In the p < /a>resent work, the scattering differential cross section has been investigated for ion-multi electron atoms collision in the charge transfer channel. For this purpose, an active electron model was implemented and the collision process was considered as a three-body impact in the high energy range. A semi-classical formalism was used with the eikonal distorted wave function to describe the system, and the first and second order scattering amplitude of the Brinkman-Kramers approximation was employed to calculate the differential cross section. In this work, the screening Coulomb Effect and the static potential were implemented to calculate the eikonal wave function. The differential cross section was calculated for Proton-Helium, Proton-Carbon, Proton-Neon and Proton-Argon impacts by using the static Brinkman-Kramers, screening Coulomb Brinkman-Kramers, the potential Brinkman-Kramers effect, and the second order static Brinkman-Kramers approximation. The findings were then compared with the available experimental and theoretical results.