#### Abstract

On the assumption that the most important configurations in the description of the ${3/2}^{+}$-hole states in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}$ and ${}_{}{}^{47}{}_{}{}^{}\mathrm{Sc}$ are ${[{\left(\pi {d}_{\frac{3}{2}}\right)}^{-1\mathrm{}}\times {}_{}{}^{A+1}{}_{}{}^{}\mathrm{Ti}\mathrm{}(I\left)\right]}_{\left(\frac{3}{2}\right)m}(I={0}^{+}\mathrm{and}{2}^{+})$ and ${[{\left(\pi {s}_{\frac{1}{2}}\right)}^{-1\mathrm{}}\times {}_{}{}^{A+1}{}_{}{}^{}\mathrm{Ti}({2}^{+}\left)\right]}_{\left(\frac{3}{2}\right)m}$ empirical wave functions are deduced that fit both the magnetic moments and the severely inhibited $M2\mathrm{}$ decays of the states. The data require a 10-15% admixture of the $\pi {s}_{\frac{1}{2}}$ hole. The fitted wave functions are compared with the shell-model eigenfunctions that are obtained when the model space consists of nucleons in the $1{f}_{\frac{7}{2}}$ shell and a single hole in either the $1{d}_{\frac{3}{2}}$ or $2{s}_{\frac{1}{2}}$ orbits. Although the shell-model wave functions are very similar to the empirical ones [the probability ${\left|\u3008\psi \right(\mathrm{fit}\left)\right|\psi \mathrm{}\left(\mathrm{sm}\right)\mathrm{}\u3009|}^{2}$ is at least 0.94], the experimental data are not extremely well reproduced with these wave functions. The implications of this result are discussed in detail. Considering the fact that the values of the quantities to be described are anomalously small we conclude that this model space provides an adequate description of the ${3/2}^{+}$ states in question. The magnetic moment of the ${d}_{\frac{3}{2}}$ hole state in ${}_{}{}^{45}{}_{}{}^{}\mathrm{Ti}$ is calculated on the basis of the shell model and shown to be in agreement with a recent experiment.

NUCLEAR STRUCTURE Shell-model calculation for magnetic moments and $M2\mathrm{}$ decays of the ${\frac{3}{2}}^{+}$-hole states in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{47}{}_{}{}^{}\mathrm{Sc}$, and ${}_{}{}^{45}{}_{}{}^{}\mathrm{Ti}$.

DOI: http://dx.doi.org/10.1103/PhysRevC.16.1609

- Received 22 April 1977
- Published in the issue dated October 1977

© 1977 The American Physical Society