Abstract: In this paper, we study the scattering theory for a 2×2 matrix Schrödinger operator P=−h2d2/dx2I2+V(x)+hR(x,hDx) on L2(R)⌖L2(R), where V(x) is a real diagonal matrix, the eigenvalues of which are never equal. Under some assumptions of analyticity and decay at infinity of V, we describe the asymptotic behavior of the scattering matrix S=(sij)1≤i,j≤4 associated with P when the semi-classical parameter h goes to zero. Moreover, we obtain the estimate ‖S12‖+‖S21‖=O(e−δ/h), where S12 and S21 are the two off-diagonal elements of S and δ>0 is a constant which is explicitly related to the behavior of V(x) in the complex domain.
