α decay law of excited nuclei and its role in stellar decay rates

$\alpha$ decay is one of the prominent decay modes in the nucleosynthesis of heavy and superheavy elements synthesized at temperatures of the order of gigakelvin. To facilitate the investigation of the role played by the $\alpha$ decay half-lives of thermally excited nuclei in nucleosynthesis calculations, an empirical formula based on a model for the $\alpha$ decay of nuclei in their ground and excited states to daughter nuclei in their ground or excited states is presented. Constants appearing in the analytical expression for the $\alpha$ decay half-life obtained within the model are treated as adjustable parameters and fitted to experimental data on 342 $\alpha$ decays in the range of 82 $\le Z_p\le$ 94, to obtain an excitation energy-dependent decay law. Under the assumption that thermal equilibrium has been reached between nuclear states, temperature ($T$) dependent half-lives, $t_{1/2}\left(T\right)$, for several of the experimentally studied $\alpha$ emitters with 65 $\le Z_p\le$ 94 are presented using available data on the half-lives of excited nuclei. Though the general trend is a decrease in $t_{1/2}\left(T\right)$ at elevated temperatures, exceptional cases with increased half-lives are found in the case of some isomeric states. A list of such isomers provided in this paper motivates future work involving considerations of their thermal equilibration and role in shaping kilonova light curves.