Alpha decay of thermally excited nuclei

One of the prominent decay modes of heavy nuclei which are produced in astrophysical environments at temperatures of the order of $10^9$ K is the $\alpha$ ($^4$He) decay. Thermally enhanced $\alpha$ decay rates are evaluated within the standard scheme of a tunneling decay where the $\alpha$ particle tunnels through the potential barrier formed by its interaction with the daughter nucleus. Following the observation that there exist several excited levels with the possibility of an $\alpha$ decay when the daughter nucleus is at a shell closure, we focus in particular on decays producing daughter nuclei with the neutron number, N = 126. Within a statistical approach we find that the half-lives, $t_{1/2}(T)$, for temperatures ranging from $T$ = 0 to 2.4 GK can decrease by 1 - 2 orders of magnitude with the exception of the decay of $^{212}$Po which decays to the doubly magic daughter $^{208}$Pb, where $t_{1/2}(T)$ decreases by 5 orders of magnitude. The effect of these thermally enhanced $\alpha$ decays on the $r$-process nucleosynthesis can be significant in view of the mass build up at the waiting point nuclei with closed neutron shells.