Corrections to the free-nucleon values of the single-particle matrix elements of theM1and Gamow-Teller operators, from a comparison of shell-model predictions withsd-shell data

Abstract

The magnetic dipole moments of states in mirror pairs of the $\mathrm{sd}$-shell nuclei and the strengths of the Gamow-Teller beta decays which connect them are compared with predictions based on mixed-configuration shell-model wave functions. From this analysis we extract the average effective values of the single-particle matrix elements of the $l$, $s$, and ${[{Y}^{(2)}\ensuremath{\bigotimes}s]}^{(1)}$ components of the $M1$ and Gamow-Teller operators acting on nucleons in the $0{d}_{\frac{5}{2}}$, $1{s}_{\frac{1}{2}}$, and $0{d}_{\frac{3}{2}}$ orbits. These results are compared with the recent calculations by Towner and Khanna of the corrections to the free-nucleon values of these matrix elements which arise from the effects of isobar currents, mesonic-exchange currents, and mixing with configurations outside the $\mathrm{sd}$ shell.RADIOACTIVITY $A=17\ensuremath{-}39$ nuclei, magnetic dipole moments and Gamow-Teller beta-decay strengths; shell-model wave functions, complete $0\ensuremath{\hbar}\ensuremath{\omega}$ $0{d}_{\frac{5}{2}}\ensuremath{-}1{s}_{\frac{1}{2}}\ensuremath{-}0{d}_{\frac{3}{2}}$ basis space, empirical Hamiltonian; extraction of empirical normalizations of the $l$, $s$, and ${[{Y}^{(2)}\ensuremath{\bigotimes}s]}^{(1)}$ single-particle operators.