Molecular predissociation resonances below an energy level crossing

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 trans...

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Bibliographic Details
Published inAsymptotic analysis Vol. 107; no. 3-4; pp. 135 - 167
Main Author Ashida, Sohei
Format Journal Article
LanguageEnglish
Published Amsterdam IOS Press BV 01.01.2018
Subjects
Chemical bonds
Energy levels
Operators (mathematics)
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Summary: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.
ISSN:0921-7134
1875-8576
DOI:10.3233/ASY-171453