INVERSE SCATTERING-THEORY FOR DIRAC OPERATORS

We derive a reconstruction procedure of the potential from the scatter ing matrix of the 3-dimensional Dirac operator by using the method of Faddeev for the multi-dimensional inverse scattering theory for Schrod inger operators. We consider two problems in almost the same framework s: the reconstruction of slowly decreasing potentials from the scatter ing matrices for all high energies and that of exponentially decreasin g potentials from the scattering matrix for a fixed energy.