Real time and real space analysis for coherent QENS and its application to liquid bismuth

Abstract

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.