$\text{Ab initio}$ electronic factors of the $A$ and $B$ hyperfine structure constants for the $5s^{2}5p6s{}^{1,3}{P}_1^{\mathrm{o}}$ states in Sn I

Abstract

Large-scale $\text{ab initio}$ calculations of the electric field gradient, which constitutes the electronic contribution to the electric quadrupole hyperfine constant $B$, were performed for the $5s^{2}5p6s$ ${}^{1,3}{P}_1^{\mathrm{o}}$ excited states of tin, using three independent computational strategies of the variational multiconfiguration Dirac-Hartree-Fock method and a fourth approach based on the configuration interaction Dirac-Fock-Sturm theory. For the $5s^{2}5p6s$ ${}^1{P}_1^{\mathrm{o}}$ state, the final value of $B/Q=703(50)$ MHz/b differs by $0.4\%$ from the one recently used by Yordanov $etal.$ [Communications Physics $3$, 107 (2020)] to extract the nuclear quadrupole moments, $Q$, for tin isotopes in the range ${}^{(117-131)}$Sn from collinear laser spectroscopy measurements. Efforts were made to provide a realistic theoretical uncertainty for the final $B/Q$ value of the $5s^{2}5p6s{}^1{P}_1^{\mathrm{o}}$ state based on statistical principles and on correlation with the magnetic dipole hyperfine constant $A$.

47 pages, 4 figures