Shell corrections to electronic stopping powers from orbital mean excitation energies

Shell corrections to electronic stopping powers are obtained from a theory which utilizes different orbital mean excitation energies for the atomic shell and which determines the shell correction from knowledge of the atomic velocity distribution. When summed over all shells, and taking into account the "effective" occupation of the shells, the orbital mean excitation energies yield the total mean excitation energy $I$. Orbital mean excitation energies are much larger than $I$ for $K$ shells and less than $I$ for the outer valence shells. The atomic velocity distributions are obtained from numerical Hartree-Fock calculations. We report shell corrections for Al and Ar. We find very good agreement between other theoretical and experimental shell corrections and the present calculation. We find that the $L$ shell gives the dominant contribution to the shell corrections for low projectile velocities while $K$-shell corrections dominate for larger velocities. The total shell correction is relatively insensitive to the choice of the total mean excitation energy. We have also investigated the validity of expanding the shell correction in powers of $v^{-2\mathrm{}}$.