Assuming that the polarization of a free electron gas about an electron moving through it gives rise to an exponential screening of the Coulomb potential, a method is given by which the screening parameter can be calculated. With such an interaction, a method is found for calculating the frequency of collisions and the rate of loss of energy of an excited electron in an electron gas. From these calculations the X-ray absorption line-width and the stopping power for electrons of the electron gas are deduced. High-energy asymptotic expansions are found for both quantities. When the time-dependent perturbation method is applied to the same problem, the usual simplifying assumptions are seen to be incompatible. A possible case of the same sort of failure in the calculation of Auger-effect transition probabilities in an isolated atom is pointed out.