Abstract
The work is performed within the framework of a cascade-probabilistic method, the relevance of which is beyond doubt, since the models obtained make it possible to trace the entire process in dynamics and can later be used in industry to obtain materials with predefined properties. Algorithms for calculating the spectra of primary knocked-on atoms for protons have been developed. The features of the selection of approximate expressions and approximation coefficients for proton irradiation are considered. Calculations have been made for the concentrations of vacancy clusters in copper irradiated by protons.