Localized states of multiparticle quantum system with small relative energy

It is shown that the system of several quantum particles (N ≥ 3) can be localized at zero relative energy that is to exist as much as is desired in a final volume. This property of quantum particles depends sufficiently on dimensional representation of the space where particles are assigned and on the type of interaction between them. Necessary and sufficient conditions of N(N ≥ 3) quantum particle localization were established by specially developed method of spectral analysis of multiparticle Schroedinger operator. In this method the number of bound states of the N-particle system is put in correspondence with the number of operator eigenvalues of integral equations of N-body scattering theory at the energy equal to the value beginning the continuous spectrum of Schroedinger operator of the given system. Localization conditions of three bodies with pair attractive forces were considered and generalization for more bodies was given. Possibility of existence of localized neutron clusters with zero relative energy was discussed