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Potential energy function from differential cross‐section data: An inverse quantum scattering theory approach
Author(s) -
Lemes N. H. T.,
Borges E.,
Sousa R. V.,
Braga J. P.
Publication year - 2008
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.21701
Subject(s) - inverse scattering problem , inverse problem , scattering , inversion (geology) , uniqueness , quantum inverse scattering method , scattering theory , quantum , function (biology) , cross section (physics) , scattering length , born approximation , scattering cross section , physics , mathematics , mathematical analysis , quantum mechanics , inverse scattering transform , paleontology , structural basin , evolutionary biology , biology
Important physical and chemical information can be extracted from scattering experiments data. This kind of problem is usually ill‐posed in the sense that one of the three conditions, existence, uniqueness, and continuity, is not satisfied. For example, the inversion of intermolecular potential functions from scattering data, such as experimental cross section, is an ill‐posed problem which can be modeled as a Fredholm integral equation. In this work, an inversion method based on recursive neural networks is proposed to solve this inverse quantum scattering problem within the Born approximation. As physical example, the repulsive component of the potential function for the interaction Ar–Ar is obtained from differential cross‐section data. The sensitivity of the potential energy function to be inverted, in relation to the differential cross‐section data, is also analyzed. The present approach is simple, general, and numerically stable. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008