Ground-state $g$ factor of highly charged $^{229}$Th ions: an access to the M1 transition probability between the isomeric and ground nuclear states

TL;DR

This paper proposes a method to determine the M1 nuclear transition amplitude and the lifetime of the $^{229}$Th nuclear clock transition by measuring the ground-state g factor of highly charged ions, utilizing nuclear hyperfine mixing effects.

Contribution

It introduces a novel approach to measure nuclear transition properties through atomic g factor measurements in highly charged ions, providing insights into nuclear hyperfine mixing and nuclear magnetic moments.

Findings

Potential to measure the M1 transition amplitude and lifetime of the nuclear clock transition.

First experimental evidence of nuclear hyperfine mixing in atomic ions.

Improved accuracy in nuclear magnetic moment determination.

Abstract

A method is proposed to determine the $M1$ nuclear transition amplitude and hence the lifetime of the "nuclear clock transition" between the low-lying ($\sim 8$ eV) first isomeric state and the ground state of $^{229}$Th from a measurement of the ground-state $g$ factor of few-electron $^{229}$Th ions. As a tool, the effect of nuclear hyperfine mixing (NHM) in highly charged $^{229}$Th-ions such as $^{229}$Th$^{89+}$ or $^{229}$Th$^{87+}$ is utilized. The ground-state-only $g$-factor measurement would also provide first experimental evidence of NHM in atomic ions. Combining the measurements for H-, Li-, and B-like $^{229}$Th ions has a potential to improve the initial result for a single charge state and to determine the nuclear magnetic moment to a higher accuracy than that of the currently accepted value. The calculations include relativistic, interelectronic-interaction, QED, and nuclear effects.