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 derive a formula to calculate scattered intensities (including both elastic and inelastic scattering) from the estimates obtained with a single-particle continuum model under conditions typical for CDI studies with XFELs. We demonstrate through numerical simulations that it describes the scattered signal with good accuracy. Two-particle correlation effects manifest themselves only in the region of low momentum transfers, together with the effects of the finite size of the sample. We also show that inelastic scattering on bound electrons can have a significant impact on the measured intensities: it contributes to the background that reduces the contrast of the recorded image. This effect is even more pronounced at larger momentum transfers. Therefore, whereas inelastic scattering can be neglected for nanocrystals, where Bragg scattering dominates, and in experiments imaging single objects at low resolution, it should be taken into account when planning atomic resolution imaging of nonperiodic samples. Finally, we show the effect of the electronic damage on the recorded total signal. Progressing damage does not change the positions of intensity peaks that correspond to the (fixed) positions of imaged ions. It only changes the contrast between intensity minima and maxima, which reduces the image contrast. Our results have implications for imaging-oriented studies of radiation damage performed with continuum models, as they define the limits of applicability of these models for CDI simulations.