Me. Bachlechner et al., ENERGY-LOSS FUNCTION IN THE 2-PAIR APPROXIMATION FOR THE ELECTRON LIQUID, Physical review. B, Condensed matter, 54(4), 1996, pp. 2360-2373
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.