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

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.