NILSSON MODEL CALCULATIONS OF Mu CAPTURE RATES IN 2s-1d NUCLEI

Journal Article · Mon May 11 04:00:00 EDT 1964 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.134.B542· OSTI ID:4008209

Silbar, R R

Theoretical calculations of mu capture rates in 2s-- 1d nuclei are compared with experiment in the hope of elucidating the coupling constants of the interaction. Working from Primakoff's closure-approxiniation expression for the total average capture rate, the nuclear matrix element is treated in the context of the Nilsson unified model. A HillWheeler integration must be performed to avoid extraneous coordinates in the A-particle wave function. The one- and two- particle parts of the matrix element are broken up into the various shell contributions, since all of the angular momentum properties reside in the shell wave function for the nucleons outside the /sup 16/O core. The closed-shell matrix elements are easily treated with standard angular-momentum techniques. The method for reducing the outer-shell matrix elements to a form amenable to evaluation by a computer is given. Radial integrals are obtained from the Ford- Wills muon wave functions. The average neutrino momentum (v) is chosen on the basis of Kaplan's Fermi-gas model for the capture process and the subsequent comparison with neutron evaporation rates. The choice of nuclear parameters for / sup 19/F, /sup 20/Ne, /sup 28/Si, /sup 35/Cl, and /sup 37/Cl is discussed a nd numerical results are given. Comparing with experimental rates, the possibility that the Fermi part of the interaction is absent is not excluded. If a V--A theory is assumed, however, it is concluded that the induced pseudoscalar coupling is probably present. The induced pseudoscalar with the wrong'' sign, g/sub p/ = --8g/sub A/, is definitely excluded, and the large'' pseudoscalar, g/ sub p/ = 16g/sub A/, seems to fit the data better at nu = 0.75. (auth)

• Research Organization: Univ. of Michigan, Ann Arbor
• NSA Number: NSA-18-021277
• OSTI ID: 4008209
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 134; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANGULAR MOMENTUM
CAPTURE
CHLORINE 35
CHLORINE 37
COLLECTIVE MODEL
CONFIGURATION
COUPLING CONSTANTS
FLUORINE 19
INTERACTIONS
MATRICES
MOMENTUM
MUONS
NEON 20
NEUTRINOS
NILSSON-MOTTELSON MODEL
NUCLEAR MODELS
NUCLEI
NUMERICALS
OXYGEN 16
PHYSICS
PROGRAMMING
PSEUDOSCALAR
QUANTUM MECHANICS
SILICON 28
V-A THEORY
VECTORS