suitable for analysis in terms of a y-V correlation. The correlations for these transitions are interpreted in terms of the induced pseudoscaler coupling constant in the muon capture Hamiltonian. The measured yields to states 12 12 in B from muon capture in C are also interpreted in terms of the weak interaction coupling constants involved. GEORGE H. MILLER DEPARTMENT OF PHYSICS THE COLLEGE OF WILLIAM AND MARY IN VIRGINIA vii I. INTRODUCTION Negative muons of a few keV kinetic energy can be captured into atomic orbits of