Lattice effects in fast electron energy losses by plasmon excitation in metals

Abstract It is well known that a fast electron moving through a metal can excite plasma oscillations and the theory has been fully worked out for a homo-geneous electron gas. The object of this work is to take-into account the periodic lattice in calculating the energy losses and angular distribution offast particles, due to excitation of pleamon modes. We first formulate this problem in general terms, but in order to expose the new features introduced by the lattice we treat the lattice potential as weak. The principal conclusions are : (i) The usual uniform electron gas result remains unchanged by the first-order term in the lattice potential unless the velocity vector v of the fast electron is along a lattice vector in either the direct or the reciprocal lattice. (ii) When v is along a lattice vector, the effects of the lattice can be ex-pressed in terms of the Fourier components of the ground-state charge density, which are themselves accessible to experiment from X-ray intensities at the Bragg reflections. The general form of the angular distribution of the scattered electrons is modified in a way determined by the reciprocal lattice vectors orthogonal to the trajectory. The theory presented here may have direct relevance to energy losses in high-voltage electron microscopy.