High-resolution monochromatization of neutrons and X-rays by multiple Bragg reflection

Abstract

A simple scheme for obtaining highly monochromatic, reproducible beams of slow neutrons or X-rays at fixed wavelengths by means of crystal diffraction is described. The method is based on the well known phenomenon of `umweganregung', in which a `forbidden' Bragg reflection is simulated under conditions of multiple reflection, i.e. when three or more reciprocal lattice points lie on an Ewald sphere. It is shown that there are orientations at which the Bragg angle (and wavelength) of a simulated reflection has local maxima. With only coarse collimation in the neighborhood of these extrema, perfect crystals can give wavelength resolutions of Δλ/λ ≃ 10−5. Mosaic crystals would give less resolution but greater intensity. Since the various simulations of a `forbidden' reflection may interfere with each other, it is necessary to carry out systematic computer calculations to check for interference after the extrema have been located. The scheme is applicable to a large set of crystals, including several diamond-structure and hexagonal close-packed elements and compounds such as quartz and calcite. Detailed numerical results show that germanium can reflect about 80 potentially useful wavelengths in the range 1.2 to 5 Å (neutron energy 0.003 to 0.05 eV). A number of other interesting properties of such beams are pointed out. Potential uses in neutron research and several problems are discussed briefly.