Coulomb energy contribution to the excitation energy in $^{229}$Th and enhanced effect of $\alpha$ variation

TL;DR

This paper calculates how Coulomb energy differences in $^{229}$Th affect its low-energy nuclear transition, revealing an enhanced sensitivity to variations in the fine structure constant, which could improve tests of fundamental physics.

Contribution

It demonstrates that Coulomb energy changes significantly between nuclear states, suggesting an amplified effect of alpha variation on the $^{229}$Th nuclear clock transition.

Findings

Coulomb energy difference can reach hundreds of keV between states.

Variation of alpha could be amplified by a factor of 10^4 in the nuclear clock transition.

Enhanced sensitivity may improve tests of fundamental constant variations.

Abstract

We calculated the contribution of Coulomb energy to the spacing between the ground and first excited state of $^{229}$Th nucleus as a function of the deformation parameter $\delta$. We show that despite the fact that the odd particle is a neutron, the change in Coulomb energy between these two states can reach several hundreds KeV.This means that the effect of the variation of the fine structure constant $\alpha=e^2/\hbar c$ may be enhanced $\Delta U_C/E \sim 10^4$ times in the $E=$7.6 eV "nuclear clock" transition between the ground and first excited states in the $^{229}$Th nucleus.