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

TL;DR

This study uses advanced ab initio methods to calculate hyperfine interactions in 109Cd, leading to a refined nuclear quadrupole moment value that improves upon previous estimates.

Contribution

It provides a new, more accurate value for the nuclear quadrupole moment of 109Cd based on comprehensive ab initio calculations and analysis of hyperfine interactions.

Findings

New value of Q(109Cd) = 0.634(22) b, about 5% larger than previous estimates.

Demonstrated sensitivity of electric field gradient calculations to electron correlation effects.

Established a methodology for estimating theoretical uncertainties in hyperfine parameter calculations.

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 $A$.