$\alpha$ and cluster decays are analyzed for heavy nuclei located above ${}^{208}\mathrm{Pb}$ on the chart of nuclides: ${}^{216–220}\mathrm{Rn}$ and ${}^{220–224}\mathrm{Ra}$, which are also candidates for observing the $2\alpha$ decay mode. A microscopic theoretical approach based on relativistic energy density functionals (EDF), is used to compute axially symmetric deformation-energy surfaces as functions of quadrupole, octupole, and hexadecupole collective coordinates. Dynamical least-action paths for specific decay modes are calculated on the corresponding potential-energy surfaces. The effective collective inertia is determined using the perturbative cranking approximation, and zero-point and rotational energy corrections are included in the model. The predicted half-lives for $\alpha$ decay are within one order of magnitude of the experimental values. In the case of single-$\alpha$ emission, the nuclei considered in the present study exhibit least-action paths that differ significantly up to the scission point. The differences in $\alpha$-decay lifetimes are not only driven by $Q$ values, but also by variances of the least-action paths prior to scission. In contrast, the $2\alpha$ decay mode presents very similar paths from equilibrium to scission, and the differences in lifetimes are mainly driven by the corresponding $Q$ values. The predicted ${}^{14}\mathrm{C}$ cluster decay half-lives are within three orders of magnitudes of the empirical values, and point to a much more complex pattern compared with the $\alpha$-decay mode.

• Received 25 November 2022
• Revised 3 January 2023
• Accepted 1 March 2023

DOI:https://doi.org/10.1103/PhysRevC.107.034311