The electron-hydrogen scattering problem has been a nemesis to theoretical atomic physicists due to the fact that even the most sophisticated of theoretical calculations, both perturbative and nonperturbative, do not agree with experiment. The current opinion is that the perturbative approach cannot be used for this problem since recent second-order calculations are not in agreement with the experimental data and higher-order calculations are deemed impractical However, these second-order calculations neglected second-order exchange. We have now added exchange to the second-order calculation and have found that the primary source of disagreement between experiment and theory for intermediate energies is attributable not to higher-order terms but to second-order exchange
D. H. Madison et al., "Effect of Second-Order Exchange in Electron-Hydrogen Scattering," Physical Review Letters, vol. 64, no. 19, pp. 2265-2268, American Physical Society (APS), May 1990.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.64.2265
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