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In this work we describe two different models for interpreting and predictingReflection Electron Energy Loss (REEL) spectra and we present results of astudy on metallic systems comparing the computational cost and the accuracy ofthese techniques. These approaches are the Monte Carlo (MC) method and theNumerical Solution (NS) of the Ambartsumian-Chandrasekhr equations. The formeris based on a statistical algorithm to sample the electron trajectories withinthe target material for describing the electron transport. The latter relies onthe numerical solution of the Ambartsumian-Chandrasekhar equations using theinvariant embedding method. Both methods receive the same input parameters todeal with the elastic and inelastic electron scattering. To test theirrespective capability to describe REEL experimental spectra, we use copper,silver, and gold as case studies. Our simulations include both bulk and surfaceplasmon contributions to the energy loss spectrum by using the effectiveelectron energy loss functions and the relevant extensions to finite momenta.The agreement between MC and NS theoretical spectra with experimental data isremarkably good. Nevertheless, while we find that these approaches arecomparable in accuracy, the computational cost of NS is several orders ofmagnitude lower than the widely used MC. Inputs, routines and data are enclosedwith this manuscript via the Mendeley database.

A Comparison between Monte Carlo Method and the Numerical Solution of  the Ambartsumian-Chandrasekhar Equations to Unravel the Dielectric Response  of Metals