  A consistent theory, which describes the incoherent scattering of classically
moving relativistic particles by the nuclei of crystal planes without any
phenomenological parameter is presented. The basic notions of quantum mechanics
are applied to introduce a fundamental compact formula for the mean square
incoherent scattering angle per unit length of particle trajectory. The latter
is used to implement the effects of the crystal atom distribution inhomogeneity
into the Coulomb scattering simulations without noticeable elongation of the
simulation time. The theory essentially reconsiders the nature of positively
charged particle dechanneling from the low nuclear density regions, being
essential in both the crystal undulators and envisaged measurements of the
specific electromagnetic momenta of short living particles.
