Excitation of the $^{229}$Th nucleus by the hole in the inner electronic shells

TL;DR

This paper explores how creating a hole in the inner electronic shells of $^{229}$Th can excite its nucleus to a long-lived isomeric state, suggesting potential experimental approaches in solid-state materials.

Contribution

It provides estimates of nuclear excitation probabilities via electronic shell vacancies and discusses experimental setups in crystal materials.

Findings

Hyperfine interaction can induce nuclear state mixing with a probability of about 10^{-3}

Inner shell holes can excite the nucleus to the isomeric state with measurable likelihood

Proposes experimental methods in Th-doped crystals for nuclear excitation studies.

Abstract

The $^{229}$Th nucleus has a long-lived isomeric state $A^*$ at 8.338(24) eV [Kraemer et al, Nature, \textbf{617}, 706 (2023)]. This state is connected to the ground state by an M1 transition. For a hydrogenlike Th ion in the $1s$ state the hyperfine structure splitting is about 0.7 eV. This means that the hyperfine interaction can mix the nuclear ground state with the isomeric state with a mixing coefficient $\beta$ about 0.03. If the electron is suddenly removed from this system, the nucleus will be left in the mixed state. The probability to find the nucleus in the isomeric state $A^*$ is equal to $\beta^2\sim 10^{-3}$. For the $2s$ state the effect is roughly two orders of magnitude smaller. An atom with a hole in the $1s$ or $2s$ shell is similar to the hydrogenlike atom, only the hole has a short lifetime $\tau$. After the hole is filled, there is a non-zero probability to find the nucleus in the $A^*$ state. Estimates of this probability are presented along with a discussion of possible experiments on Th-doped xenotime-type orthophosphate crystals and other broad band gap materials.