Splitting Sensitivity of the Ground and 7.6 eV Isomeric States of 229Th

TL;DR

This paper investigates the sensitivity of the 229Th isomeric transition energy to variations in fundamental constants, finding no enhanced sensitivity and highlighting the complexity and limitations in constraining such variations.

Contribution

It provides a detailed analysis of the nuclear structure and sensitivity of the 229Th isomeric state to fundamental constant variations, emphasizing the challenges in precise predictions.

Findings

No enhanced sensitivity to the fine-structure constant variation.

Energy splitting depends complexly on multiple interaction parameters.

Current models cannot constrain sensitivity better than a few tens of keV.

Abstract

The lowest-known excited state in nuclei is the 7.6 eV isomer of 229Th. This energy is within the range of laser-based investigations that could allow accurate measurements of possible temporal variation of this energy splitting. This in turn could probe temporal variation of the fine-structure constant or other parameters in the nuclear Hamiltonian. We investigate the sensitivity of this transition energy to these quantities. We find that the two states are predicted to have identical deformations and thus the same Coulomb energies within the accuracy of the model (viz., within roughly 30 keV). We therefore find no enhanced sensitivity to variation of the fine-structure constant. In the case of the strong interaction the energy splitting is found to have a complicated dependence on several parameters of the interaction, which makes an accurate prediction of sensitivity to temporal changes of fundamental constants problematical. Neither the strong- nor Coulomb-interaction contributions to the energy splitting of this doublet can be constrained within an accuracy better than a few tens of keV, so that only upper limits can be set on the possible sensitivity to temporal variations of the fundamental constants.