Experimental evidence of threshold effects in the energy loss of protons in carbon and aluminum due to inner shell ionization

We explore the contributions of inner shell ionization to the energy loss of 7 to 270 keV protons in C and Al foils under experimental conditions such that the product of the observation angle and the projectile energy is kept constant. By normalizing these energy loss measurements to the energy loss in the forward direction we observe a pronounced rising behavior with increasing energy. This effect appears in the same range of energies where the respective K- and L-shell ionization cross sections of these elements show a similar threshold behavior. Based also on various theoretical considerations we interpret these results as clear evidence of the inner shell ionization contribution to the energy loss.     

A comparative study of threshold effects in the energy loss moments of protons,electrons and positrons using dielectric models for band-gap materials

A comparative study of the energy loss, mean free path and straggling of protons, positrons and electrons in an electron gas is performed using three dielectric models which represent the case of metals (Lindhard model for a free electron gas) and the cases of semiconductors and insulators (Levine and Louie model and Brandt and Reinheimer model for systems with a band gap). The properties of individual and collective contributions according to each model and for each of the particles are analyzed. In particular, the effects produced by the band gap of the material and by the properties of the incident particle are analyzed in detail. Significant differences related to the mass and to the indistinguishability (in the case of electrons) are described. Analytical expressions for the high-energy limit are derived in a simple way using the plasmon-pole approximation.     

Loop-Erased Walks and Random Matrices

Journal of Statistical Physics - It is well known that there are close connections between non-intersecting processes in one dimension and random matrices, based on the reflection principle. There...     

Energy loss and plasmon excitation during electron emission in the proximity of a solid surface

We study the interaction with bulk and surface modes of electrons emitted in the proximity of a solid surface. We analyze the modifications in the energy loss, and in bulk and surface plasmon excitations, taking into account the effects due to the sudden creation of the electron and residual atomic hole, and the finite distance to the surface. The process is described using the dielectric function formulation and the specular reflection model. We derive expressions for the electrostatic potential in the medium and in vacuum, which include all the terms due to bulk and surface modes. The effect of each term in the energy loss rate and in the average number of plasmon excitations is discussed. The results illustrate in detail the different spatial dependences of the electron and ion interactions with the bulk and surface perturbations, through the relevant range of distances for studies of electron emission in the proximity of solid surfaces.     

Hydrodynamical model for bulk and surface plasmons in cylindrical wires

In this paper, we study the electrostatic surface and volume modes of a cylindrical wire using the hydrodynamical model of plasmon excitation, which allows an analytical study of dispersion effects. We solve the hydrodynamical equations for a cylindrical wire geometry, obtaining new analytical expressions for the bulk and surface modes. New dispersion relations are obtained for each type of mode and numerical solutions are given. We analyze in detail the characteristics of the solutions and their differences with previous treatments based on non-dispersive models. These differences become important for wires of small radii, particularly in the range of few nanometers.     

Energy losses of muons, pions, protons, and deuterons channeled in Si

The energy loss of positive muons, pions, protons, and deuterons channeled in Si crystals has been investigated by computer simulation. The model considers the individual trajectories of particles inside the target and calculates the electronic energy loss for each particle history. The results show important differences in the energy loss distributions, stopping powers, and straggling values for low and intermediate energies, as a consequence of channeling effects.