Impact-parameter-dependent stopping of swift ions

Abstract

Quantitative theory of the stopping of channeled ions needs impact-parameter-dependent electronic energy loss as input. In the previous paper, binary stopping theory has been expanded to provide such data primarily for the classical regime, i.e., for beam energies below 100 2 1 keV/u. The theory incorporates the Barkas-Andersen effect, charge-dependent projectile screening and pertinent atomic properties. A stringent test on the scheme is channeling measurements under frozen-charge conditions, where minimum energy losses have been measured. We have applied the scheme to the stopping of B, C, N, O and F ions in the (111) planar channel of Au, and of F, Mg, Si, S and Cl ions in the [110] axial channel of Si. The Si target has been characterized in terms of atomic charge distributions for the three principal shells. The Au target has been characterized by atomic charge distributions for all subshells except the 6s electrons which are described in terms of a homogeneous electron gas. Better than 10 pct agreement has been achieved without the use of adjustable parameters with experimental data for 2 MeV/u ions in Au and 3 MeV/u in Si for all measured charge states. We find that a description in terms of the impact-parameter dependence is essential in the analysis, in particular with regard to the influence of the charge state. The discussion emphasizes the fact that unlike in random motion, the stopping force follows a 2 1 relation quite closely.

Expanded PASS stopping code

“…• Impact-parameter-dependent energy loss [51] with application to channeling [52] as well as correlated straggling, i.e., bunching and packing caused by the proximity of target electrons [53],…”

Impact-parameter-dependent electronic stopping of swift ions

“…while the last term reduces to zero because e e = 0 (22) for a distribution exhibiting mirror symmetry. It is important to notice here that the spatial average is taken over the longitudinal direction, while the averaging over the velocity goes over the transverse plane.…”

“…Therefore, after specifying the formalism and the computational procedure, the prime purpose of the present paper is testing the output of the code against existing theoretical results based on similar input. Applications to practical problems and comparisons with experimental data are considered in further studies, in particular the subsequent paper [22].…”

“…) up to the second order. Here a term containing e e has been dropped: It vanishes by the same argument as the term in eq (22)…”

Note on measuring electronic stopping of slow ions

“…The theory, which has been implemented in the PASS code [15] and applied in extensive tabulations of stopping cross sections [21], also allows calculations of the dependence of the mean energy loss on impact parameter [22]. Calculations involving PASS in this paper have been performed with standard input applied in ref.…”