Impact-parameter dependence of the electronic energy loss of protons in collisions with atoms

We calculate the energy transferred by a swift incident particle to a stationary atom as a function of the impact parameter. The calculation is based on a local-density approximation and on the electron-gas model. We apply Thomas-Fermi and Lenz-Jensen atomic models, and we study the general scaling properties of the energy loss as a function of the impact parameter and velocity, in terms of the target atomic number $Z_2$. With the same description we calculate the stopping cross section as a function of $Z_2$, and compare it with existing experimental results. Finally, we compare our theory with the experimental results of Eckardt et al. for the angular dependence of the energy loss of protons transmitted through thin solid foils.