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A consistent relativistic theory of electron scattering by atoms

The authors show that the (N+1)-electron problem defined by the elastic scattering of a projectile electron from a target of N electrons can be reduced to a Dirac-type one-particle equation which has to be solved self-consistently for the (N+1)-electron states in question. The derivation tests on a relativistic extension of the generalized density functional theory recently put forward by Fritsche. The four-component spinor equation can be further reduced to a two-component Pauli-type equation without loss of generality. The new scheme has already been applied by Fritsche et al. to electron scattering by various closed and open shell atoms. Calculated differential cross sections and scattered induced polarization show very satisfactory agreement with the experimental data of Kessler et al. This favourable state of affairs can be further improved by applying the refined version of the authors' theory reported in the present paper.