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

• Main Author: Lucchese, Robert Ross
• Format: Others
• Published: 1982
• Online Access: https://thesis.library.caltech.edu/6501/1/Lucchese_rr_1982.pdf; 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 <https://resolver.caltech.edu/CaltechTHESIS:06062011-113312144>

<p>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.</p> <p>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.</p> <p>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.</p>