Effect of two-particle correlations on x-ray coherent diffractive imaging studies performed with continuum models

Coherent diffraction imaging (CDI) of single molecules at atomic resolution is a major goal for the x-ray free electron lasers (XFELs). However, during an imaging pulse, the fast laser-induced ionization may strongly affect the recorded diffraction pattern of the irradiated sample. The radiation tolerance of the imaged molecule should then be investigated 'a priori' with a dedicated simulation tool. The continuum approach is a powerful tool for modeling the evolution of irradiated large systems consisting of more than a few hundred thousand atoms. However, this method follows the evolution of average single-particle densities, and the experimentally recorded intensities reflect the spatial two-particle correlations. The information on these correlations is then inherently not accessible within the continuum approach. In this paper we analyze this limitation of continuum models and discuss the applicability of continuum models for imaging studies. We propose a formula to calculate scattered intensities (including both elastic and inelastic scattering) from the estimates obtained with a single-particle continuum model. We derive this formula for systems under conditions typical for CDI studies with XFELs.