An Exact Second-Order Theory and its Application to Electron-Hydrogen Excitation
Recent technological advances have produced increasingly detailed experimental measurements. These results have often revealed problems associated with the standard first-order perturbation series theoretical approaches. For several scattering problems, it is becoming evident that a good second-order theory is needed. However, theoretical calculations of second-order amplitudes typically resort to several simplifying approximations to make the calculation tractable. A new approach is developed which reduces the exact evaluation of a second-order amplitude to a tractable form. The utility of the method is demonstrated through a practical calculation of the exact second-order distorted-wave amplitude for electron excitation of the 2p state of hydrogen. For this case, the second-order results are in significantly better agreement with experimental data than the first-order results.
D. H. Madison et al., "An Exact Second-Order Theory and its Application to Electron-Hydrogen Excitation," Journal of Physics B: Atomic and Molecular Physics, vol. 18, no. 13, pp. 2737-2761, Institute of Physics, Sep 1985.
The definitive version is available at https://doi.org/10.1088/0022-3700/18/13/022
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