On the dispersion relations for electron-atom scattering

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Abstract
The analytic behaviour of the ordinary (f) and exchange (g) amplitudes appearing in the dispersion relation for e--H(1s) scattering is examined via comparatively simple configuration-space arguments. It is found that the quantity f-fB is everywhere analytic in the energy (E) plane at energies where the total Green's function G(E) is analytic, in agreement with assumptions made by Gerjuoy and Krall (1960, 1962) in deriving dispersion relations for e--H(1s) scattering; here the subscript B denotes the first Born approximation. However, the amplitude g-gB is found to be singular at certain negative real energies, in disagreement with Gerjuoy and Krall's assumptions, but consistent with the recent conclusions of several groups.

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