A new formulation of the quantum inverse scattering problem

The inverse problem of the quantum scattering theory is solved in a new formulation. The main idea is that the experimentally known phase shifts measured at fixed physical values of the momentum k and orbital momentum l and depending on the Coulomb constant a may be used to restore the potential U(r) of interaction between the charged particle and the components of the isotopic multiplet or between two isotopic multiplets. Properties of U(r) are studied and the quasipotential of the π±p interaction in the S31 state is written at laboratory energies of 263.7 and 310 MeV. The phase shift is divided in a pure nuclear phase shift and nuclear-Coulomb interference phase shift making use of the complex Coulomb coupling constant method. The pN interaction in the 1S0 state at low energies is treated as an example. The low-energy phase shift of the pp-bar scattering in the 1S0 state is calculated