Nonlinear theory of scattering by localized potentials in metalsNonlinear theory of scattering by localized potentials in metals
Faculty of Sciences. Physics

Department of Physics

article

2003London, 2003

Physics

Journal of physics: A: mathematical and general. - London, 1968 - 2006

36(2003):45, p. 11451-11463

0305-4470

000187023500008

E

English (eng)

University of Antwerp

In early work, March and Murray gave a perturbation theory of the Dirac density matrix gamma (r, r) generated by a localized potential V (r) embedded in an initially uniform Fermi gas to all orders in V (r). For potentials sufficiently slowly varying in space, they summed the resulting series for r' = r to regain the Thomas-Fermi density rho(r) proportional to [mu - V(r)](3/2), with mu the chemical potential of the Fermi gas. For an admittedly simplistic repulsive central potential V (r) = \A\ exp(-cr), it is first shown here that what amounts to the sum of the March-Murray series for the s-wave (only) contribution to the density, namely p, (r, A), can be obtained in closed form. Furthermore, for specific numerical values of A and c in this exponential potential, the long-range behaviour of p, (r, it) is related to the zero-potential form of March and Murray, which merely suffers a it-dependent phase shift. This result is interpreted in relation to the recent high density screening theorem of Zaremba, Nagy and Echenique. A brief discussion of excess electrical resistivity caused by nonlinear scattering in a Fermi gas is added; this now involves an off-diagonal local density of states. Finally, for periodic lattices, contact is made with the quantum-mechanical defect centre models of Koster and Slater (1954 Phys. Rev. 96 1208) and of Beeby (1967 Proc. R. Soc. A 302 113), and also with the semiclassical approximation of Friedel (1954 Adv. Phys. 3 446). In appendices, solvable low-dimensional models are briefly summarized.

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