Effects of electrons on nuclear clock transition frequency in $^{229}$Th ions

TL;DR

This paper investigates how the electron configuration in thorium ions significantly affects the nuclear clock transition frequency, revealing large shifts that impact precision measurements and isotope comparisons.

Contribution

It provides detailed calculations of the electron-dependent energy shifts of the $^{229}$Th nuclear clock transition, highlighting the importance of electron configuration in nuclear frequency stability.

Findings

Electron removal causes a ~10^{-7} shift in nuclear frequency.

Nuclear frequency varies significantly across Th ionization states.

The shift between neutral Th and bare nucleus is about 1%.

Abstract

We perform calculations of the energy shift of the nuclear clock transition frequency $^{229}$Th as a function of the number of electrons in Th ion. We demonstrate that the dependence of the nuclear frequency on electron configuration is significant. E.g., removing one electron from the atom leads to relative shift of the nuclear frequency $\sim 10^{-7}$, which is twelve orders of magnitude larger than expected relative uncertainty of the nuclear clock transition frequency ($\sim 10^{-19}$). This leads to difference of the nuclear clock frequencies in Th~IV, Th~III, Th~II and Th~I. The relative change of the nuclear frequency between neutral Th and its bare nucleus is 1\%. We also calculate the field shift constants for isotopic and isomeric shifts of atomic electron transitions in Th ions.