Precision calculation of hyperfine constants for extracting nuclear moments of ²²⁹Th.

Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work, we improve the precision of such a method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of ²²⁹Th³⁺ in the framework of such relativistic coupled-cluster single double triple (CCSDT) method. We present a detailed study of

various corrections to all calculated properties. Using the theory results and experimental data we found the nuclear magnetic dipole and electric quadrupole moments to be

μ = 0.366(6) μ_N and Q = 3.11(2) eb and reducing the uncertainty of the quadrupole moment by a factor of three. The Bohr-Weisskopf effect of the finite nuclear magnetization is investigated, with bounds placed on the deviation of the magnetization distribution from the uniform one.