The resolution function of a pulsed-source neutron chopper spectrometer

We introduce a formulation for the evaluation of the incident neutron intensity distribution for a chopper time-of-flight spectrometer at a pulsed neutron source. This treatment, incorporated with an assumed scattering function of the sample and the detector geometry, enables calculations of the shape of the time-of-flight intensity profiles of the incident and the scattered neutrons sensed by a neutron detector, thus providing direct comparison with experimental results. The resolution function, R(Q, E), is calculated for a nondispersive scatterer at a resonant energy E. The results of the calculations on the basis of this theory are substantiated by measured spectra obtained by the two chopper spectrometers, HRMECS and LRMECS, at the Argonne Intense Pulsed Neutron Source under a variety of experimental conditions. In all cases we find excellent agreement between calculations and experiments. Using these results we present a procedure for the determination of the mean incident neutron energy and the calibration of the energy-transfer scale for pulsed-source chopper spectrometers. These latter do not follow accurately from simple analysis, and are the main objects of this paper. (orig.)