Ground-State <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi></mml:math> Factor of Highly Charged <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Th</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>229</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> Ions: An Access to the M1 Transition Probability between the Isomeric and Ground Nuclear States
V. M. Shabaev, D. A. Glazov, A. M. Ryzhkov, C. Brandau, G. Plunien, W. Quint, A. M. Volchkova, D. V. Zinenko
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 ($\ensuremath{\sim}8\text{ }\text{ }\mathrm{eV}$) first isomeric state and the ground state of $^{229}\mathrm{Th}$ from a measurement of the ground-state $g$ factor of few-electron $^{229}\mathrm{Th}$ ions. As a tool, the effect of nuclear hyperfine mixing in highly charged $^{229}\mathrm{Th}$ ions such as ${^{229}\mathrm{Th}}^{89+}$ or ${^{229}\mathrm{Th}}^{87+}$ is used. The ground-state-only $g$-factor measurement would also provide first experimental evidence of nuclear hyperfine mixing in atomic ions. Combining the measurements for H-, Li-, and B-like $^{229}\mathrm{Th}$ 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.