Mean Free Path for Discrete Electron Energy Losses in Metallic Foils

The discrete energy losses observed when a beam of electrons passes through a thin foil have been studied as a function of incident energy. Foils of Al, Mg, and Cu ranging in thickness from 14 to 85 μg/${\mathrm{cm}}^2$ have been bombarded with electrons of energies 25 to 115 kev. Losses appear at multiples of 14.9 ev and 10.7 ev respectively for Al and Mg whereas only one loss is found in Cu at 22.6 ev. Mean free paths for the losses lie in the range 25±10 μg/${\mathrm{cm}}^2$, 165±55 μg/${\mathrm{cm}}^2$, and 90±30 μg/${\mathrm{cm}}^2$ for the three metals. The magnitudes of the losses agree with the plasma oscillation theory of Pines and Bohm for Al and Mg if the number of free electrons per atom is chosen about equal to the valence. In addition the mean free path as a function of energy for Al agrees closely with the theoretical curve.