Theory of elastic scattering of fast particles in the quasiclassical approximation

Quasiclassical solution of the Dirac equation for fast electron in the external static field is discussed. The correspondence between the Born, eikonal and quasiclassical approximations and the Furry–Sommerfeld–Maue approximation is clarified. The amplitude of the elastic scattering of electrons (positrons) at small scattering angles is evaluated. The conditions are found, under which the quasiclassical amplitude leads to the results of classical mechanics and to the results of quantum-mechanical perturbation theory. Elastic scattering of fast particles by the chain of atoms, is considered.