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In the paper expressions are obtained for the event rates expected inexperiments aimed at direct detection of dark matter (DM) particles. Theseexpressions allow one to estimate the rates taking into account simultaneouslyelastic (coherent) and inelastic (incoherent) channels of DM particleinteraction with nuclei. The nonzero nuclear excitation energies are used inthe calculation of the inelastic scattering contributions. A strong correlationbetween the excitation energy and the recoil energy of the excited nucleuslimits the possibility of the inelastic channel detection with a number ofnuclei. Together with the standard model of the DM distribution in the Galaxysome models are considered, which allow higher speeds of the DM particle. Asthe nuclear recoil energy, TA, increases, the dominance of the elasticinteraction channel is smoothly replaced by the dominance of the inelastic one.Therefore, if a detector is set up to detect only elastic scattering events, itstarts to lose capability of seeing anything. The only way to notice theinteraction remains the gamma radiation from the deexcitation of the nucleus.In the case of spin-independent DM interaction, as TA increases, the inelasticcontribution quickly dominates. If the DM particle interacts onlyspin-dependently, the detectors focused on registration of the elasticspin-dependent DM signal will see nothing, since the signal goes through theinelastic channel. It looks like the desired DM interaction could have anoticeable intensity, but the DM detector is unable to detect it. Therefore, asetup aimed at the direct DM detection should register two signals. The firstis the nuclear recoil energy and the second is the gamma-quanta with a certainenergy from the target nucleus deexitation. The experiment will provide thecomplete information about the DM interaction.

On underestimation of the inelastic interactions in the direct dark matter search