Quasiclassical green function in an external field and small-angle scattering processes

A representation is obtained for the quasiclassical Green functions of the Dirac and Klein-Gordon equations allowing for the first nonvanishing correc tion in an arbitrary localized potential which generally possesses no spher ical symmetry. This is used to obtain a solution of these equations in an a pproximation similar to the Furry-Sommerfeld-Maue approximation. It is show n that the quasiclassical Green function does not reduce to the Green funct ion obtained in the eikonal approximation and has a wider range of validity . This is illustrated by calculating the amplitude of small-angle scatterin g of a charged particle and the amplitude of Delbruck forward scattering. A correction proportional to the scattering angle was obtained for the ampli tude of charged particle scattering in a potential possessing no spherical symmetry. The real part of the Delbruck forward scattering amplitude was ca lculated in a screened Coulomb potential. (C) 2000 MAIK "Nauka/Interperiodi ca".