Contribution of close collisions to the Barkas effect : the classical picture

Abstract

According to a previous estimation made by Lindhard [Nucl. Instrum. Method Phys. Res. 132, 1 (1976)] on the basis of qualitative arguments and dimensional analysis, the contribution of close collisions to the Barkas effect in the energy loss of swift ions in solids yields a significant fraction of the total effect, being almost equal to the contribution coming from distant collisions. Here the classical estimation by Lindhard is reconsidered and subjected to a tight numerical test. We analyze in quantitative terms the classical description of the Barkas effect following the line of arguments proposed by Lindhard. We consider a swift ion of charge Z₁ interacting with the electrons via a screened potential assuming spherical and nonspherical screening models. We calculate by numerical integration the differential and total transport cross sections and find an important asymmetry of both with respect to the sign of Z₁, as well as a departure from the Z₁² behavior. These effects are particularly important for impact parameters in the range of the classical collision radius (rcl=Z₁e² /mv²2). This approach clearly shows the contribution of close collisions to the Barkas effect. We analyze the behavior of the Barkas asymmetry with respect to ion charge and velocity, obtaining a good quantitative agreement with Lindhard’s prediction. However, an additional term predicted for nonspherical potentials cannot be reproduced.