Changes in nonlinear potential scattering theory in electron gases brought about by reducing dimensionality

Recent work has shown the essential equivalence of stopping power, force-force correlation function, and phase-shift analysis for nonlinear potential scattering in a three-dimensional electron gas. In the present study, we first demonstrate that the above situation is markedly different when the scattering occurs from a localized potential in a two-dimensional (2D) electron gas. Only to second order in the potential do the three methods referred to above precisely agree. However, all these methods can still be applied in 2D, some fully nonlinear evaluation proving possible. The one-dimensional case is also discussed, albeit more briefly. Scattering from a two-center modeling of the localized potential is also calculated, but now only in the Born approximation, due to the added complication of a noncentral potential.