Small-energy analysis for the self-adjoint matrix Schrodinger operator on the half line

The matrix Schrodinger equation with a self-adjoint matrix potential is considered on the half line with the most general self-adjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the related Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3640029]