Calculation of the multifold differential cross section of the electron-impact ionization of molecular hydrogen by prolate spheroidal external complex scaling method with second Born corrections

We introduce the second Born dipole corrections in our recently developed ab initio procedure based on the driven Schroedinger equation formalism and the external scaling method for the determination of the multifold differential cross sections of the single and double ionization of molecular hydrogen by electron impact. To test our procedure, we first apply it to the excitation-ionization process of a He atom and compare the results to those of equivalent theoretical results, which are available. We then show that the introduction of the second Born correction including only dipole terms improves the agreement with the experimental results only in the case of the simple ionization. We think that the introduction of nondipole contributions in the second Born term which are not taken into account in the present work is necessary in the case of the double ionization process.