Abstract
The work was performed within in the context of cascade?probabilistic method, the essence of which is to obtain and further application of cascade?probabilistic 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.
Highlights
Were described the basics of the cascade−probabilistic method and its applications in the physics of cosmic rays, radiation and positron physics
Since the process is continuous on depth of penetration and the particle is always at a certain depth, instead of the sum we have the integral, which is taken over the entire depth of h' to h
Consider the case where after the collision particle does not change its direction of movement, the flow rate depends on time, and on the penetration depth, i.e. (Kupchishin et al, 2010)
Summary
Were described the basics of the cascade−probabilistic method and its applications in the physics of cosmic rays, radiation and positron physics. The basics of modelling of radiation defects within the cascade−probabilistic method were obtained. It should be noted that the problems of radiation defect formation in the interaction of ions with matter are presented in a large number of works, for example (Agranovich & Kirsanov, 1976, Orlova & Trushina, 1979, Ackerman et al, 1972, Caro, 1993, Zou et al, 1993, Audouard et al, Fink et al, 1993, Konopleva et al, 1971). Since the mileage of interaction λ [lambda] for formation of primary knock−on atoms (PKA) is strongly dependent on the energy, it is necessary to obtain the mathematical and physical models of the charged particles through substance. Calculations show that the neglect of the real dependencies of various parameters of the elementary act and others on energy, angle, depth, etc. can lead to significant errors in the calculations
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