On the approximate solution of the delay integral equation of the statistical theory of radiation damage

Abstract

In the statistical theory of radiation damage, the mean number of atoms displaced in the atomic cascade is given by a delay integral equation with specified initial conditions. Numerical procedures the use spline functions in conjuction with appropriate quadrature rules are presented for the construction of continuous approximations to the mean number of displaced atoms, represented by the delay integral. The methods presented are shown to be stable and to be of order ( m + 1) for spline functions of degree m. Finally, the method for quadratic splines is used to compute the mean number of displaced atoms for atomic collisions with Firsov potentials, and with truncated Coulomb potentials.