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A fully relativistic description of valence energy losses suffered by fast electrons passing near finite clusters of arbitrarily disposed dielectric objects is presented using an accurate technique suited to solve Maxwell's equations. The method is based upon an expansion of the electromagnetic field in terms of multipoles around each of the objects of the cluster. Multiple elastic scattering of those multipole expansions is then performed until convergence is achieved. The energy loss,doi:10.1103/physrevb.60.6103 fatcat:c5y6ajonibgzrfwspopc7ow5ri