Inverse scattering problem in the operator interpolation method

The inverse scattering method for separable potentials is considered in the framework of the operator interpolation method for the description of intercluster dynamics. It is shown that by means of the elastic-scattering phase shifts it is possible, in principle, to get information on the projections of the many-particle states into the external space of relative motion and energies of these states which are result of diagonalization of the many-particle Hamiltonian on the finite-dimensional subspace of the states of the composite system. As a result, the uncertainties of the operator interpolation method can be parity cancelled. If the projections of the many-particle states onto the external space of relative motion are known, a simple version of the inverse scattering problem is proposed