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Calculation of e⁻-H Atom Scattering Processes using Hyperspherical Coordinates


Hood, Diane Marie (1986) Calculation of e⁻-H Atom Scattering Processes using Hyperspherical Coordinates. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xj5h-me61.


A method is presented for accurately solving the Schrödinger equation for the scattering of an electron from a hydrogen atom in three dimensions, which uses hyperspherical coordinates. Our motivation for using this new technique is that previous methods -- coupled channel expansions using target atom eigenfunctions,1 polarization functions and pseudostates,2 and variational methods3 -- have all proven unsatisfactory. The coupled channel calculations tend to have difficulty obtaining convergence with respect to basis set size, and the variational method interjects spurious resonances. Previous applications of hyperspherical coordinates4 have used methods that, while adequate for computing the energy level of the bound state of H-, are not appropriate to full scattering calculations.

We have obtained converged surface functions at a set of discrete values of the hyperradius, which acts as a parameter. The surface functions are further expanded in a basis set that involves 1-dimensional functions of the hyperspherical angle, which are obtained by a finite difference method.

The surface functions have been used to expand the scattering functions. The resulting coupled equations are solved numerically. The wavefunctions are obtained separately at each energy and are converged with respect to the number of basis functions used. Calculations performed so far give converged results for J = 0 through J = 5 up to the n = 4 threshold. The method is both accurate and efficient, and has been implemented on a VAX 11/780 with an FPS164 attached processor.

Both the magnitude and phase of elements of the scattering matrix have converged. Integral cross sections have been obtained for energies up to the n = 4 threshold of hydrogen. Feshbach resonances have been detected below each threshold, and they have been characterized and classified.

1P. G. Burke, S. Ormonde, and W. Whitaker, Proc. Phys. Soc. 92, 319, (1967).

2S. Geltman and P. G. Burke, J. Phys. B 3, 1062, (1970).

3J. Callaway, Phys. Rev. A 26, 199, (1982).

4C. D. Lin, Phys. Rev. A 23, 1585, (1981).

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Chemistry
Degree Grantor:California Institute of Technology
Division:Chemistry and Chemical Engineering
Major Option:Chemistry
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McKoy, Basil Vincent
Thesis Committee:
  • McKoy, Basil Vincent (chair)
  • Kuppermann, Aron
  • Dougherty, Dennis A.
  • Goddard, William A., III
Defense Date:7 January 1986
Record Number:CaltechTHESIS:10172019-161305619
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11823
Deposited By: Mel Ray
Deposited On:17 Oct 2019 23:39
Last Modified:16 Apr 2021 22:12

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