Theoretical Predictions for the Magnetic Dipole Moment of ${}^{229m}\mathrm{Th}$

A recent laser spectroscopy experiment [J. Thielking , Nature, (London) 556, 321 (2018)] has determined for the first time the magnetic dipole moment of the 7.8 eV isomeric state ${}^{229m}\mathrm{Th}$. The measured value differs by a factor of approximately 5 from previous nuclear theory predictions based on the Nilsson model, raising questions about our understanding of the underlying nuclear structure. Here, we present a new theoretical prediction based on a nuclear model with coupled collective quadrupole-octupole and single-particle motions. Our calculations yield an isomer magnetic dipole moment of ${\mu }_{\mathrm{IS}}=-0.35{\mu }_N$ in surprisingly good agreement with the experimentally determined value of $-0.37(6){\mu }_N$, while overestimating the ground state dipole moment by a factor 1.4. The model provides further information on the role and strength of the Coriolis mixing and the most probable value of the gyromagnetic ratio $g_R$ and its consequences for the transition probability $B(M1)$. The key role of the magnetic moment values as constraints in the determination of the isomer decay rates is discussed.