Abstract
The asymptotic density of a free noninteracting electron gas is discussed in the presence of a general potential , where X is a vector in one, two, and three dimensions corresponding, respectively, to the potential of a surface barrier, an edge dislocation, and an impurity. At zero temperature, oscillations in the density have the form , where is the dimensionality of X, is the Fermi momentum, and is a phase angle. The amplitude is determined by the backward scattering amplitude at the Fermi energy for the potential . At a finite temperature the amplitude of the oscillations in normal metals is reduced approximately by the factor , where , and is the reciprocal of the thermal energy . In the high-density limit, the results of the dielectric theory become the Born-approximation version of the exact scattering theory. Mild restrictions on the potential to guarantee certain analytical properties of the scattering matrix are imposed.
- Received 7 January 1966
DOI:https://doi.org/10.1103/PhysRev.146.379
©1966 American Physical Society