Relativistic electron scattering from a two-centre potential

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Abstract
A method of studying the scattering of a high-energy electron from a two-centre Coulomb potential is presented. The Dirac equation for the problem is solved by a generalised form of the Sommerfeld-Maue approximation, using a spheroidal phase shift analysis at the final stage. For a screened potential, the total cross section has been calculated and averaged over a random orientation of the axes of the two-centre systems. For a long-range potential, the differential cross section can be obtained after the averaging is done numerically. The spheroidal phase shifts are obtained by comparing the asymptotic behaviour of the radial equation with that of the central Coulomb radial equation and using a generalised JWKB method. The method is studied by considering the simple case of two fixed point charges. Some results, for this case, are also presented.

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