Influence of velocity difference of correlated particles on the stopping power and vicinage effect

We theoretically investigate the influence of the velocity difference of charged particles moving closely in a metallic target on the stopping power and vicinage function, as well as the energy loss of a pair of charged particles penetrating coherently in the target medium. These correlated charged particles are considered as a degenerate electron gas with appropriate density. Based on the dielectric formalism, the mathematical expressions for the stopping power, vicinage effects and related quantities for two correlated protons in an aluminium target are given. Plasmon-pole approximation without dispersion is used to describe the target response. We show that the energy loss is slightly enhanced with a small relative velocity difference. The interference between such protons exhibits a maximum at certain velocity, and exhibits an oscillating behaviour when product of the relative difference velocity and time is beyond a threshold value. The results can be applied to, for example, the energy deposition of high current density ion beams.