Nuclear energy density functional and the nuclear alpha decay

The nuclear $\alpha$ decay of heavy nuclei is investigated based on the nuclear energy density functional, which leads to the $\alpha$ potential inside the parent nucleus in terms of the proton and neutron density profiles of the daughter nucleus. We use the Skyrme force model, Gogny force model, and relativistic mean field model to get the nucleon density profiles inside heavy nuclei. Once the nucleon density profiles are determined, the parameters of the nuclear $\alpha$ potential are fitted to the observed $\alpha$ decay half-lives of heavy nuclei. This approach is then applied to predict unknown $\alpha$ decay half-lives of heavy nuclei. To estimate the $Q$ values of unobserved $\alpha$ decays, we make use of the liquid droplet model.