Reflection of neutrons from a resonant potential structure oscillating in space

Highlights: • Plane wave reflects from a resonant potential structure oscillating in space. • In resonance, the group delay time increases by several orders of magnitude. • At a large group delay time value, scattering with energy transfer is suppressed. • Suppression of scattering with energy transfer is due to the motion with acceleration. • Acceleration effect depends on the object acceleration and the interaction time. The work is devoted to the theoretical study of the interaction of a plane wave with a resonant potential structure oscillating in space. An approximate analytical solution to the non-stationary Schrödinger equation for this problem is given. A numerical quantum calculation of the problem of a wave packet reflection from such a structure has been performed. The results of three solution methods are compared in order to determine the degree of the reflection time influence on the spectrum of the reflected state. It was found that under resonance conditions, when the reflection time increases significantly, there is a strong suppression of scattering with energy transfer. It is shown that this effect is due to combination of the long interaction time with the spatial oscillation of the potential. Such effect is absent in the case of the reflection from the potential oscillating in magnitude and characterized by the same reflection time.