The problem of slow-neutron interaction with moving matter is consider
ed. The concept of an effective potential is used to take into account
medium effects. It is shown that such interactions change the neutron
energy (this is in accord with the results of previous investigations
). For a given potential, this phenomenon is purely classical far rath
er wide variations of the parameters characterizing the motion in ques
tion. The energy spectra of interacted neutrons are found for some par
ticular cases of the accelerated motion of a slab of matter. Essential
ly quantum phenomena occur in the reflection of neutrons from an accel
erated mirror if the latter is separated from the incident beam. The s
hape of the spectrum of neutron velocities exceeding classically acces
sible values is found for this case. Experiments to observe changes in
the energy of neutrons interacting with moving samples are proposed.