| タイトル | Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering |
| 本文（外部サイト） | http://hdl.handle.net/2060/19940020325 |
| 著者（英） | Weatherford, Charles A. |
| 著者所属（英） | Florida Agricultural and Mechanical Univ. |
| 発行日 | 1993-12-17 |
| 言語 | eng |
| 内容記述 | 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. |
| NASA分類 | ATOMIC AND MOLECULAR PHYSICS |
| レポートNO | 94N24798
NASA-CR-194774
NAS 1.26:194774 |
| 権利 | No Copyright |
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