A new perturbation treatment of the scattering and bound-state problem

Abstract

A new object called the distortion operator is introduced into the theory and consequences of such introduction are investigated: The relation of the distortion operator to the common quantities as the transition operator and S-matrix is stated and an equation for it is deduced. This equation is shown to be nonsingular (contrary to the Lippmann-Schwinger equation). The Neumann series following from it has a greater radius of convergence than the original Born series and it converges more rapidly than the Born series does; in the first order the unitarity is satisfied. An approximation of a given interaction is obtained and it is shown to be separable in the momentum partial wave representation. Expressions for phase shifts, scattering lengths and binding energies in the potential theory are given. Results of computations performed are encouraging; they are very similar to those following from Weinberg's quasiparticle theory. Different other methods are observed to be related to our approach either as special cases or having some of the same features.