Time focussing and resolution in resonance detector neutron spectrometers

Nuclear recoil produces a variation in time of arrival of neutrons scattered through different angles in pulsed-source resonance detector neutron spectrometers. The coupled variation of recoil energy shifts and of scattering angles and lengths of different paths from source to sample to detector leads to conditions on the orientation of source, sample and detector which minimize the resolution of these spectrometers. The conditions depend upon the mass of the scatterer, the excitation energy of the recoiling unit, the mean scattering angle and relative incident and scattered neutron flight paths, and apply strictly only for a single value of the excitation energy. We develop general expressions for the geometric contributions to the resolution, from which the focussing conditions emerge. The focussing effect on the resolution is significant, and is similar to that in time of flight diffractometers. (orig.)