Population of mixed-symmetry states viaαtransfer reactions

Abstract

Within the neutron-proton interacting boson model we study the population of mixed-symmetry states via $\ensuremath{\alpha}$ transfer processes. Closed expressions are deduced in the case of the limiting ${U}_{\ensuremath{\pi}+\ensuremath{\nu}}(5)$ and ${\mathit{SU}}_{\ensuremath{\pi}+\ensuremath{\nu}}(3)$. We find that the population of the lowest mixed-symmetry ${2}^{+}$ state, vanishing along the ${N}_{\ensuremath{\pi}}={N}_{\ensuremath{\nu}}$ 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 $\ensuremath{\alpha}$ transfer leading to $^{140}\mathrm{Ba}$.