Microscopic Description of 2 α Decay in Po 212 and Ra 224 Isotopes

A microscopic calculation of half-lives for both the $\ensuremath{\alpha}$ and $2\ensuremath{\alpha}$ decays of $^{212}\mathrm{Po}$ and $^{224}\mathrm{Ra}$ is performed, using a self-consistent framework based on energy density functionals. A relativistic density functional and a separable pairing interaction of finite range are used to compute axially symmetric deformation energy surfaces as functions of quadrupole, octupole, and hexadecapole collective coordinates. Dynamical least-action paths are determined, that trace the $\ensuremath{\alpha}$ and $2\ensuremath{\alpha}$ emission from the equilibrium deformation to the point of scission. The calculated half-lives for the $\ensuremath{\alpha}$ decay of $^{212}\mathrm{Po}$ and $^{224}\mathrm{Ra}$ are in good agreement with data. A new decay mode, the symmetric $2\ensuremath{\alpha}$ emission, is predicted with half-lives of the order of those observed for cluster emission.