Population of mixed-symmetry states via $\alpha$ transfer reactions

Within the neutron-proton interacting boson model we study the population of mixed-symmetry states via $\alpha$ transfer processes. Closed expressions are deduced in the case of the limiting $U_{\pi +\nu }(5)$ and ${\mathit{SU}}_{\pi +\nu }(3)$. We find that the population of the lowest mixed-symmetry $2^{+}$ state, vanishing along the $N_{\pi }=N_{\nu }$ line, depends on the number of active bosons and is normally smaller than that of the lowest full symmetric $2^{+}$ state. In particular, for deformed nuclei where the number of bosons is normally large, the relative population of the mixed-symmetry $2^{+}$ state is of the order of a few percent. More favorable cases can be found near shell closures, as in the case of $\alpha$ transfer leading to ${}^{140}\mathrm{Ba}$.

Figure 1

Schematic representation of the $L=2$ $\alpha$ transfer intensities studied in this work in the $\mathit{SU}(3)$ (left) and $U(5)$ (right) states.