We systematically investigate the $\alpha$-decay and spontaneous fission half-lives for heavy and superheavy nuclei with proton number $Z⩾90$. The $\alpha$-decay half-lives are obtained by the deformed version of the density-dependent cluster model (DDCM). In the DDCM, the microscopic potential between the $\alpha$ particle and the daughter nucleus is evaluated numerically from the double-folding model with the M3Y interaction. The influence of the core deformation on the double-folding potential is also properly taken into account by the multipole expansion method. The spontaneous fission half-lives of nuclei from ${}^{232}\mathrm{Th}$ to ${}^{286}114$ are calculated with the parabolic potential approximation by taking nuclear structure effects into account. The agreement between theoretical results and the newly observed data is satisfactory for both $\alpha$ emitters and spontaneous fission nuclei. The competition between $\alpha$ decay and spontaneous fission is analyzed in detail and the branching ratios of these two decay modes are predicted for the unknown cases.

• Received 15 June 2008

DOI:https://doi.org/10.1103/PhysRevC.78.044329