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A study of pseudoresonances in the application of the schwinger variational principle to electron scattering from atomic hydrogen
Author(s) -
Weatherford Charles A.,
Odom Gregory,
Tucker Roy
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560360813
Subject(s) - scattering , gravitational singularity , separable space , variational principle , wave function , matrix (chemical analysis) , electron scattering , variational method , physics , basis (linear algebra) , electron , hydrogen atom , quantum mechanics , first principle , mathematical physics , mathematics , chemistry , mathematical analysis , density functional theory , geometry , chromatography , group (periodic table)
The Schwinger variational principle is applied to s ‐wave electron‐hydrogen atom scattering. We show computationally, that, consistent with a recent paper by Apagyi, Lévay, and Ladányi [Phys. Rev. A 37, 4577 (1988)], there are pseudoresonances at the static exchange level of approximation, but not at the static level. We employed the T ‐matrix as well as the K ‐matrix version of the Schwinger principle, with a real Slater basis, and obtain the same results in both. We are able to identify the origin of the pseudoresonances as resulting from singularities in the separable potential that is effectively employed in the Lippman–Schwinger equation from which the Schwinger variational principle can be derived. The determination of the pseudoresonance parameters from the separable potential is computationally inexpensive and may be used to predict the pseudoresonance parameters for the scattering calculations so as to avoid them.