Stringent Tests of Shell Model Calculations infpShell Nuclei46,48Tiand50,52Crfrom Measurements ofgFactors andB(E2)Values

Measurements of magnetic moments and lifetimes of $2_1^{+}$ and $4_1^{+}$ states of ${}^{46,48}\mathrm{Ti}$ and ${}^{50,52}\mathrm{Cr}$ were performed with high accuracy via projectile Coulomb excitation and the technique of transient magnetic fields. The high quality of the data allows for the first time to establish stringent constraints on large scale shell model calculations. Whereas the global behavior of the data is well explained by full $\mathrm{fp}$ shell model calculations, distinct deviations in the $g$ factors and $B\left(E2\mathrm{}\right)$ values of ${}^{46,48}\mathrm{Ti}$ from theoretical predictions can be attributed to excitations of the ${}^{40}\mathrm{Ca}$ core. This suggestion is supported by recent Monte Carlo calculations which provide evidence that ${}^{48}\mathrm{Ca}$ is a better inert core.