  In the paper expressions are obtained for the event rates expected in
experiments aimed at direct detection of dark matter (DM) particles. These
expressions allow one to estimate the rates taking into account simultaneously
elastic (coherent) and inelastic (incoherent) channels of DM particle
interaction with nuclei. The nonzero nuclear excitation energies are used in
the calculation of the inelastic scattering contributions. A strong correlation
between the excitation energy and the recoil energy of the excited nucleus
limits the possibility of the inelastic channel detection with a number of
nuclei. Together with the standard model of the DM distribution in the Galaxy
some models are considered, which allow higher speeds of the DM particle. As
the nuclear recoil energy, TA, increases, the dominance of the elastic
interaction channel is smoothly replaced by the dominance of the inelastic one.
Therefore, if a detector is set up to detect only elastic scattering events, it
starts to lose capability of seeing anything. The only way to notice the
interaction remains the gamma radiation from the deexcitation of the nucleus.
In the case of spin-independent DM interaction, as TA increases, the inelastic
contribution quickly dominates. If the DM particle interacts only
spin-dependently, the detectors focused on registration of the elastic
spin-dependent DM signal will see nothing, since the signal goes through the
inelastic channel. It looks like the desired DM interaction could have a
noticeable intensity, but the DM detector is unable to detect it. Therefore, a
setup aimed at the direct DM detection should register two signals. The first
is the nuclear recoil energy and the second is the gamma-quanta with a certain
energy from the target nucleus deexitation. The experiment will provide the
complete information about the DM interaction.
