Ab initio calculations of the hyperfine structure of 109Cd, 109Cd+ and reevaluation of the nuclear quadrupole moment Q(109Cd)

Abstract

Large scale ab initio calculations of the electric contribution (i.e. the electric field gradient) to the electric quadrupole hyperfine interaction constants \(B\) for the \(5p~^2P_{3/2}\) state in \(^{109}\)Cd\(^+\) ion and the \(5s5p~^3P_{1,2}\) states in neutral \(^{109}\)Cd atom were performed. To probe the sensitivity of \(B\) to different electron correlation effects, six sets of variational multi-configuration Dirac-Hartree-Fock and relativistic configuration interaction calculations employing different strategies were carried out. The calculated electric field gradients, together with experimental values of \(B\), allow us to extract a new value of the nuclear electric quadrupole moment \(Q\)(\(^{109}\)Cd) = 0.634(22) b which is about 5\% larger than the recommended value [Stone, At. Data Nucl. Data Tables 111-112, 1 (2016); Pyykk\"{o}, Mol. Phys. 116, 1328 (2018)]. Efforts were made to provide a realistic theoretical uncertainty for the final \(Q\) value based on statistical principles and correlation with the magnetic dipole hyperfine interaction constant \(A\).