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Role of resonances in building cross sections: A comparison between the Mittag-Leffler and the Lippman Schwiger approaches
Stockholm University, Faculty of Science, Department of Physics.
2007 (English)In: International Journal of Quantum Chemistry, ISSN 0020-7608, Vol. 107, no 6, 1301-1315 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2007. Vol. 107, no 6, 1301-1315 p.
URN: urn:nbn:se:su:diva-12441DOI: 10.1002/qua.21257ISI: 000244771500003OAI: diva2:178961
Available from: 2008-01-15 Created: 2008-01-15 Last updated: 2009-03-16Bibliographically approved
In thesis
1. Ways of determining and characterising resonances in scattering processes
Open this publication in new window or tab >>Ways of determining and characterising resonances in scattering processes
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Scattering cross sections very often display structures. To clarify if these structures correspond to resonances one has to check if they are poles of the scattering matrix (S-matrix) in the fourth quadrant of the complex momentum plane. Furthermore, the states corresponding to these poles also need to have an appropriate scattering amplitude.

The complex energies of resonances associated with several potentials were computed by solving complex dilated differential equations using both a Numerov method and a Finite Element Method as well as by solving integral equations with a δ-potentials technique combined with the complex dilation method.

The influence of resonances on the s-wave cross section for model one channel potentials was studied using the Mittag-Leffler and the Green's function expansion formalisms and comparisons made between these two approaches. It is demonstrated how the partial wave S-matrix can be continued into a sector in the fourth quadrant of the complex momentum plane where its poles and residues can be determined. These two formally equivalent methods were found to produce numerically identical S-matrix residues. However, both methods have essential drawbacks and, therefore, a technique for identifying the contribution of individual resonances to the cross section, which is based on the S-matrix residue, is suggested. This involves defining both a reduced partial wave S-matrix and reduced cross section. The technique presented here is successfully applied to the two-channel Noro-Taylor potential and a more realistic scattering process, namely the N3+ + H → NH3+ → N2+ + H+ reaction.

Note that my name can be spelt in different ways. In official documents it is Kseniya Shyliayeva but in all papers I used another spelling, namely: Ksenia Shilyaeva.


Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2009. 55 p.
quantum scattering theory, complex scaling, resonances
National Category
Atom and Molecular Physics and Optics
Research subject
urn:nbn:se:su:diva-26218 (URN)978-91-7155-838-1 (ISBN)
Public defence
2009-04-24, FA 32, Roslagstullsbacken 21, AlbaNova universitetcentrum, 10:00 (English)
Available from: 2009-04-03 Created: 2009-03-13 Last updated: 2009-03-17Bibliographically approved

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Shilyaeva, KseniaElander , Nils
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