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A method is proposed to determine the M1 nuclear transition amplitude and hence the lifetime of the "nuclear clock transition" between the low-lying (∼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 in highly charged ^{229}Th ions such as ^{229}Th^{89+} or ^{229}Th^{87+} is used. The ground-state-only g-factor measurement would also provide first experimental evidence of nuclear hyperfine mixing in atomic ions.

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Department of Chemistry, Nanoporous Materials Genome Center, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455-0431, USA.

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