ENERGY-LOSS FUNCTION IN THE 2-PAIR APPROXIMATION FOR THE ELECTRON LIQUID

The imaginary part of the proper polarizability, Im Pi, arising due to excitations of two electron-hole pairs, is studied in detail for elec tron systems of arbitrary dimensionality, and taking into account arbi trary degeneracy of the electron bands. This allows an application to semiconductors with degenerate valleys, and to ferromagnetic metals. T he results obtained not only confirm expressions already known for par amagnetic systems in the high-frequency region, but are also rigorousl y shown to be valid for all frequencies outside the particle-hole cont inuum. For a sufficiently high momentum transfer a cutoff frequency (b elow which Im Pi=0) is established for not only two-pair but also any n-pair processes. In contrast, there is no upper cutoff for n>1. The e nergy-loss function, including the discussed two-pair contributions, i s calculated, The effects of screening are investigated. Numerical res ults, illustrating various aspects and properties of this function, es pecially showing finite-width plasmon peaks, are obtained for a two-di mensional electron gas.