A method to measure the validity of trajectory simulation by removing the boundary-dependent coherent scattering contribution

A method is shown for measuring the validity of trajectory simulation, as compared to exact quantum calculation. The object is to calculate the differential cluster cross section obtained by multiple elastic scattering of a particle in a cluster of N randomly distributed point scatterers. After discussing the application of the analytic Foldy theory to the calculation of the coherent part of the cluster cross section, i.e. the diffraction pattern that is associated with the finite size of the cluster, it is shown that, for N up to ∼103, this coherent part can be removed by a simple, exact procedure, allowing the trajectory simulation to be compared with the remaining incoherent part. A scalar measure of the relative error in the trajectory differential cluster cross section is introduced. In the examples shown, this relative error is negligible at a low density of scatterers, but increases substantially with increasing density. The relevance for low-energy electron scattering is discussed.