A dispersion relation for forward scattering, as formulated by Gerjuoy and Krall (1960) is studied numerically for electron and positron scattering by helium. The real part of the scattering amplitude for elastic scattering at impact energy E and scattering angle zero is evaluated from this relation and compared with its experimental or theoretical value. For electrons, it is shown that the dispersion relation of Gerjuoy and Krall has to be modified. The results suggest that an extra term should be included, which is related to the nonanalyticity of the exchange part of the scattering amplitude for negative energies.
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Heer et al. (1976) studied this question.
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