Relationship between markov chains and radiation defect formation processes by ion irradiation

The work was performed within in the context of cascade-probabilistic method, the essence of which is to obtain and further application of cascade-probability functions (CPF) for different particles. CPF make sense probability of that a particle generated at some depth h' reaches a certain depth h after the n-th number of collisions. We consider the interaction of ions with solids and relationship between radiation defect formation processes and Markov processes and Markov chains. It shows how to get the recurrence relations for the simplest CPF from the Chapman-Kolmogorov equations. In this case the particle does not change its direction of movement after the collision, the flow rate does not depend on time, and consequently, on the depth of penetration. We also obtained recurrence relations for the CPF with the energy loss of ions from the Kolmogorov-Chapman equations, the flow rate depends on the depth of penetration.