Nuclear structure of the stable even-A calcium isotopes based on new experiments and shell model calculations

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 $g({2}_{1}^{+})$ 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 $^{46}\mathrm{Ca}({2}_{1}^{+}),g=\ensuremath{-}0.19(12)$, 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 $B(E2;{0}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ deduced from the remeasured $^{46}\mathrm{Ca}({2}_{1}^{+})$ lifetime is indeed substantially smaller than the corresponding value for $^{42}\mathrm{Ca}$, again contrary to LSSM predictions. Both $g({2}_{1}^{+})$ and $B(E2)$ in $^{46}\mathrm{Ca}$ can be explained by full $fp$ shell model calculations using the FPD6 interaction without invoking core excitations.