Rearrangement and improvement of convergence of the born series in scattering theory on the basis of orthogonal projections

A method is proposed for rearranging the Born series in scattering theory by means of the recently proposed [1] orthogonally projecting pseudopotentials (OPP). It is proved rigorously that even if the system contains bound states the rearranged Born series will converge for all negative and small positive energies. It is shown how scattering operators can be introduced accurately in the orthogonal subspaces. The OPP method is compared with the projection technique developed by Feshbach. Physical applications of the method are discussed.