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Multiconfiguration Hartree-Fock (MCHF) and multiconfigurationDirac-Hartree-Fock (MCDHF) calculations are performed for the$2p^{5}~^{2}P^{o}$, $2p^4(^{3}P)3s~^{4}P$, $2p^4(^{3}P)3s~^{2}P$ and$2p^4(^{3}P)3p~^{4}S^o$ states of $^{19}$F~I to determine their hyperfineconstants. Several computing strategies are considered to investigate electroncorrelation and relativistic effects. High-order correlation contributions areincluded in MCHF calculations based on single and double multireference (SD-MR)expansions. The largest components of the single reference MCHF wave functionsare selected to define the MR sets. In this scheme, relativistic correctionsare evaluated in the Breit-Pauli approximation. A similar strategy is used forthe calculation of MCDHF relativistic wave functions and hyperfine parameters.While correlation and relativistic corrections are found to be rather small forthe ground state, we highlight large relativistic effects on the hyperfineconstant $A_{3/2}$ of $2p^4(^{3}P)3p~^{4}S^o$ and, to a lesser extent, on$A_{1/2}$ of $2p^4(^{3}P)3s~^{4}P$. As expected for such a light system,electron correlation effects dominate over relativity in the calculation of thehyperfine interaction of all other levels considered. We also revisit thehyperfine constants of $2p^3(^{4}S)3s~^{5}S^{o}$ and $2p^3(^{4}S)3p~^{5}P$ in$^{17}$O using similar strategies. The results are found to be in excellentagreement with experiment.

Theoretical Hyperfine Structures of $^{19}$F~I and $^{17}$O~I