Excitation of Electrons in Metals by Primary Electrons

Abstract

The excitation of conduction electrons represented by Bloch wave functions through Coulomb interaction with a medium-fast primary is discussed. It is brought out that when the excitation energy is much smaller than the primary energy, the probabilities of transitions in which momentum is exchanged with the lattice (umklapp processes) are proportional to the corresponding probabilities for excitation by light (as was shown by Rudberg and Slater), and that the excitation rate varies roughly as the reciprocal of the primary energy. For cubic metals, the number of transitions per unit primary path with excitation energy in a differential range near $\ensuremath{\epsilon}=h\ensuremath{\nu}$ proves to be a simple factor multiplied by the photoelectric absorbing power for light of frequency $\ensuremath{\nu}$. Using this relationship, and accepting Butcher's interpretation of their optical properties, a rather detailed picture is obtained of the umklapp processes which might be of importance for secondary emission from several alkali metals. The contribution of such transitions appears to be small, but not entirely negligible, in comparison with what would be expected from a free-electron gas. Some remarks are made on the possibility that innershell electrons make an important contribution to secondary emission.