A Monte Carlo algorithm for computing SESANS correlation functions in real space: Hard sphere liquids

Abstract

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 algo- rithm for many-body systems, two liquid models are considered, including hard sphere °uids 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 PY integral equation theory is resorted to compute 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 °uids in the future. Furthermore, we ¯nd 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.