Description of multiparticle scattering by a projection method

It is suggested to describe scattering in a few-body system by means of the projection formalism based on separation of a finite-dimensional “inner” subspace. If this “inner” subspace is sufficiently large, the kernels of the modified integral equations of the Faddeev–Yakubovsky type become small, thereby justifying the use of the perturbation theory. The expressions for the zero-order amplitudes are obtained which are completely determined by the inhomogeneous terms in the equations and approach the exact amplitudes when the “inner” subspace is enlarging.