Numerical study of the dispersion relation for e--H scattering

Numerical studies of the dispersion relation for forward scattering are reported for electrons scattered by atomic hydrogen. As has previously been shown for electron-helium scattering, the relation of Gerjuoy and Krall (Phys. Rev.; 119:705 (1960). Phys. Rev.; 127:2105 (1962)) has been modified. The extra term to be included, the so-called discrepancy function Δ(E), is related to the non-analyticity of the exchange part of the scattering amplitude for negative energies. This function, which corresponds to an integral over the left-hand cut discontinuity, is evaluated. (author)