Goos–Hänchen effect in neutron optics and the reflection time of neutron waves

The Goos–Hänchen (GH) effect, a longitudinal shift of a wave beam at total internal reflection, is well known in optics and has been repeatedly observed for light, micro-, and ultrasonic waves. We consider the GH effect for a massive particle reflected from a material boundary. A close relation is shown to exist between the longitudinal shift and the time delay of reflection. In the case of a neutron reflected from a planar resonant system, a giant longitudinal shift of either positive or negative sign can occur, corresponding to a large reflection group delay time. This time can also be negative, which does not contradict the causality principle. Prospects of the experimental observation of the GH effect and group delay time for neutron reflection are reviewed.