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 et al. (1960, 1972) has to be modified. The extra term to be included, the so-called discrepancy function Delta (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.