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Guaranteed resonance enclosures and exclosures for atoms and molecules.

Boegli, Sabine and Brown, B. Malcolm and Marletta, Marco and Tretter, Christiane and Wagenhofer, Markus (2014) 'Guaranteed resonance enclosures and exclosures for atoms and molecules.', Proceedings of the Royal Society A : mathematical, physical and engineering sciences., 470 (2171). p. 20140488.


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. A24, 1636–1639 (doi:10.1103/PhysRevA.24.1636)) and Korsch et al. (1982 Phys. Rev. A26, 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. A24, 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. A26, 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. A34, 57–72 (doi:10.1088/0305-4470/34/1/304)).

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Publisher statement:© 2014 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Date accepted:No date available
Date deposited:17 December 2019
Date of first online publication:08 November 2014
Date first made open access:17 December 2019

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