In previous work devoted to ab initio calculations of hyperfine-structure constants in nitrogen and fluorine atoms, we observed sizable 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 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.

• Received 2 August 2021
• Accepted 30 November 2021

DOI:https://doi.org/10.1103/PhysRevA.104.062813