MATRIX ANALYSIS OF NEUTRON SPIN-ECHO

We describe the general action of a neutron spin-turn coil by a rotation matrix, and the nett action of a sequence of spin-turns is then evaluated as the product of the relevant matrices. In the ideal neutron spin-echo configuration, the spin-turn sequence used is shown to have a resultant action described by the unit matrix if there is only elastic scattering, so that an initially polarized beam is transmitted with unchanged polarization. This is spin-echo focussing. Measurement of changes in the final polarization then provides information on the sample dynamics. Spin-echo focussing permits high resolution to be coupled with a broad incident wavelength spread. We calculate in detail the effect of this polychromaticity on the spinturn coils involved, and present experimental confirmation. General spin-echo configurations are then considered. Finally, we take into account the effect of spin-flip scattering from spin-incoherent samples, and show that spin-flip effects may be decoupled from dynamic effects in the analysis of spin-echo intensity. The techniques evolved are relevant to both monochromatic and polychromatic spinecho spectrometry. Emphasis has been placed on practical aspects of establishing correct spin-turn conditions and analysing spectrometer response in terms of relative transmitted intensity. © 1978 Springer-Verlag.