The approach proposed earlier for describing the scattering of weakly interacting nonrelativistic massive neutral particles off nuclei is used as the basis to derive explicit expressions for the event countingrate expected in experiments aimed at directly detecting dark matter (DM) particles. These expressions make it possible to estimate the rates in question with allowance for both elastic (coherent) and inelastic (incoherent) channels of DM particle interaction with a target nucleus. Within this approach, the effect of a nonzero excitation energy of the nucleus involved is taken into account for the first time in calculating the contribution of inelastic processes. A correlation between the excitation energy and admissible values of the kinetic recoil energy of the excited nucleus constrains substantially the possibility of detection of the inelastic channel with some nuclei. In addition to the standard model of the DM distribution in theMilkyWay Galaxy, the effect of some other models that allow significantly higher velocities of DMparticles is considered. A smooth transition from from the dominance of the elastic channel of the DM particle–nucleus interaction to the dominance of its inelastic channel occurs as the nuclear recoil energy TA grows. If the DM detector used is tuned to detecting elastic-scattering events exclusively, then it cannot detect anything in the casewhere the nuclear recoil energy turns out to be belowthe the detection threshold. As TA grows, such a detector loses the ability to see anything, since elastic processes quickly become nonexistent. Radiation associated with the deexcitation of the nucleus becomes the only possible signature of the interaction that occurred. In the case of a spin-independent interaction, the inelastic contribution becomes dominant rather quickly as TA grows, while the differential event counting rate decreases insignificantly. If a DMparticle interacts with nucleons via a spin-dependent coupling exclusively, detectors traditionally setup to detect an elastic spin-dependent DMsignal will be unable to to see anything since the signal entirely goes through the inelastic channel. It looks like the sought interactions ofDM particles may have a sizable intensity, but the instrument is unable to detect them.Therefore, experiments aimed at directly detecting DM particles should be planned in such a way that it would be possible to detect simultaneously two signals—that of the recoil energy of the nucleus involved and that of gamma rays having a specific energy and carrying away its excitation. A experiment in this implementation will furnish complete information about the DM interaction that occurred.
