Guaranteed resonance enclosures and exclosures for atoms and molecules

Boegli, Sabine, Brown, B. Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046, Tretter, Christiane, Tretter, Christine and Wagenhoffer, Markus 2014. Guaranteed resonance enclosures and exclosures for atoms and molecules. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470 (2171) , 20140488. 10.1098/rspa.2014.0488

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Abstract

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:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Computer Science & Informatics
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Additional Information:	Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Publisher:	Royal Society, The
ISSN:	1364-5021
Funders:	EPSRC, Leverhulme Trust, Swiss National Science Foundation
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	1 September 2014
Last Modified:	04 Oct 2023 03:46
URI:	https://orca.cardiff.ac.uk/id/eprint/64130

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