Strengths of transitions between $0^{+}$ and $1^{+}$ states and their relationship to inelastic electron scattering form factors: Example of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$

The strengths of transitions in $A=24\mathrm{}$ between $J^{\pi }=1^{+}$, $T=1\mathrm{}$ states and the lowest $J^{\pi }=0^{+}$ states of $T=0\mathrm{} \mathrm{and} 2$ are calculated from shell-model wave functions constructed in the full eight-particle $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ configuration space. The model Hamiltonian is an empirical interaction which yields a good accounting of the energies of intra-$\mathrm{sd}$-shell states throughout the $A=17-39\mathrm{}$ region. With these same wave functions the ($e, e^{\prime }$) form factors for the magnetic dipole excitation of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ to its lowest five states of $J^{\pi }=1^{+}$, $T=1\mathrm{}$ are calculated in the plane-wave Born approximation. The predicted form factors and the associated predictions for $B\left(M1\mathrm{}\right)\mathrm{}$ and $B$ (Gamow-Teller) are compared to existing experimental values.

NUCLEAR STRUCTURE Predicted strengths of isospin-changing $M1\mathrm{}$, Gamow-Teller, and ($p, n$) transitions between $J=0^{+} \mathrm{and} 1^{+}$ states in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and form factors for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}(e, e^{\prime })$; shell-model wave functions, complete $\mathrm{sd}$-shell basis space, universal $\mathrm{sd}$-shell Hamiltonian.