Perturbation Calculation of the Elastic Scattering of Electrons by Hydrogen Atoms

A perturbation calculation has been carried out for the scattering of electrons by hydrogen atoms, using as the perturbation only the interaction between the two electrons, and retaining in the result only terms of the highest power in the incident energy of the electron. The results are then compared with more conventional first-order perturbation calculations for this problem. It is found that to the order in the energy that we retain, the results for direct-scattered amplitudes obtained by the two perturbation procedures are the same, whereas in the results for the exchange-scattered amplitudes there is a difference in the energy dependence. While no conclusions can be drawn as to which perturbation procedure is more accurate, some reasons are given for preferring the calculation performed here.