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

No abstract

No abstract

The energy loss of a pair of charges in correlated motion through an electron gas is calculated using Lindhard's dielectric function, The results of numerical integrations are presented and in particular the cases of low and high velocities are described. Analytical expressions for the energy loss are given for the case of high velocities, which are in excellent agreement with the numerical results. A clear relationship between the energy loss of fast correlated charges and the partition rule for the stopping does not follow from this study.The results. are in agreement with experimental data for the energy-loss ratio between molecular and atomic ions in thin carbon foils. 18

No abstract

No abstract

We present a fully relativistic formulation of the energy loss of a charged particle traversing a conductive monoatomic layer and apply it to the case of graphene in a transmission electron microscope (TEM). We use two models of conductivity appropriate for different frequency regimes: (a) THz (terahertz) frequency range and (b) optical range. In each range we distinguish two types of contributions to the electron energy loss: the energy deposited in graphene in the form of electronic excitations (Ohm losses), and the energy that is emitted in the form of radiation. We find strong relativistic effects in the electron energy loss spectra, which are manifested, e.g., in the increased heights of the principal π and σ + π peaks that may be observed in TEM in the optical range. While the radiative energy losses are suppressed in the optical range in comparison to the Ohmic losses, we find that these two contributions are comparable in magnitude in the THz range, where the response of doped graphene is dominated by the Dirac plasmon polariton (DPP). In particular, relative contributions of the Ohmic and radiative energy losses are strongly affected by the damping of DPP. In the case of a clean graphene with low damping, the angular distribution of the radiated spectra at the sub-THz frequencies exhibit strong and possibly observable skewing towards graphene.

No abstract