Guaranteed resonance enclosures and exclosures for atoms and molecules

Bögli, Sabine; Brown, B. Malcolm; Marletta, Marco; Tretter, Christiane; Wagenhofer, Markus (2014). Guaranteed resonance enclosures and exclosures for atoms and molecules. Proceedings of the Royal Socociety London. Series A Mathematical and Physical Sciences, 470(2171), 20140488, 17. 10.1098/rspa.2014.0488

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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)).

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Bögli, Sabine; Marletta, Marco and Tretter, Christiane

Subjects:

500 Science > 510 Mathematics

ISSN:

1364-5021

Language:

English

Submitter:

Mario Amrein

Date Deposited:

14 Apr 2015 15:34

Last Modified:

07 Oct 2015 10:25

Publisher DOI:

10.1098/rspa.2014.0488

BORIS DOI:

10.7892/boris.66707

URI:

https://boris.unibe.ch/id/eprint/66707

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