  The paper presents a theoretical approach to the description of the
relativistic scattering of a massive (neutral) lepton on a nucleus, in which
the latter retains its integrity. The measurable cross section of this process
includes the elastic (or coherent) contribution, when the nucleus remains in
its original quantum state and the inelastic (incoherent) contribution, when
the nucleus goes into another (excited) quantum state. Transition from the
elastic scattering regime to the inelastic scattering regime is regulated
automatically by the dependence of the form factors on the momentum transferred
to the nucleus. At small momentum transfers elastic scattering dominates. AS
the transferred momentum increases, the contribution of the inelastic
scattering increases, and the latter becomes dominant at sufficiently large
transferred momenta. The scattering of massive (anti)neutrinos interacting with
nucleons through the $V\mp A$ currents of the Standard Model is considered in
detail. Because of the nonzero masses, an additional channel arises for elastic
and inelastic scattering of these (anti)neutrinos on nuclei due to the
possibility of changing the helicity of these (anti)neutrinos. The expressions
obtained for the cross sections are applicable to any precision data analysis
involving neutrinos and antineutrinos, especially when non-zero neutrino masses
can be taken into account. These expressions can also be used in the analysis
of experiments on direct detection of (neutral) massive weakly interacting
relativistic dark matter particles since, unlike the generally accepted case,
they simultaneously take into account both elastic and inelastic interactions
of the particles. The presence of an "inelastic signal" with its characteristic
signature may be the only registrable evidence of interaction of the dark
matter particle with the nucleus.
