Benchaou M., Martinez A.
Estimations exponentielles en th\'eorie de la diffusion pour des
op\'erateurs de Schr\"odinger matriciels
(73K, LATeX 2e)
ABSTRACT. In relation with the Born-Oppenheimer approximation, we study the
scattering operator $S$ associated to a 2x2 semiclassical matricial
Schr\"odinger operator, near a non-trapping energy level. Under some gap
condition and assumptions of analyticity and decay at infinity, we show
that the two off-diagonal elements of $S$ are exponentially small as the
semiclassical parameter tends to zero. Moreover, the rate of exponential
decay can be explicited depending on the behaviour in the complex domain
of the two electronic levels.