Impact-parameter dependence of the electronic energy loss of protons in solids

We calculate the electronic energy loss of the low- and intermediate-energy proton in collision with a solid atom as a function of the impact-parameter by using the linear response dielectric theory, the semiclassical approximation and local electron density approximation. The correlation and exchange interaction of the electron gas in solids is taken into consideration by using a local-field-correction dielectric function. With the formalism we also calculate the electronic stopping cross section of protons in solids