Energy loss of correlated charges in an electron gas.

Abstract

The energy loss of charged particles in a degenerate electron gas has been a topic of great interest since the work of Lindhard and Winther, be-cause it became of considerable importance for the study of the energy loss of charged particles in real media. Whereas the energy loss of single atomic particles in matter has been widely studied for many years, the energy loss of swift ion clusters has been the subject of much more recent work, concerned with the incidence of swift molecular ions on thin solid films. Molecular effects on the energy loss have been theoretically described as a result of interference effects in the energy dissipated in the material, when its electrons are perturbed by the fields of external charges in correlated motion. Both of these treatments dealt with valence band electron excitations and made use of high-velocity approximations in calculating the energy loss, wherein the random motion of the electrons is neglected. Brandt, Ratkowski and Ritchie have proposed a relation between the energy loss of ion clusters and the partition rule for the contribution of individual and collective electronic excitations to the stopping, which will be further analyzed here. On the other hand, Arista and Ponce performed an analytical calculation of the energy loss, using simplified models to describe long-wavelength collective excitations and short-range individual excitations (for k « kc) and k » k c, respectively, where k c is an appropriate cutoff wave number for the electron gas), and interpolating through the more complicated intermediate region (k~k c). We consider in this paper a more appropriate treatment for the energy loss of charges in correlated motion through an electron gas, using Lindhard’ s expression for the dielectric constant of the medium. This provides a good description of collective and single-particle excitations with a self-consistent treatment of screening effects. Using the dielectric formalism we calculate the energy loss of two correlated charges; we present the results of numerical integrations, and also approximations valid at low and high velocities. These results are in addition compared with previous high-velocity approximations and several conclusions are drawn. In Sec. n we express the energy loss of a cluster of nonrelativistic charges moving in a material medium, in term s of the longitudinal dielectric constant (k , w). In Sec. III we treat the special case of two correlated charges moving in a degenerate electron gas, and present the results of full numerical integrations of the energy-loss expressions. In Sec. IV we consider in particular the case of low velocities and we show that interference effects in the energy loss are important when the internuclear separation is not large compared with the wavelength of the electrons at the Fermi surface. Using an appropriate approximation for the dielectric constant we obtain in Sec. V an analytical expression for the energy loss at high velocities, which is compared with the numerical results of Sec. III. The proposed relations between the energy loss of swift ion clusters and the partition rules for the energy loss of single charges is considered in Sec. VI, and is found not to be in general agreement with the results of this work. In Sec. VII we summarize our conclusions and finally make some comments in relation with current studies of swift molecular ions traversing solid films.