On the Born-Oppenheimer approximation of diatomic molecular resonances

摘要

We give a new reduction of a general diatomic molecular Hamiltonian, withoutmodifying it near the collision set of nuclei. The resulting effectiveHamiltonian is the sum of a smooth semiclassical pseudodifferential operator(the semiclassical parameter being the inverse of the square-root of thenuclear mass), and a semibounded operator localised in the elliptic regioncorresponding to the nuclear collision set. We also study its behaviour onexponential weights, and give several applications where molecular resonancesappear and can be well located.