Develop a Model to Study the Energy Distribution of Cascades of Atomic Collisions

In this paper, based on the solution of the Boltzmann kinetic equation, we determine the energy distribution function describing the steady-state deceleration of the cascade of moving atoms taking into account their multiplication at the power interaction potential U∼1/rⁿ. A new approach to the solution of the kinetic equation based on the extended concept of primary knocked-on atoms (PKA) is used for its calculation. One of the advantages of using the power interaction potential is that in this case it is possible to obtain simple analytical formulas for the distribution function of the cascade of slowing-down atoms taking into account their multiplication and demonstrate the simplicity and convenience of the proposed new approach to the solution of the kinetic equation. On the other hand, based on the obtained results it is possible to estimate the accuracy of various approximate solutions. It is shown that this approach will be applicable to other interatomic interaction potentials, if the average PKA energy loss in individual collisions decreases monotonically with decreasing energy, and the relative PKA energy loss in individual collisions will be small

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