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It is demonstrated that the amplitude for electron-hydrogen-atom forward scattering has the third-order pole at the point E=-13.6 eV, E being the energy of the incident electron. The coefficients which characterize the pole are calculated exactly. The invalidity of the Born approximation is proved. The contribution of the pole singularity to the dispersion relation for the scattering amplitude is discussed.
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Amusia et al. (1982) studied this question.
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