  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.
