Threshold energy of Frenkel defect formation by fast particles

The cross section sigma(E) is calculated for Frenkel defect formation in the elastic scattering of a fast particle of energy E by a crystal atom. Account is taken of the actual dependence W(T) of the defect formation probability on the energy transfer T, which is by no means a step function. The resulting sigma(E) tends to zero at a value of E denoted by E/sub d/. However, the cross section for defect formation at high energies is found not to be related to this E/sub d/ by the usual expression sigma(E) proportional (T/sub max//E/sub d/-1); such a relationship, which is widely used in the literature, is not valid, since it follows from the incorrect step form of W(T). The function sigma(E) obtained is in qualitative agreement with experiment for silicon and germanium, and good agreement of the theoretical and experimental curves can be achieved by suitable choice of the numerical values of the characteristic parameters in the theory.