A compound parabolic concentrator as an ultracold neutron spectrometer

The design principles of nonimaging optics are applied to ultracold neutrons (UCN). In particular a vertical compound parabolic concentrator (CPC) that efficiently redirects UCN vertically into a bounded spatial volume where they have a maximum energy mga that depends only on the initial phase space cross sectional area π a 2 creates a spectrometer which can be applied to neutron lifetime and gravitational quantum state experiments.