Shell model plus cluster description of negative parity states in 212 Po

The intraband electromagnetic transitions in ${}^{210}$Po and ${}^{210}$Pb are well described within the shell model approach. In contrast, similar transitions in ${}^{212}$Po are one order of magnitude smaller than the experimental values, suggesting the existence of an $\ensuremath{\alpha}$-cluster component in the structure of this nucleus. To probe this assumption we introduced Gaussian-like components in the single-particle orbitals. We thus obtained an enhancement of intraband transitions, as well as a proper description of the absolute $\ensuremath{\alpha}$-decay width in ${}^{212}$Po. We analyzed the recently measured unnatural parity states ${I}^{\ensuremath{-}}$ in ${}^{212}$Po in terms of the collective octupole excitation in ${}^{208}$Pb coupled to positive parity states in ${}^{210}$Pb. They are connected by relatively large dipole transitions to yrast positive natural parity states. We described $E1$ transitions by using the same $\ensuremath{\alpha}$-cluster component and an effective neutron dipole charge ${e}_{\ensuremath{\nu}}=\ensuremath{-}eZ/A$. $B(E2)$ values and absolute $\ensuremath{\alpha}$-decay width in ${}^{212}$Po are simultaneously described within the shell model plus a cluster component depending upon one free strength parameter.