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Born-Oppenheimer asymptotic for the molecular predissociation (case of regular potentials). (Asymptotique de Born-Oppenheimer pour la prédissociation moléculaire (cas de potentiels réguliers).) (French) Zbl 0812.35109

Summary: We study the operator \(P=- h^ 2 \Delta_ x- \Delta_ y +V(x,y)\) on \(\mathbb{R}_ x^ n\times \mathbb{R}_ y^ p\) when \(h\) tends to zero, and \(V\) is a smooth potential. We consider a case where two electronic levels cross in the classical forbidden region, and where resonances of \(P\) appear. We prove that \(P\) has resonances with a real asymptotic expansion in \(h^{1/2}\) and that their widths are exponentially small as \(h\) tends to zero.

MSC:

35Q40 PDEs in connection with quantum mechanics
35P05 General topics in linear spectral theory for PDEs
81U05 \(2\)-body potential quantum scattering theory
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