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The impact of the strongly attractive electromagnetic field of heavy nucleion electrons in quasi-elastic (e,e') scattering is often accounted for by theeffective momentum approximation. This method is a plane wave Bornapproximation which takes the twofold effect of the attractive nucleus oninitial and final state electrons into account, namely the modification of theelectron momentum in the vicinity of the nucleus, and the focusing of electronstowards the nuclear region leading to an enhancement of the corresponding wavefunction amplitudes. The focusing effect due to the attractive Coulomb field ofa homogeneously charged sphere on a classical ensemble of charged particlesincident on the field is calculated in the highly relativistic limit andcompared to results obtained from exact solutions of the Dirac equation. Theresult is relevant for the theoretical foundation of the effective momentumapproximation and describes the high energy behavior of the amplitude ofcontinuum Dirac waves in the potential of a homogeneously charged sphere. Ourfindings indicate that the effective momentum approximation is a usefulapproximation for the calculation of Coulomb corrections in (e,e') scatteringoff heavy nuclei for sufficiently high electron energies and momentum transfer.

Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation