Nuclear charge radii of $^{229}$Th from isotope and isomer shifts

TL;DR

This paper combines theoretical calculations and experimental measurements to precisely determine nuclear charge radii differences in thorium isotopes and isomers, crucial for nuclear laser applications and fundamental constant studies.

Contribution

It provides the first combined theoretical and experimental determination of nuclear charge radii differences in $^{229}$Th and its isomer, enhancing understanding for nuclear laser and fundamental physics.

Findings

Measured hyperfine structure and isotope shifts in Th$^{2+}$.

Calculated isotope shifts with configuration interaction and coupled-cluster methods.

Derived precise differences in nuclear charge radii for isotopes and isomers.

Abstract

The isotope $^{229}$Th is unique in that it possesses an isomeric state of only a few eV above the ground state, suitable for nuclear laser excitation. An optical clock based on this transition is expected to be a very sensitive probe for variations of fundamental constants, but the nuclear properties of both states have to be determined precisely to derive the actual sensitivity. We carry out isotope shift calculations in Th$^+$ and Th$^{2+}$ including the specific mass shift, using a combination of configuration interaction and all-order linearized coupled-cluster methods and estimate the uncertainty of this approach. We perform experimental measurements of the hyperfine structure of Th$^{2+}$ and isotopic shift between $^{229}$Th$^{2+}$ and $^{232}$Th$^{2+}$ to extract the difference in root-mean-square radii as $\delta \langle r^{2} \rangle^{232,229}=0.299(15)$ fm$^2$. Using the recently measured values of the isomer shift of lines of $^{229\textrm{m}}$Th, we derive the value for the mean-square radius change between $^{229}$Th and its low lying isomer $^{229\textrm{m}}$Th to be $\delta \langle r^2 \rangle^{229\textrm{m},229} = 0.0105(13)\,{\rm fm}^2$.