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[en] We calculated new neutron resonances for the systems of two nuclei in the energy range close to conventional neutron-nucleus resonances. We were focused on the study of the three-body resonance effects at scattering of neutrons on a subsystem of two isotopes when distances between these nuclei are taken into account. All stated above opens up opportunities to use specialized piezo-crystals and to assure control over the target parameters in the experiments with thermal resonance neutrons. For example, it is possible to set up the thermal neutron scattering experiments with different targets such as CdS and CdSe crystals. One should note that the new neutron resonances are created by interactions in three-body systems. They supplement the well-known phenomena such as Bragg’s scattering (Bragg’s law and neutron diffraction). However, the new neutron resonances have a different origin - they are obliged the rescattering of resonance neutrons on heavy nuclei. As in the Mossbauer effect, crystal structure accepts the recoil momentum, which give the strengthening of neutron resonances.