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 ${[Y^{\mathrm{}\left(2\right)\mathrm{}}\otimes s]}^{\mathrm{}\left(1\right)\mathrm{}}$ components of the $M1\mathrm{}$ and Gamow-Teller operators acting on nucleons in the $0d_{\frac{5}{2}}$, $1s_{\frac{1}{2}}$, and $0d_{\frac{3}{2}}$ 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 $A=17-39\mathrm{}$ nuclei, magnetic dipole moments and Gamow-Teller beta-decay strengths; shell-model wave functions, complete $0\hslash \omega$ $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ basis space, empirical Hamiltonian; extraction of empirical normalizations of the $l$, $s$, and ${[Y^{\mathrm{}\left(2\right)\mathrm{}}\otimes s]}^{\mathrm{}\left(1\right)\mathrm{}}$ single-particle operators.

• Received 19 May 1983

DOI:https://doi.org/10.1103/PhysRevC.28.2397