Soumia Belmouhoub, Bekkai Messirdi, Tahar Bouguetaia
abstract:
We study in this paper resonances of Schrödinger
operators. Resonance energies are accessible from a general class of complex
distortions, they also coincide with the poles of the meromorphic continuation
of the resolvent. We prove that in the Born--Oppenheimer approximation for
diatomic molecules, this study can be reduced to the one of a matrix of
semiclassical pseudodifferential operators with operator-valued symbols, without
modifying the Hamiltonian near the collision set of nuclei. We consider here the
case where two electronic levels cross, and where molecular resonances appear
and can be well located. We also investigate the action of the effective
Hamiltonian on WKB solutions and show that these resonances have an imaginary
part exponentially small.
Mathematics Subject Classification: 35P15, 47A75, 47G30, 35S30, 35C20
Key words and phrases: Analytic dilation, analytic distorsion, resonances, Born--Oppenheimer approximation, effective Hamiltonian, pseudodifferential operators, width