Transformation of S(Q,E) to G(r,t) with MEM

Kikuchi, Tatsuya  

Dynamic structure factor, S(Q,E), which can be obtained by Inelastic neutron scattering directly, is a function of scattering vector, Q, and energy transfer, E. In recent years, importance of the studies on dynamics that cannot be well described by Q and E in substances such as battery materials has increased. S(Q,E) is defined as a Fourier-transformed function from van Hove's space-time correlation function, G(r,t), which is a function in real space and time. G(r,t) is important to express local motions of atoms and molecules directly on these substances. However, the calculation of G(r,t) has been hardly performed even though it is so easy mathematically, because it requires spectrum in both high resolution and wide range in Q-E space. By the progress of the recent neutron sources and spectrometers, the measurements with wide range and high resolution in Q-E space are becoming easy. We measured high-resolution S(Q,E)s using AMATERAS spectrometer installed at J-PARC and calculated G(r,t)s. We used the maximum entropy method to lower the bias of truncation errors for the calculation of G(r,t).