Energy-loss straggling with higher-order effects and electron correlations taken into account

Abstract

The approach suggested previously to treat the mean energy loss of charged projectiles in terms of induced currents is extended to describe the energy-loss straggling. It has been shown that, provided the perturbed wave function of electrons is known, the phenomenon can be represented in a form of distributions of densities of energy and energy squared within the target volume. These distributions satisfy respective continuity equations with the source terms defining the local deposition of energy and energy squared. The approach is applied to treat the canonical phenomenon, the stopping in a uniform electron gas, and provides a possibility to account for the spatial correlation of electrons. Two types of approximations for the perturbed state of electrons are considered, the impulse and continuum distorted-wave approximations. Together with the effect of electron correlations, these nonperturbative approaches permit one to evaluate the higher-order correction over the projectile charge. The origin of this correction is similar to the origin of Barkas correction in the stopping power; it can be argued also that there is no place in straggling for the Bloch correction. These properties, i.e., nonlinear electron response and electron correlations, can result in significant effects, both capable of changing dramatically the straggling at small projectile energies. However, in the case of positively charged projectiles, the two effects mainly compensate for one another. For negatively charged projectiles, due to the impossibility of close approaches of the collision partners, both effects are effectively smeared out.