Anomalous Hyperfine Structure of the $^{229}$Th Ground-State Doublet in Muonic Atom

TL;DR

This study calculates the hyperfine structure of $^{229}$Th in a muonic atom, revealing an anomalously weak hyperfine splitting and potential for direct observation of the isomeric transition around 120-140 eV.

Contribution

It introduces a detailed calculation of hyperfine splitting considering nuclear magnetization distribution, showing significant deviations from point nucleus models and predicting observable nuclear transitions.

Findings

Hyperfine splitting of the $3/2^+$ isomeric state is nearly suppressed.

Partial inversion of the $^{229}$Th ground-state doublet levels occurs.

The isomeric transition energy is estimated at 120-140 eV.

Abstract

The hyperfine splitting of the ground and low-energy $3/2^+(7.8 \pm 0.5$ eV) levels in the $^{229}$Th nucleus in muonic atom ($\mu^-_{1S_{1/2}}{}^{229}$Th$)^*$ has been calculated considering the distribution of the nuclear magnetization in the framework of collective nuclear model with the wave functions of the Nilsson model for the unpaired neutron. It is shown that (a) the hyperfine splitting of the $3/2^+$ isomeric state is anomalously weak, and the reduction of hyperfine structure in comparison with the model of a point nuclear magnetic dipole is close to 100\%, (b) partial inversion of levels of the $^{229}$Th ground-state doublet and spontaneous decay of the ground state with excitation of the isomeric state take place, (c) the energy of the isomeric transition lies in the range of 120--140 eV, which makes possible the direct observation of the transition, registration of conversion electrons and measurement of the nuclear matrix element.