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.

Figure 1

$Q$ values for $\alpha$ decays of nuclei between $Z=106$ and 118. The numerical values can be found in Table 4. A small horizontal offset is used for better visibility for a given value of $Z$.

Figure 2

Float charts for $\alpha$ decay chains for ${}_{118}{}^{294}\mathrm{Og}$ and ${}_{118}{}^{296}\mathrm{Og}$. The measured half-life of ${}_{114}{}^{286}\mathrm{Fl}_{}$ is about 0.13 s. Since the branching ratio of its $\alpha$ decay is about 60% [45, 46], however, the half-life of its $\alpha$ decay is about 0.22 s.

Figure 3

The $\alpha$ nuclear and Coulomb potentials, $V_N+V_C$, for ${}_{118}{}^{296}\mathrm{Og}$ in the models of the present paper. The double folding potential for ${}_{118}{}^{296}\mathrm{Og}$ of Ref. [47] is also presented for comparison.