Monte Carlo test of the T-expansion approach to range and depth calculations at low energies

Abstract

The transport equations for the range and depth are derived in the approximation of equal spacing between collisions. The T-expansion solutions of these equations are compared with results from Monte Carlo simulations in the reduced energy interval from ε = 3.16 × 10−4 to ε = 10−1 for four projectile–target pairs. In the critical region of equal projectile and target masses, the T-expansion solutions for the mean depth were found to converge more rapidly than the mean-range solutions as higher order terms were retained. The greatest errors observed in the first approximation to the mean depth and mean range were, respectively, 21% for Bi on Ge and 59% for Au on Au. In addition, for the case of a heavy projectile on a light target, the standard method of extracting stopping cross sections (S) from experimental range data was investigated. This method, which is based upon the equation for the first approximation to the range, led to an overestimation of S of up to 49% when the method was applied to the Monte Carlo results for Bi on Ge.