  The particular advantages of using the diatomic molecule radium monofluoride
(RaF) as a versatile molecular probe for physics beyond the Standard Model are
highlighted. i) RaF was previously suggested as being potentially amenable to
direct cooling with lasers. As shown in the present work, RaF's energetically
lowest electronically excited state is of ${}^{2}\Pi$ symmetry (in contrast to
BaF), such that no low-lying ${}^{2}\Delta$ state prevents efficient optical
cooling cycles. ii) The effective electric field acting on the unpaired
electron in the electronic ground state of RaF is estimated larger than in YbF,
from which the best restrictions on the electron electric dipole moment (eEDM)
were obtained experimentally. iii) Favourable crossings of spin-rotational
levels of opposite parity in external magnetic fields exist, which are
important for the measurement of the nuclear anapole moment of nuclei with a
valence neutron. Thus, RaF appears currently as one of the most attractive
candidates for investigation of parity-odd as well as simultaneously parity-
and time-reversal-odd interactions in the realms of molecular physics.
