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

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.