Sensitivity of $^{229}$Th nuclear clock transition to variation of the fine-structure constant

TL;DR

This paper evaluates the sensitivity of the thorium-229 nuclear clock transition to variations in the fine-structure constant, finding a significant enhancement factor that could improve detection of fundamental constant changes and dark matter interactions.

Contribution

The study provides a new estimate of the enhancement factor for alpha variation sensitivity using existing charge radius data and supports the constant nuclear density assumption with nuclear theory.

Findings

Enhancement factor for alpha variation is approximately -8200.

Frequency shift due to alpha variation could reach 200 Hz per year.

The nuclear clock could detect variations in alpha much more precisely than current limits.

Abstract

Peik and Tamm [Europhys. Lett. 61, 181 (2003)] proposed a nuclear clock based on the isomeric transition between the ground state and the first excited state of thorium-229. This transition was recognized as a potentially sensitive probe of possible temporal variation of the fine-structure constant, $\alpha$. The sensitivity to such a variation can be determined from measurements of the mean-square charge radius and quadrupole moment of the different isomers. However, current measurements of the quadrupole moment are yet to achieve an accuracy high enough to resolve non-zero sensitivity. Here we determine this sensitivity using existing measurements of the change in the mean-square charge radius, coupled with the ansatz of constant nuclear density. The enhancement factor for $\alpha$ variation is $K = -(0.82 \pm 0.25) \times 10^4$. For the current experimental limit, $\delta\alpha/\alpha \lesssim 10^{-17}$ per year, the corresponding frequency shift is $\sim\!200$ Hz per year. This shift is six orders of magnitude larger than the projected accuracy of the nuclear clock, paving the way for increased accuracy of the determination of $\delta \alpha$ and interaction strength with low-mass scalar dark matter. We verify that the constant-nuclear-density ansatz is supported by nuclear theory and propose how to verify it experimentally. We also consider a possible effect of the octupole deformation on the sensitivity to $\alpha$ variation, and calculate the effects of $\alpha$ variation in a number of M\"ossbauer transitions.