Based on the Boltzmann kinetic equation, an exact expression is obtained for describing the spatial distribution of vacancies formed by a cascade of atomic collisions in a solid. This expression is represented in a simple dimensionless form depending on single dimensionless parameter epsilon(0) = E-0/epsilon(d) (E-0 is the energy of primary knocked-on atoms and epsilon(d) is the binding energy of atoms at lattice sites). In solving the kinetic equation, it was assumed that the solid consists of identical atoms, the scattering of moving atoms is elastic and spherically symmetric in the center-of-mass system, and the interaction cross section is a constant quantity.
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