A Monte Carlo algorithm for computing spin echo small angle neutron scattering correlation functions in real space: Hard sphere liquids.

A Monte Carlo algorithm is developed to compute the autocorrelation function of liquids and the corresponding spatial correlation function from spin echo small angle neutron scattering (SESANS) spectra. The accuracy of the simulation algorithm is tested with isolated hard spheres and single dumbbells consisting of two hard spheres separated by a given distance. The simulation results accurately reproduce the exact expressions of these two models. To further test the algorithm for many-body systems, two liquid models are considered including hard sphere fluids and hard spheres with an attractive tail. The many-particle Monte Carlo simulation is carried out to obtain the ensemble average of these correlation functions. Meanwhile, the Percus-Yevic (PY) integral equation theory is resorted to compute the autocorrelation function and SESANS spatial correlation function for a density that the PY theory is reasonably applicable. The agreement between simulation and theory indicates that the algorithm is quite robust and can be extended to more complex fluids in the future. Furthermore, we find that the SESANS spatial correlation function is highly sensitive to the interaction potential between particles, which may serve as a useful tool to explore particle interactions in a liquid.