Quasi-energy of ultracold neutrons

A solution is found to the problem of the propagation of a neutron beam transmitted through a periodically acting high-speed chopper. It is a generalization of the Moshinsky's problem of the evolution of a plane wave in the right half-space after an ideal absorber at the origin of coordinates has been instantaneously removed. The energy spectrum of transmitted neutrons is found to be discrete and corresponding to their quasi-energy. Interference of the states corresponding to different satellite lines leads to a complex spatial pattern with typical beats. A number of experiments with ultracold neutrons are suggested and discussed. 12 refs.; 1 fig