Ab Initio Calculations of Processes in Low Energy Electron-Molecule Scattering

Author: Levin, Deborah Ann

Year: 1979

Degree: Dissertation (Ph.D.)

Advisor: McKoy, Basil Vincent

Committee Member: Unknown, Unknown

Option: Chemistry

DOI: 10.7907/k96t-xc35

Abstract

Chapter I

Calculations are reported for low energy e-N2 scattering cross sections in the static-exchange approximation. The approach used involves solving the Lippmann-Schwinger equation for the transition operator in a sub-space of Gaussian functions. New features of the method are analytic evaluation of matrix elements of the free particle Green's function and analytic transformation to obtain single-center expansion coefficients for the scattering amplitude. Results are presented for the total elastic and rotational excitation cross sections and the momentum transfer cross section for incident electron energies of 0.5 to 10 eV. Comparison with other theoretical and experimental data is included.

The second paper of this chapter presents cross sections for e--CO scattering in the static exchange approximation. The method of calculation is the T-matrix discrete-basis-set method as updated by Fliflet, Levin, Ma and McKoy (previous paper) along with the variational correction approach of Fliflet and McKoy. We extract the 2π resonance parameters at equilibrium internuclear separation and compare with other theoretical and semi-empirical results. Momentum transfer cross sections are compared with the experimental data of Land and the theoretical calculation of Chandra.

Chapter II

Results are presented in this first paper for rotational and vibrational-rotational excitation of H2 by electron impact in the static-exchange approximation. Using the T-matrix discrete-basis-set approach as described in the first paper of Chapter I we solve the fixed-nuclei scattering problem at several internuclear separations. Comparisons of our results with the experimental data of Linder and Schmidt and with other calculated results are given.

In the second paper of this chapter we obtain vibrational and vibrational-rotational excitation cross sections of N2 by electron impact via the 2Πg resonance in the static-exchange approximation. To obtain highly accurate phase shifts in the Πg channel we use the variational correction of Fliflet and McKoy applied to the discrete-basis- set method of Fliflet, Levin, Ma and McKoy. As in e-H2 vibrational excitation, the approach involves solving the fixed-nuclei scattering problem at several internuclear separations. From these calculations one extracts the parameters necessary to calculate resonant vibrational cross sections in a compound state model. Our results are compared with the experimental data of Wong et al., and other theoretical calculations.

Finally, the last paper discusses a simple model to include polarization effects in shape resonances. The position and width of the 2eV shape resonance in e-N2 scattering are calculated by solving the T-matrix equations with the static-exchange field of the N2 case of the N2- compound state. Resonance parameters obtained at the equilibrium separation of the molecule agree well with semi-empirical results. Most importantly, the procedure can be readily applied at several internuclear separations.

Chapter III

As was mentioned in Chapter I, an important refinement of the original T-matrix method is the analytic evaluation of Gaussian matrix elements of the free particle Green's function. Previous calculations evaluated these matrix elements by a numerical quadrature which was in practice restricted to cases of axial symmetry. In this chapter the derivation of a method for generating higher order Gaussian matrix elements is presented. Although this procedure is applicable to polyatomic systems, we list here only the types of matrix elements necessary for Σ, Π and Δ symmetries of a linear molecule.

Chapter IV

In this chapter a method for obtaining scattering wave functions at arbitrary energies is presented. Minimization of the variance integral for a trial wave function expanded in discrete basis functions only provides a criterion for choosing the expansion coefficients of the wave function. By using a separable representation of the scattering potential only one new class of matrix elements appears in the evaluation of the variance integral which is not already required in the diagonalization of the Hamiltonian. The method is applied to some model potentials and to s-wave scattering for helium in the static-exchange approximation.

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