Superslow neutrons and the dispersion law for neutron waves in matter

The behavior of superslow neutrons with velocities lower than {≈}0.1 m/s cannot be described by employing the notion of an average or optical potential. Owing to the existence of such a region, the wave vector in the medium becomes complex when a scattering length of an individual nucleus is positive. As a consequence, slow infiltration deep into the substance of ultracold neutrons with energies lower than the boundary energy takes place. Taking into account the weak absorption results in the appearance of a second branch in the neutron wave spectrum. It is characterized by a significantly longer damping length than predicted by the conventional theory of a complex potential. In the Conclusion possibilities of experimental verification of the theory are discussed.