Multiply Bragg-reflected neutrons in ideally imperfect crystals

The solution of the general form of the integral transport equation is expanded in terms of orders of scattering. The method is applied to the analysis of multiply Bragg-reflected neutrons in mosaic crystals, making evident the vertical broadening of the reflected beam as well as the consequential neutron leakage in crystal spectrometers. A wavelength-dependent effective vertical mosaic spread of the crystal is defined as a function of the mean number of reflections. A detailed mathematical treatment is performed within the frames of an infinite-plane slab model (both in reflection and in transmission geometry) largely used in the literature in the studies of crystal reflectivity. Experimental results are also presented.