Guaranteed resonance enclosures and exclosures for atoms and molecules.
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 Rittbyet al.(1981Phys. Rev. A24, 1636-1639 (doi:10.1103/PhysRevA.24.1636)) and Korschet al.(1982Phys. 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, toenclose and toexclude resonances with guaranteed certainty. The efficiency of our approach is demonstrated by the fact that we are able to show that the approximations in Rittbyet al.(1981Phys. Rev. A24, 1636-1639 (doi:10.1103/PhysRevA.24.1636))dolie near true resonances, whereas the approximations of higher resonances in Korschet al.(1982Phys. Rev. A26, 1802-1803 (doi:10.1103/PhysRevA.26.1802)) donot, and further that there exist two new pairs of resonances as suggested in Abramovet al.(2001J. Phys. A34, 57-72 (doi:10.1088/0305-4470/34/1/304)).
Mathematisches Institut, Universität Bern , Alpeneggstrasse 22, 3012 Bern, Switzerland.
Sabine
S
Bögli
School of Computer Science, Cardiff University , 5 The Parade, Cardiff CF24 3AA, UK.
B Malcolm
BM
Brown
School of Mathematics, Cardiff University , 21-23 Senghennydd Road, Cardiff CF24 4AG, UK.
Marco
M
Marletta
Mathematisches Institut, Universität Bern , Sidlerstrasse 5, 3012 Bern, Switzerland ; Matematiska institutionen, Stockholms universitet , 10691 Stockholm, Sweden.
Christiane
C
Tretter
Im Gallmoos 11, 93128 Regenstauf, Germany.
Markus
M
Wagenhofer
complex potential; eigenvalue; interval arithmetic; resonance