The Iterative Schwinger Variational Method Applied to Electron-Molecule Continuum Processes

Citation

Lucchese, Robert Ross (1982) The Iterative Schwinger Variational Method Applied to Electron-Molecule Continuum Processes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/JS31-4A21. https://resolver.caltech.edu/CaltechTHESIS:06062011-113312144

Abstract

We have developed the iterative Schwinger variational method to study electron-molecule scattering problems within the Hartree-Fock approximation. The method is based on the iterative use of the Schwinger variational principle and can obtain exact static-exchange scattering solutions. This approach has been implemented using standard single-center expansion techniques. We present results using the Schwinger variational expression for e-He and e-He⁺ collisions and find very rapid convergence of the phase shifts with increasing basis set size. We then discuss the iterative use of the Schwinger variational expression and give results for e-H₂ and e-H⁺₂ scattering which show very rapid convergence of the iterative method. We have applied this method to low energy 3-CO₂ scattering and obtained differential and integral elastic scattering cross sections. We determined that the ²π_u shape resonance in this system occurs at an energy of 5.39 eV with a width of 0.64 eV in contrast to previously published static-exchange results.

We have also used the iterative Schwinger variational method to study the valence shell photoionization of N₂ and CO₂ as well as the K-shell photoionization of CO₂. These results agree well with available experimental data. The vibrational branching ratios for photoionization of 3σ_g level of N₂ were found to agree quantitatively with experimental measurements when an adequate number of internuclear spacings were considered. The effects of vibrational averaging on 4σ_g photoionization of CO₂ were also studied. A detailed comparison of the results obtained using the Schwinger method and other theoretical methods for studying photoionization has been made.

The iterative Schwinger variational method has proven to be an accurate and efficient method for obtaining Hartree-Fock level scattering solutions, and it has allowed us to study electron-molecule continuum processes in more detail and for larger systems than previously possible.

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