On the hyperfine structures of the ground state(s) in the ${}^{6}$Li and ${}^{7}$Li atoms

TL;DR

This paper calculates hyperfine structures of ground states in lithium isotopes and beryllium ions using numerical electron density values, achieving results that align with experimental data and extending the method's applicability.

Contribution

The paper introduces a numerical approach to determine hyperfine structures in three-electron atoms and ions, including lithium isotopes and beryllium ions, with potential for broader application.

Findings

Predicted hyperfine constants for ${}^{6}$Li and ${}^{7}$Li agree with experimental data.

Extended predictions for short-lived lithium isotopes ${}^{8}$Li, ${}^{9}$Li, and ${}^{11}$Li.

Method can be generalized to triplet states of four-electron atoms and ions.

Abstract

Hyperfine structure of the ground $2^{2}S-$states of the three-electron atoms and ions is investigated. By using our recent numerical values for the doublet electron density at the atomic nucleus we determine the hyperfine structure of the ground (doublet) $2^{2}S-$state(s) in the ${}^{6}$Li and ${}^{7}$Li atoms. Our predicted values (228.2058 $MHz$ and 803.5581 $MHz$, respectivly) agree well with the experimental values 228.20528(8) $MHz$ (${}^{6}$Li) and 803.50404(48) $MHz$ (${}^{7}$Li (R.G. Schlecht and D.W. McColm, Phys. Rev. \textbf{142}, 11 (1966))). The hyperfine structures of a number of lithium isotopes with short life-times, including ${}^{8}$Li, ${}^{9}$Li and ${}^{11}$Li atoms are also predicted. The same method is used to obtain the hyperfine structures of the three-electron ${}^{7}$Be$^{+}$ and ${}^{9}$Be$^{+}$ ions in their ground $2^{2}S-$states. Finally, we conclude that our approach can be generalized to describe the hyperfine structure in the triplet $n{}^{3}S-$states of the four-electron atoms and ions.