Decay of the low-energy nuclear Th229m isomer via atomic Rydberg states

Abstract

In the paper, a unique process of the decay of the $^{229m}\mathrm{Th}(3/{2}^{+},8.28\ifmmode\pm\else\textpm\fi{}0.17$ eV) low-energy nuclear isomer via the internal conversion (IC) channel on Rydberg states is considered for the first time. The Rydberg atom $^{229m}\mathrm{Th}^{+}+{e}_{Ry}^{\ensuremath{-}}$ is a unique object where IC is possible exclusively on the Rydberg electron ${e}_{Ry}^{\ensuremath{-}}$. It is shown that in the $^{229m}\mathrm{Th}^{4+}+{e}_{Ry}^{\ensuremath{-}}$ system (a) IC on the electron states with relatively small values of the principal quantum number $n$ and the orbital moment $l$ is practically completely suppressed, (b) IC probability, ${W}_{IC}$, on the ${\ensuremath{\psi}}_{n{s}_{1/2}}(\mathbf{r})$ states is proportional to $|{\ensuremath{\psi}}_{n{s}_{1/2}}{(0)|}^{2}$ and can be related with the energy of the hyperfine interaction of the Rydberg electron with the nucleus, (c) ${W}_{IC}$ decreases rapidly with the increase of $n$ in the range from 10 to 50, and in the range $n\ensuremath{\gtrsim}150\phantom{\rule{4pt}{0ex}}{W}_{IC}$ changes as $\text{const}/{n}^{3}$ typical for hydrogen-like ions, and (d) at $n\ensuremath{\approx}10$--30, ${W}_{IC}$ as a function of $l$ has a characteristic ``knee'' between $l=3$ and $l=4$, i.e., a decrease of three orders of magnitude in ${W}_{IC}$ due to the qualitative change in the ratio between the centrifugal and shielding potentials.