  The interaction of standard model's particles with the axionic Dark Matter
field may generate oscillating nuclear electric dipole moments (EDMs),
oscillating nuclear Schiff moments and oscillating nuclear magnetic quadrupole
moments (MQMs) with a frequency corresponding to the axion's Compton frequency.
Within an atom or a molecule an oscillating EDM, Schiff moment or MQM can drive
transitions between atomic or molecular states. The excitation events can be
detected, for example, via subsequent fluorescence or photoionization. Here we
calculate the rates of such transitions. If the nucleus has octupole
deformation or quadrupole deformation then the transition rate due to Schiff
moment and MQM can be up to $10^{-16}$ transition per molecule per year. In
addition, an MQM-induced transition may be of M2-type, which is useful for the
elimination of background noise since M2-type transitions are suppressed for
photons.
