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The paper presents a theoretical approach to the description of therelativistic scattering of a massive (neutral) lepton on a nucleus, in whichthe latter retains its integrity. The measurable cross section of this processincludes the elastic (or coherent) contribution, when the nucleus remains inits original quantum state and the inelastic (incoherent) contribution, whenthe nucleus goes into another (excited) quantum state. Transition from theelastic scattering regime to the inelastic scattering regime is regulatedautomatically by the dependence of the form factors on the momentum transferredto the nucleus. At small momentum transfers elastic scattering dominates. ASthe transferred momentum increases, the contribution of the inelasticscattering increases, and the latter becomes dominant at sufficiently largetransferred momenta. The scattering of massive (anti)neutrinos interacting withnucleons through the $V\mp A$ currents of the Standard Model is considered indetail. Because of the nonzero masses, an additional channel arises for elasticand inelastic scattering of these (anti)neutrinos on nuclei due to thepossibility of changing the helicity of these (anti)neutrinos. The expressionsobtained for the cross sections are applicable to any precision data analysisinvolving neutrinos and antineutrinos, especially when non-zero neutrino massescan be taken into account. These expressions can also be used in the analysisof experiments on direct detection of (neutral) massive weakly interactingrelativistic dark matter particles since, unlike the generally accepted case,they simultaneously take into account both elastic and inelastic interactionsof the particles. The presence of an "inelastic signal" with its characteristicsignature may be the only registrable evidence of interaction of the darkmatter particle with the nucleus.

On massive neutral lepton scattering on nucleus