$\textit{Ab initio}$ electronic factors of the $A$ and $B$ hyperfine structure constants for the $5s^25p6s \; ^{1,3}\! P^{\rm o}_{1}$ states in Sn I

TL;DR

This paper presents large-scale ab initio calculations of the electric field gradient and hyperfine constants for specific excited states in tin, refining previous values and estimating uncertainties using advanced computational methods.

Contribution

The study introduces multiple independent computational strategies to accurately calculate hyperfine constants in tin, providing a more reliable value for nuclear quadrupole moments.

Findings

Calculated B/Q value for the $^{1} m P^{ m o}_1$ state is 703(50) MHz/b.

The computed B/Q differs by only 0.4% from previous experimental-based estimates.

Efforts to quantify theoretical uncertainties improve the reliability of hyperfine constant predictions.

Abstract

Large-scale $\textit{ab initio}$ calculations of the electric field gradient, which constitutes the electronic contribution to the electric quadrupole hyperfine constant $B$, were performed for the $5s^25p6s$ $^{1,3}\!P^{\rm o}_1$ 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 $5s^25p6s$ $^{1}\!P^{\rm o}_1$ state, the final value of $B/Q =703(50)$ MHz/b differs by $0.4\%$ from the one recently used by Yordanov ${\it et~al.}$ [Communications Physics ${\bf 3}$, 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 $5s^25p6s\,^{1}\!P^{\rm o}_1$ state based on statistical principles and on correlation with the magnetic dipole hyperfine constant $A$.