Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering. Final report

Technical Report · Wed Dec 01 04:00:00 EST 1993

OSTI ID:5172294

Weatherford, C A

One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi[sup 1]Sigma[sub g](+) yields b[sup 3]Sigma[sub u](+) excitation.

• Research Organization: Florida Agricultural and Mechanical Univ., Tallahassee, FL (United States)
• OSTI ID: 5172294
• Report Number(s): N-94-24798; NASA-CR--194774; NAS--1.26:194774; CNN: NCC2-492
• Country of Publication: United States
• Language: English

Related Subjects

664300* -- Atomic & Molecular Physics-- Collision Phenomena-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
CALCULATION METHODS
CARBON COMPOUNDS
CARBON MONOXIDE
CARBON OXIDES
CHALCOGENIDES
COLLISIONS
ELASTIC SCATTERING
ELECTRON COLLISIONS
ELECTRON-MOLECULE COLLISIONS
ELEMENTS
HYDROGEN
MOLECULE COLLISIONS
NONMETALS
OXIDES
OXYGEN COMPOUNDS
SCATTERING
SCHWINGER VARIATIONAL METHOD
VARIATIONAL METHODS