Modulation spectroscopy of neutrons: Conceptual study of a new TOF-approach to phonons

The problem of measuring phonon dispersion curves by neutron time-of-flight is considered as a process of classification of probabilistic rather than deterministic events. The measuring system requires a pulsed source, a sample, placed at a goniometer, a bank of detectors at constant radius from the sample, a Fourier chopper installed between the source and the sample, and a special data acquisition system. It is shown that three different scans can be accomplished by combining in three distinct ways the delayed state of the source pulse and the delayed state of the chopper. Two of them are the familiar direct and indirect geometry scans. The third one, the so-called radial scan takes place along straight radial lines to the origin of the momentum space, possible in the deterministic classification scheme only, if dynamically oriented crystal analyzer is used. If the radial scan is chosen to pass through any of the reciprocal lattice points of the crystal, next or second next to the origin, the polarization factor is 1 for the longitudinal phonons, but 0 for the transversal phonons, which thus give no contribution at all.