Title 



Nonlinear theory of scattering by localized potentials in metals
 
Author 



 
Abstract 



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 ThomasFermi 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 MarchMurray series for the swave (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 longrange behaviour of p, (r, it) is related to the zeropotential form of March and Murray, which merely suffers a itdependent 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 offdiagonal local density of states. Finally, for periodic lattices, contact is made with the quantummechanical 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 lowdimensional models are briefly summarized.   
Language 



English
 
Source (journal) 



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



London : 2003
 
ISSN 



03054470
 
Volume/pages 



36:45(2003), p. 1145111463
 
ISI 



000187023500008
 
Full text (Publisher's DOI) 


  
Full text (publisher's version  intranet only) 


  
