Weak Correlation and Strong Relativistic Effects on the Hyperfine Interaction in Fluorine

TL;DR

This study reveals that relativistic effects significantly influence hyperfine interactions in fluorine, even more than electron correlation, and demonstrates the importance of relativistic $LS$-term mixing for accurate predictions.

Contribution

The paper identifies new fluorine levels where relativistic effects dominate hyperfine structure calculations, highlighting the importance of relativistic $LS$-term admixtures over correlation effects.

Findings

Relativistic effects can dominate hyperfine interactions in light atoms.

Breit-Pauli approximation effectively describes hyperfine structures with $LS$-term mixing.

Multiconfiguration Dirac-Hartree-Fock supports the relativistic analysis.

Abstract

In previous work devoted to {\it ab initio} calculations of hyperfine structure constants in nitrogen and fluorine atoms, we observed sizeable relativistic effects, a priori unexpected for such light systems, that can even largely dominate over electron correlation. We observed that the atomic wave functions calculated in the Breit-Pauli approximation describe adequately the relevant atomic levels and hyperfine structures, even in cases for which a small relativistic $LS$-term mixing becomes crucial. In the present work we identify new levels belonging to the spectroscopic terms $2p^4(^3\!P) 3d ~ \; ^{2,4}\!(P,D,F)$ of the fluorine atom, for which correlation effects on the hyperfine structures are small, but relativistic $LS$-term admixtures are decisive to correctly reproduce the experimental values. The Breit-Pauli analysis of the hyperfine matrix elements nails cases with large cancellation, either between $LS$ pairs for individual hyperfine operators, or between the orbital and the spin-dipole contributions. Multiconfiguration Dirac-Hartree-Fock calculations are performed to support the Breit-Pauli analysis.