98-738 Benchaou M., Martinez A.

Estimations exponentielles en th\'eorie de la diffusion pour des op\'erateurs de Schr\"odinger matriciels (73K, LATeX 2e) Dec 2, 98

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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.

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