  Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration
Dirac-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 hyperfine
constants. Several computing strategies are considered to investigate electron
correlation and relativistic effects. High-order correlation contributions are
included in MCHF calculations based on single and double multireference (SD-MR)
expansions. The largest components of the single reference MCHF wave functions
are selected to define the MR sets. In this scheme, relativistic corrections
are evaluated in the Breit-Pauli approximation. A similar strategy is used for
the calculation of MCDHF relativistic wave functions and hyperfine parameters.
While correlation and relativistic corrections are found to be rather small for
the ground state, we highlight large relativistic effects on the hyperfine
constant $A_{3/2}$ 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 the
hyperfine interaction of all other levels considered. We also revisit the
hyperfine 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 excellent
agreement with experiment.
