Probing shape coexistence by $\alpha$ decays to $0^{+}$ states

We analyze the $\alpha$-decay fine structure to excited $0_2^{+}$ states in Hg and Rn isotopes. These states are described as minima in the potential energy surface (PES) provided by the standard deformed Woods-Saxon plus pairing approach. We also investigate $\alpha$ decay from the excited state $P\left(0_2^{+}\right)$ in the parent nucleus by evaluating the corresponding hindrance factor (HF). By analyzing the experimental HF's we find the remarkable property that the ground and excited states $D\left(0_1^{+}\right)$ and $D\left(0_2^{+}\right)$ in the daughter nuclei are occupied with almost equal probabilities if there is no excited $P\left(0^{+}\right)$ states in the parent nucleus. Moreover, if there exists an excited state $P\left(0_2^{+}\right)$ then the occupation probability of this state is 25%.

Figure 1

PES of ${}^{182}\mathrm{Hg}$. Local minima for the ground state (gs) $\left({\beta }_2=-0.13\right)$ and excited $0_2^{+}$ state $\left({\beta }_2=0.27\right)$ are shown by circles.

Figure 2

Spectroscopic factor for the transition ${}^{180}\mathrm{Hg}$(gs) $\to {}^{176}\mathrm{Pt}\left(0_2^{+}\right)$ + $\alpha$ between BCS states with $k=1$ in Eq. (4). The parent (initial) state corresponds to an oblate deformation with ${\beta }_2^{\left(1\right)}B=-0.12$. The daughter (final) state carries a deformation ${\beta }_2^{\left(2\right)}$ as given in the abscissa. The dashed curve was obtained by considering the overlap between the parent and daughter BCS states as unity (i.e., $\langle P|D\rangle =1)$ while for the full curve that overlap is the one provided by our calculation. Vertical lines denote the deformations provided by the PES calculation for the minima corresponding to the $0_1^{+}$ $\left(k^{\prime }=1\right)$ and $0_2^{+}$ $\left(k^{\prime }=2\right)$ states.