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.