  An efficient approach for the simulation of ion scattering from solids is
proposed. For every encountered atom, we take multiple samples of its thermal
displacements among those which result in scattering with high probability to
finally reach the detector. As a result, the detector is illuminated by
intensive "showers", where each event of detection must be weighted according
to the actual probability of the atom displacement. The computational cost of
such simulation is orders of magnitude lower than in the direct approach and a
comprehensive analysis of multiple and plural scattering effects becomes
possible. We use the new method for two purposes. First, the accuracy of the
approximate approaches, developed mainly for ion-beam structural analysis, is
verified. Second, the possibility to reproduce a wide class of experimental
conditions is used to analyze some basic features of ion-solid collisions: the
role of double violent collisions in low-energy ion scattering; the origin of
the "surface peak" in scattering from amorphous samples; the low-energy tail in
the energy spectra of scattered medium-energy ions due to plural scattering;
the degradation of blocking patterns in 2D angular distributions with
increasing depth of scattering. As an example of simulation for ions of MeV
energies, we verify the time-reversibility for channeling/blocking of 1 MeV
protons in a W crystal. The possibilities of analysis that our approach offers
may be very useful for various applications in particular for structural
analysis with atomic resolution.
