Enhanced $\alpha$-Transfer population of the $2^{+}_{ms}$ mixed-symmetry state in $^{52}$Ti

The residual nucleon-nucleon interaction plays a crucial role in nuclear structure physics. In spherical even-even nuclei the quadrupole interaction leads to so called proton-neutron mixed symmetry states, which are sensitive to the underlying subshell structure. We present new data using the MINIBALL germanium array. States in $^{52}$Ti were populated via the $\alpha$-transfer reaction $^{48}$Ca($^{12}$C,$^{8}$Be)$^{52}$Ti using a $^{48}$Ca beam from the Maier-Leibnitz-Laboratory in Munich. In the frame work of IBM-2, Alonso $et$ $al.$ have shown that the population of the 2$^{+}_{ms}$ state is strictly forbidden for the alpha transfer from a doubly magic nucleus. In contrast, we measured a large relative cross section into the 2$^{+}_{2}$ mixed-symmetry state in $^{52}$Ti relative to the $2^+_1$ state of 31.1(20)$\%$. This value exceeds earlier measurements in the $^{140}$Ba nucleus, representing the case of a particular strong population of the 2$^{+}_{ms}$ state. This points towards effects of core polarizations of $^{48}$Ca in the low-lying structure of $^{52}$Ti. We have performed ab-initio shell model calculations to understand the origin of the discovered discrepancies.