On bound states of a neutron in an atomic plane or chain

The existence of bound neutron states localized on an isolated atomic plane or chain at a positive energy is demonstrated. It is found that the energy is always less than a characteristic quantity $E_a$, which depends on the lattice constant. A theory of such states is constructed, and for a model of a singular interaction potential it gives exact expressions for the binding energy, effective mass, velocity, and other characteristics of the neutron in the chain.