Direct model fitting of uncorrected time-of-flight data from quasi-elastic neutron scattering experiments

A new approach to the analysis of quasi-elastic scattering data from time-of-flight spectrometers is described. The uncorrected time-of-flight data are simulated directly by a model containing relatively few variable parameters. The time-of-flight model, the full derivation of which is given, provides a general representation of the composite scattered neutron profile in the quasi-elastic (small energy transfer) region, applicable to most types of microscopic diffusive motions having sufficiently short correlation times. Though the general model is not in all cases a directly physical description of the motion, it is frequently adequate to completely describe the data. Its parameters therefore contain all the available information, and morevover lend themselves readily to quantitative comparisons with more realistic models. The advantages of the direct fitting methods over conventional analysis procedures [in which the data are transformed into S(Q, ω) or l(Q, t) forms] are that the correct statistical weight of each experimental point is preserved, and that any errors inherent in transforming the data are avoided. The accuracy of the information extracted using this technique (as a function of experimental resolution and counting statistics) is discussed. The results of tests on artificially generated spectra (with known parameters) are given. (Auth.)