Angular momentum sum-rule analysis ofT=12mirror nuclei in the2s−1dshell

Abstract

Empirical data from single-particle transfer reactions on the stable members of $T=\frac{1}{2}$ mirror pairs in the $2s\ensuremath{-}1d$ shell are analyzed using sum rules to obtain information about the expectation values of neutron and proton angular momenta, and spins of states in neighboring nuclei. The analysis provides estimates of the renormalization required for the various data sets, and of the errors in relative spectroscopic strengths. The angular momentum expectation values are compared with values calculated from measured magnetic moments and $\ensuremath{\beta}$-decay $\mathrm{ft}$ values, and used in an attempt to deduce information concerning exchange-current corrections to nucleon $g$ factors and the $\ensuremath{\beta}$-decay axial vector coupling constant. For mirror pairs with only one measured magnetic moment, the particle transfer data are used to predict the unknown moment. Occupation numbers for the ${d}_{\frac{5}{2}}$, ${s}_{\frac{1}{2}}$, and ${d}_{\frac{3}{2}}$ subshells are deduced from the renormalized data sets.NUCLEAR STRUCTURE $T=\frac{1}{2}$ mirror nuclei, $2s\ensuremath{-}1d$ shell, sum rule analysis, single particle transfer data. Calculated proton, neutron $J$; $\ensuremath{\mu}$, $\mathrm{ft}$ value; exchange current corrections. Calculated proton, neutron $J$; ${J}^{\ensuremath{\pi}}$; occupation numbers; unmeasured $\ensuremath{\mu}$.