Abstract
The integral-differential equation of the cascade process for ions was solved using the Laplace transform and the method of successive approximations, taking into account the energy loss during the formation of primary-knocked-on atoms (PKA) in a one-dimensional model of an elementary atom. It is shown that the solution includes a cascade-probability function (CPF) for these particles. The main properties of CPF are considered and its graphical dependencies on the depth of registration are presented. It is shown that with the specific ionization loss coefficient k = 0, the FQM turns into the simplest cascade-probability function. When λ0→ 0, λ0→∞ and n→∞, the KV-function is equal to 0. The sum of the probabilities for all possible collisions from 0 to ∞ is 1. As the detection depth h increases, for all values of n, the CRF increases, reaches a maximum and then decreases . With increasing n, the curves shift to the right.