Space-time description of neutron spin echo spectrometry

Neutron spin echo (NSE) [F. Mezei, ed., Neutron Spin Echo, Lecture Notes in Physics Vol. 128 (Springer, Berlin, 1980)] is a technique for neutron scattering in which the energy resolution can be much narrower than the spectral width of the incident beam and it allows the direct measurement of the Fourier transform of the energy transfer spectrum, i.e. the time dependence of the density-density correlation function of the scattering system. It is normally discussed in terms of neutron Larmor precession in magnetic fields and the scattering process is described in terms of S(Q, omega). We show how a quantum mechanical treatment of the NSE technique offers new insight into the scattering process and explains how NSE directly yields the intermediate scattering function S(Q, t) or pair distribution function G(r). In addition it gives a basic picture of the physics of 'phonon focussing' in NSE and reveals the link between the spin echo time r, the resolution of the measurement and the details of the scattering process. In this paper we present three different approaches to understanding the system: (i) the usual classical Larmor precession, (ii) a semi-classical ray tracing model and (iii) a full quantum mechanical treatment. We apply these models to a spin echo spectrometer as used for various kinds of measurements.