Asymptotic method in the theory of the passage of fast charged particles through matter

The multiple elastic Coulomb scattering of fast charged particles (electrons) by a grand canonical ensemble of atoms is considered. The basic scalar equation for the wave function of the particles in the matter simplifies in the approximation of small scattering angles. The screened Coulomb potential is regularized at short distances. By means of rigorous estimates of the spatial scale of the clusters of atoms and the mean free path of the particles in the matter, asymptotic conditions are formulated for the applicability of a kinetic equation of Pauli type for the particle distribution function with collision integral linear with respect to the cluster functions of the atoms of all orders.