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Guaranteed resonance enclosures and exclosures for atoms and molecules
Stockholm University, Faculty of Science, Department of Mathematics. Universität Bern, Switzerland.
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Number of Authors: 5
2014 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 470, no 2171, 20140488Article in journal (Refereed) Published
Abstract [en]

In this paper, we confirm, with absolute certainty, a conjecture on a certain oscillatory behaviour of higher auto-ionizing resonances of atoms and molecules beyond a threshold. These results not only definitely settle a more than 30 year old controversy in Rittby et al. (1981 Phys. Rev. A 24, 1636-1639 (doi: 10.1103/PhysRevA.24.1636)) and Korsch et al. (1982 Phys. Rev. A 26, 1802-1803 (doi:10.1103/PhysRevA.26.1802)), but also provide new and reliable information on the threshold. Our interval-arithmetic-based method allows one, for the first time, to enclose and to exclude resonances with guaranteed certainty. The efficiency of our approach is demonstrated by the fact that we are able to show that the approximations in Rittby et al. (1981 Phys. Rev. A 24, 1636-1639 (doi:10.1103/PhysRevA.24.1636)) do lie near true resonances, whereas the approximations of higher resonances in Korsch et al. (1982 Phys. Rev. A 26, 1802-1803 (doi:10.1103/PhysRevA.26.1802)) do not, and further that there exist two new pairs of resonances as suggested in Abramov et al. (2001 J. Phys. A 34, 57-72 (doi:10.1088/0305-4470/34/1/304)).

Place, publisher, year, edition, pages
2014. Vol. 470, no 2171, 20140488
Keyword [en]
resonance, eigenvalue, complex potential, interval arithmetic
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Other Natural Sciences
Identifiers
URN: urn:nbn:se:su:diva-121192DOI: 10.1098/rspa.2014.0488ISI: 000360605300006OAI: oai:DiVA.org:su-121192DiVA: diva2:857393
Available from: 2015-09-29 Created: 2015-09-28 Last updated: 2017-12-01Bibliographically approved

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