Relativistic coupled-cluster calculation of hyperfine-structure constants of 229Th3+ and evaluation of the electromagnetic nuclear moments of 229Th

Th-229 is a promising candidate for developing nuclear optical clocks and searching for new physics beyond the standard model. For this purpose, it is important to have accurate knowledge of the nuclear properties of Th-229. In this work, we calculate hyperfine-structure (HFS) constants for the lowest four states of Th-229(3+) using the relativistic coupled-cluster method based on the Gaussian basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, and all linear and nonlinear terms of single and double excitations are included in the coupled-cluster calculation. Combining the measured HFS constants [Campbell et al., Phys. Rev. Lett. 106, 223001 (2011)] and the present atomic calculations, we extract the magnetic dipole moment, mu = 0.359(9), and the electric quadrupole moment, Q = 2.95(7), of the Th-229 nucleus. Our magnetic dipole moment is perfectly consistent with the recommended value from the all-order calculation by Safronova et al. [Phys. Rev. A 88, 060501(R) (2013)], but our electric quadrupole moment is smaller than their recommended value by about 5%. A detailed analysis indicates that the nonlinear terms of single and double excitations, not included in the all-order calculation, are crucial to produce a precise Q value for Th-229. In addition, we also report the magnetic octupole hyperfine-structure constants and some important nondiagonal hyperfine transition matrix elements, which are required for further extraction of the magnetic octupole moment Omega of Th-229 nucleus.

Automated summary

In this study, hyperfine-structure constants for the lowest four states of Th-229(3+) were calculated using the relativistic coupled-cluster method. By combining measured data with atomic calculations, magnetic dipole moment and electric quadrupole moment of the Th-229 nucleus were extracted. The analysis showed the importance of nonlinear terms in producing precise values for Th-229 properties.