Electronic energy loss of helium ions in aluminum using the extended-sum-rule method

Using a recently derived extension of the Friedel sum rule to finite velocities we calculate the energy loss of helium ions in aluminum. The model includes the contribution due to the excitation of valence electrons according to a quantum-mechanical picture based on scattering theory (transport cross-section approach) and gives a self consistent representation of the velocity-dependent screening for swift ions. The method provides a direct evaluation of the nonlinear effects in the more complex range of energies around the stopping power maximum. In the corresponding limits, the present results converge to the existing low- and high-velocity approximations. The stopping power values calculated with this method are in good agreement with various experimental results.