Some aspects of the energy and momentum resolution of a cold-neutron rotating-crystal spectrometer

The theories of energy and momentum resolution of the cold-neutron rotating-crystal spectrometer have been developed so as to obtain expressions which can be utilized directly for instrument design. It has been shown that the momentum resolution is largely due to geometrical considerations, particularly detector length, rather than to the velocity spread in the incident beam. General expressions have been derived for the focusing length of the spectrometer both as a function of neutron line width and time-of-flight resolution. Measurements have shown that the theories of energy resolution and focusing length are in good agreement with experiment.