Internal conversion of the low energy $^{229m}$Th isomer in the Thorium anion

Abstract

A process of the decay of the anomalously low lying nuclear isomer $^{229m}$Th$(3/2^+,8.28 \pm 0.17$ eV) in the Thorium anion (Th$^-$) via the internal conversion (IC) channel is studied. We show that the half life of the nuclear isomer in the $6d_{3/2}^37s_{1/2}^2$ ground state and in the $6d_{3/2}^2 7s_{1/2}^2 7p_{1/2}^1$ excited state of Th$^-$ is $\approx1.5$ and $\approx1.1$ times bigger than in the $6d_{3/2}^2 7s_{1/2}^2$ ground state of the Th atom. The IC probabilities in the anion decreases despite the decay via the additional $6d_{3/2}$ or $7p_{1/2}$ electrons. This counterintuitive result is a consequence: a) of a decrease in the amplitudes of the $6d_{3/2}$ and $7s_{1/2}$ wave functions near the nucleus due to an increase in their diffuseness of upon the addition of extra electron, b) of mutual compensation in the IC probability due to a kinematic factor, which depends on the energy of the conversion electron in the continuum as $E_c^{-1/2}$, and the $E_c^{1/4}$ growth of the amplitudes of the electron wave functions.