A Monte Carlo simulation of ultra-cold neutron production by Bragg reflection from a moving single crystal

A Monte Carlo simulation was performed of a 'Gedanken Experiment' where ultra-cold neutrons are produced by Bragg reflection from a moving mosaic single crystal. It is shown that ultra-cold neutrons can be obtained by using thermal or cold neutrons (in practice only the latter). The cross-section of the reflected ultra-cold neutron beam is elliptical if the incident beam has an axial symmetry. The length of the minor axis of this ellipse has an upper limit determined by the mosaic spread of the moving crystal, and the length of the major axis increases with the ratio of the velocity of the incident neutrons to the velocity of the reflected neutrons. The ultra-cold neutron flux (per unit solid angle and unit velocity interval) can be larger than the ultra-cold neutron flux emitted directly by the same neutron source of Maxwellian distribution of velocities. This result is discussed in relation to Liouville's theorem. (Auth.)