Microscopic description of the self-conjugate Xe108 and Te104 α -decay chain

Abstract

A microscopic calculation of half-lives for the recently observed $^{108}\mathrm{Xe}\ensuremath{\rightarrow}^{104}\mathrm{Te}\ensuremath{\rightarrow}^{100}\mathrm{Sn}\ensuremath{\alpha}$-decay chain is performed by using a self-consistent framework based on energy density functionals. The relativistic density functional DD-PC1 and a separable pairing interaction of finite range are used to compute axially symmetric deformation-energy surfaces of $^{104}\mathrm{Te}$ and $^{108}\mathrm{Xe}$ as functions of quadrupole, octupole, and hexadecupole collective coordinates. Dynamic least-action paths are determined that trace the $\ensuremath{\alpha}$-particle emission from the equilibrium deformation to the point of scission. The calculated half-lives, 197 ns for $^{104}\mathrm{Te}$ and $50\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ for $^{108}\mathrm{Xe}$, are compared with recent experimental values of the half-lives of superallowed $\ensuremath{\alpha}$ decay of $^{104}\mathrm{Te}$: $<18$ ns, and $^{108}\mathrm{Xe}$: ${58}_{\ensuremath{-}23}^{+106}\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$.