The behavior of superslow neutrons with velocities lower than approxim
ate to 0.1 m/s cannot be described by employing the notion of an avera
ge, 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 infiltratio
n deep into the substance of ultracold neutrons with energies lower th
an the boundary energy takes place. Taking into account the weak absor
ption results in the appearance of a second branch in the neutron wave
spectrum. It is characterized by a significantly longer damping lengt
h than predicted by the conventional theory of a complex potential. In
the Conclusion possibilities of experimental verification of the theo
ry are discussed.