Model dielectric functions for ion stopping: The relation between their shell corrections, plasmon dispersion and Compton profiles

Abstract

We describe a set of energy ( ω ) and momentum ( q )-dependent dielectric functions with the same shape of the loss function (Im − 1 / ϵ ( ω , q ) ) in the optical limit ( q = 0) and thus the same mean ionization energy I but different behavior away from q = 0. The corresponding proton stopping values differ especially at lower energies. Within the Bethe formula the stopping only depends on the mean excitation energy I . These models display thus different shell corrections, defined as the deviation from the stopping from the Bethe values. Shell-correction contributions originate equally from collisions with low momentum transfer and with high momentum transfer. Intermediate q collisions do not contribute to the shell corrections. At high q the shell corrections are related to the width of the loss function at these q values (which is proportional to the momentum distribution of the electrons [“Compton profiles”]) or, for classical models, from a shift in position. The low- q contribution is related to the plasmon dispersion.