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

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.

main paper: 7 pages, 1 figure, 2 tables; supplemental material: 5 pages, 1 figure, 4 tables