Z13dependence of the energy loss of an ion passing through an electron gas

Abstract

The theory of the energy loss of an ion with charge Z/sub 1/e passing through an electron gas is considered. The term proportional to Z/sub 1//sup 3/ in the expression for the stopping power of the medium is derived by taking a second functional derivative of the induced charge in the medium and is expressed as a product of three Green's functions. The actual evaluation is effected by separately treating the momentum transfer to distant and close collisions. Also, it is assumed that the Fermi energy E/sub F/ is less than h..omega../sub p/, the plasmon energy of the medium. The contribution to the Z/sub 1//sup 3/ term from distant collisions is similar to that obtained by others using an atomic model for the stopping medium if one replaces the atomic binding energy by h..omega../sub p/. The contribution from the region of close collisions is shown to be unimportant compared to that from distant collisions because screening of close collisions is expected to be negligible in the electron gas. This work will discuss related work by Lindhard and Esbensen, and by Arista, who arrive at different conclusions with respect to this impact-parameter dependence.