The Local Plasma Frequency Approach in Description of the Impact-Parameter Dependence of Energy Loss

Abstract

The LPF approach of Lindhard and Scharff is generalized to describe on the same basis the impact parameter dependence of energy loss in ion–atom collision. To make this feasible the energy loss is represented as an integral of the local energy deposition over the atomic shell volume. The local energy loss is determined by the induced electron current and the intensity of the projectile field at a given point. The LPF approach consists in an approximate description of the induced current using the corresponding expression for a uniform electron gas. With an appropriate description of the electron gas response, the atomic shell polarization and the state of electron motion are considered. The developed approach provides a possibility to test the accuracy of the customary approximation where the energy loss is expressed through the electron density on the ion trajectory, the local density approximation. A comparison with the available experimental results displays the adequateness of the developed approach if, additionally, the higher-order corrections over the projectile charge are taken into account.

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“…The representation (14) permits us to present [12] a comprehensive description of energy loss also for the uniform gas of interacting electrons. This is possible if the response of electrons on the projectile field is treated in the linear RPA approach.…”

“…In section 2, these features are analysed on the qualitative level. Using the introduced representation of energy loss, the Lindhard-Scharff model [11] for the stopping cross section (the local plasma frequency, LPF, approach) can be generalized [12] to describe E(b) in the linear response approach. The combination of this model with the exact description of energy loss to free electrons results in a general model [13] where both the Barkas and Bloch corrections to E(b) are described in a general scheme.…”

“…This estimate, however, loses its validity when the angle of diffraction of the electron wave, diff ≈ 1/vs ad = ω/v 2 , has a larger value. In this case, min ≈ diff and L is given by the expression (12).…”