Energy levels of radium monofluoride RaF in external electric and magnetic fields to search for P- and T,P-violation effects

The RaF molecule is considered to be a potential candidate to search for the electron electric dipole moment and other effects of the time-reversal $(T)$ and spatial parity $(P)$ symmetries violation of fundamental interactions as well as $T$-even, $P$-odd effects. Recently, the existence of a suitable laser-cooling scheme for this molecule was proven experimentally, R. F. Garcia Ruiz et al. [Nature (London) 581, 396 (2020)]. In the present paper, we study energy levels, $g$-factors, and sensitivities to the electron electric dipole moment as functions of the external electric field for the lowest rotational levels of $^{224,226,228}\mathrm{RaF}$ molecules. The state with zero sensitivity to the electron electric dipole moment suitable to test systematic effects is found. Also energy levels of $^{223,225}\mathrm{RaF}$ as functions of the external magnetic field are calculated for the lowest rotational levels. The values of magnetic fields corresponding to the crossing of the levels of opposite parity are found. For these values of the magnetic field, the off-diagonal matrix element of the nuclear spin-dependent parity violation interaction is calculated. The obtained data can be used to design experiments to search for the $T,P$- and $P$-violating effects using the RaF molecule.