Dielectric description of wakes and stopping powers in solids

Abstract

The dielectric description of the dynamical potential induced by swift protons in solids and the related stopping power is analyzed, using a combination of Mermin-type dielectric functions, which are fitted to available experimental data, to describe the optical properties of various materials. We apply this method to represent the energy loss functions of aluminum, silicon, amorphous carbon, and copper on a wide range of energy and momentum transfers. Using these functions we calculate the shape of the wake potential induced by swift protons; significant differences are obtained in the cases of carbon and copper, with respect to the results derived from simplified dielectric models. The energy loss functions are also applied to calculate the proton stopping power of each element, which are compared with experimental values. ͓S1050-2947͑98͒03007-8͔

Role of electronic excitations in the energy loss ofH2+projectiles in high-κmaterials

“…The code incorporates the stopping forces on each fragment including also the energy loss straggling. These forces were calculated using the dielectric formalism and the MELF-GOS model 36,37 to account for the electronic target response. Briefly, the MELF-GOS model describes the response of the outer-shells electrons by fitting the experimental ELF in the optical limit with Mermin-type ELFs ͑Ref.…”

Water equivalent properties of materials commonly used in proton dosimetry

“…The energy-loss magnitudes q S and 2 q : , used as input in the SEICS code, are calculated 5 by the dielectric formalism, which is based in the plane-wave Born approximation, and 6 where the target description enters through its energy loss function (ELF), which is 7 calculated by the MELF-GOS model [Abril et al, 1998, Heredia-Avalos et al, 2005. 8 Thus, the outer electron excitations are described by a sum of Mermin-type ELF 9 [Mermin, 1970], which is fitted to the experimental optical data, whereas the inner-shell 10 electrons are accounted for by their generalized oscillator strengths in the hydrogenic 11 approach.…”

“…In figure 1 20 we show our calculated stopping power S for a proton beam as a function of its 21 incident energy for several materials of interest in dosimetry, such as liquid water 22 Cu [Abril et al, 1998] and Au [Denton et al, 2008]. As can be seen in the above 25 references, a good agreement with experimental data was obtained; in particular, the 26 stopping power of liquid water for proton beams has been widely discussed and 27 compared with experimental data and other theoretical calculations [Garcia-Molina et 28 al., 2012b].…”

“…We apply the SEICS code (Simulation of Energetic Ions and Clusters 31 through Solids) based in a combination of Molecular Dynamic and Monte carlo 32 procedures to follow the trajectories of the incident projectiles [Garcia-Molina et al, 1 2011], by taking into account the electronic stopping power (including statistical 2 fluctuations through the energy-loss straggling), multiple elastic scattering collisions, 3 electronic charge-exchange processes and nuclear fragmentation reactions. An 4 important feature of our simulation is the use of accurate values for the electronic 5 energy-loss magnitudes, which are calculated within the dielectric formalism and the 6 MELF-GOS model (Mermin Energy Loss Function-Generalized Oscillator Strength) 7 [Abril et al, 1998;Heredia-Avalos et al, 2005], where the target excitation spectrum is 8 modelled by a self-consistent condensed phase description of its energy-loss function, 9 based on experimentally available optical data, over the entire energy and momentum 10 transfers space. 11…”

“…incorporates an accurate treatment of the electronic stopping force and the energy-loss 29 straggling (the main responsible of the Bragg peak position and its shape, respectively), 30 which is determined taking into account a realistic description of the target electronic 31 excitation spectrum in the condensed phase, based in the experimental optical energy 32 loss function of the target [Abril et al, 1998;Heredia-Avalos et al, 2005]. 33 This paper is structurated as follow.…”