Decay of the low-energy nuclear ${}^{229m}$Th isomer via atomic Rydberg states

Abstract

In the paper, a unique process of the decay of the ${}^{229m}$Th($3/2^{+},8.28\pm 0.17$ eV) low energy nuclear isomer via the internal conversion (IC) channel on Rydberg states is considered for the first time. The Rydberg atom ${}^{229m}$Th${}^{+}+e_{Ry}^{-}$ is a unique object where IC is possible exclusively on the Rydberg electron $e_{Ry}^{-}$. It is shown that in the ${}^{229m}$Th${}^{4+}+e_{Ry}^{-}$ 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 ${\psi }_{n{s}_{1/2}}(\mathbf{r})$ states is proportional to $|{\psi }_{n{s}_{1/2}}(0){|}^2$ 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 $n\gtrsim 150$ $W_{IC}$ changes as $\text{Const}/n^3$ typical for hydrogen-like ions, d) at $n\approx 10$--30, $W_{IC}$ as a function of $l$ has a characteristic "knee" between $l=3$ and $l=4$, i.e. a three order of magnitude decrease of $W_{IC}$ due to the qualitative change in the ratio between the centrifugal and shielding potentials.

Comments: 8 pages, 5 figures