Molecular predissociation resonances below an energy level crossing

Article type: Research Article

Authors: Ashida, Sohei

Affiliations: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan. E-mail: [email protected]

Abstract: We study the resonances of 2×2 systems of one dimensional Schrödinger operators which are related to the mathematical theory of molecular predissociation. We determine the precise positions of the resonances with real parts below the energy where bonding and anti-bonding potentials intersect transversally. In particular, we find that imaginary parts (widths) of the resonances are exponentially small and that the indices are determined by Agmon distances for the minimum of two potentials.

Keywords: Resonances, Born–Oppenheimer approximation, eigenvalue crossing, differential system, semiclassical analysis

DOI: 10.3233/ASY-171453

Journal: Asymptotic Analysis, vol. 107, no. 3-4, pp. 135-167, 2018