In view of the striking implications of the recently measured $g$ factors for the $2_1^{+}$ states of ${}^{42}\mathrm{Ca}$ and ${}^{44}\mathrm{Ca}$ we have supplemented this study with similar measurements on ${}^{46}\mathrm{Ca}$. For all three isotopes we utilized the powerful technique of projectile Coulomb excitation in inverse kinematics combined with transient magnetic fields. In contrast to the positive $g\left(2_1^{+}\right)$ factor values for both ${}^{42,44}\mathrm{Ca}$, implying large admixtures of particle-hole configurations from ${}^{40}\mathrm{Ca}$ core excitations, the $g$ factor of ${}^{46}\mathrm{Ca}\left(2_1^{+}\right),g=-0.19\left(12\right)$, is negative. This result is in very definite disagreement with the large positive value predicted by the large scale shell model (LSSM) calculations which included $sd$ shell core excitations into the $fp$ shell and accounted well for corresponding ${}^{42,44}\mathrm{Ca}$ results. The $B\left(E2;0_1^{+}\to 2_1^{+}\right)$ deduced from the remeasured ${}^{46}\mathrm{Ca}\left(2_1^{+}\right)$ lifetime is indeed substantially smaller than the corresponding value for ${}^{42}\mathrm{Ca}$, again contrary to LSSM predictions. Both $g\left(2_1^{+}\right)$ and $B\left(E2\right)$ in ${}^{46}\mathrm{Ca}$ can be explained by full $fp$ shell model calculations using the FPD6 interaction without invoking core excitations.

• Received 13 August 2003

DOI:https://doi.org/10.1103/PhysRevC.68.061302