Real time and real space analysis for quasielastic neutron scattering (QENS) by means of the regularization method to estimate a spectrum has been developed. In our formalism, a mediation function between a dynamic structure factor, S(Q, ω), and a time-space correlation function, P(r, t), is estimated to minimize the sum of the least square fitting term for S(Q, ω) in a Q-ω space and the regularization term for P(r, t) in a r-t space. On the application to liquid bismuth which shows complicate static local structure, it is shown that a distribution function for Gaussian superposition to represent S(Q, ω) has good characters as a mediating function. The S(Q, ω) calculated from the estimated mediation function showed a good agreement with the experimental Sexp(Q, ω) even for small acoustic phonon excitation in a low Q region and gave more or less reasonable estimation of dynamic structure beyond the measured Q-ω range. In addition of the main property of P(r, t) that the ability to focus onto the relaxation process at a specific atomic distance helped us to understand a complicated layered structure in liquid bismuth, possibility of easy separation of self-diffusion from coherent QENS is shown.
Read full abstract