R. H. Ritchie

Surface plasmons in solids

Abstract Some of the properties of surface plasmons in nearly-free-electron solids are reviewed. Experiment and theory bearing on the dispersion and damping of such excitations in some simple geometries will be discussed. Coupling with the radiation field may modify both of these properties. The surface plasmon may be regarded as the source of the image force at an external charge and of dispersion forces between solids. Some consequences of coupling between plasmon modes through spatial nonuniformities or spatial deviations in the linear response function of a solid are considered briefly.

The surface plasmon dispersion relation for an electron gas

Abstract The dispersion and damping of surface plasmons in a semi-infinite free electron gas has been examined using a specular reflection model for electrons at the bounding surface. It is found that this dispersion relation agrees well with the predictions of the hydro-dynamical model for small wave numbers. The damping rate, which is predicted to be zero on the hydrodynamical model, is found to be ≲ 1 % of the plasmon frequency over a substantial range of wave numbers.

Electron inelastic mean free paths and energy losses in solids II: Electron gas statistical model☆☆☆

Abstract A statistical model for the calculation of inelastic mean free paths and energy losses of electrons in solids is described. Results for the application of the model to the six solid media Al, Au, Ag, Cu, Ni, and Si are presented. Agreement between calculated mean free paths and experimental attenuation lengths indicates that the statistical model provides a useful method in the little-studied electron energy range from a few tens of electron volts to 10 keV.

Electron inelastic mean free paths and energy losses in solids: I. Aluminum metal

Abstract Inelastic mean free paths and energy losses in aluminum metal are calculated for electrons with energies from a few eV to 10 4 eV above the Fermi level. We have represented the contribution from excitations of the valence electrons by using an electron gas model. The effect of damping in the electron gas on the mean free path and energy loss is included within the context of the Mermin-Kliewer-Fuchs model of the electron gas dielectric function. The influence of core polarizability and local field corrections are discussed briefly. The contributions to the mean free path and energy loss of electrons from ionization of inner shells have been evaluated from atomic models. Comparisons are made with experimental data taken over a wide range of energies.

Straggling and plasmon excitation in the energy loss spectra of electrons transmitted through carbon

Abstract A model is described for the calculation of differential inverse mean free paths (DIMFPs) for the inelastic interactions of electrons with solids. The energy loss function Im{-1/ e ( q , ω )} is represented as a sum of Drude-type functions. The adjustable parameters in the energy loss function are fixed by a fit to the energy loss function in the optical limit ( q → 0) obtained from data on the optical constants of glassy carbon. The extension of the optical energy loss function to arbitrary values of q in this model leads to an analytical expression for the DIMFP. Energy loss spectra for low energy electrons (less than 2000 eV) transmitted through carbon foils of various thicknesses are determined by solving the transport equation using a convolution method and the DIMFPs determined as described above. Comparisons of these calculated spectra with those measured by Jacobi show that the model provides a good description of both the broad straggling distribution and the fine structure due to plasmon excitation.

Calculations of mean free paths and stopping powers of low energy electrons (⩽ 10 keV) in solids using a statistical model

A statistical model is described and employed to calculate inverse mean free paths and stopping powers for electrons of energies from a few eV to 10 keV above the Fermi level in Al, Si, Ni, Cu, Ag, and Au. Brief tables of mean free paths and stopping powers for these solids are presented. In some cases graphical displays of inverse mean free paths and stopping powers are also included. The calculations based on this model are discussed and compared with previous work.

Inelastic Interactions of Electrons with Polystyrene: Calculations of Mean Free Paths, Stopping Powers, and CSDA Ranges

A theoretical description of the inelastic interactions of electrons with solid polystyrene is presented. The response of the valence electrons to energy and momentum transfers is determined by a model insulator theory; carbon K-shell ionization cross sections are derived from atomic, generalized oscillator strengths. Contributions to the inverse mean free path and stopping power due to these two excitation processes are derived and tabulated for incident electrons with energies from 10 eV to 10 keV. Electron ranges in the continuous-slowing-down approximation are calculated and tabulated for electrons with energies from 15 eV to 10 keV.

The Z13 Correction to the Bethe-Bloch Energy Loss Formula

Corrections to the Bethe-Bloch formula for the energy loss of charged particles in matter have been of much interest since the early work of Barkas and collaborators, who found differences between the ranges of positive and negative pions of the same energy. We here report the first rigorous many-body perturbation-theoretic calculation of the Z13 correction for a wide range of particle velocities in the electron gas, Z1 being the projectile charge. Our calculations are in good agreement with recent measurements of the energy loss of protons and antiprotons.

Z31 correction to the stopping power of an electron gas for ions

Abstract A diagrammatic analysis of many-body interactions between a moving ion and an electron gas is made. The Z 3 1 correction to the stopping power of the medium for the penetrating ion is derived using Feynman diagrams, and the contributing terms leading to significant Z 1 3 corrections to the stopping power at low velocities of the ion are evaluated, as a function of the velocity of the ion, in the random-phase-approximation.

Stopping Power for Protons in Aluminum.

The electronic stopping power of aluminum metal for protons has been calculated with explicit account taken of the different charge states of the photon inside the medium. The fraction of negative ions (H-) neutral atoms (H0) and bare protons (H+) in the beam as a function of ion speed are derived from the capture and loss cross-sections. The total stopping power is then obtained by weighting the calculated partial stopping powers with the appropriate charge state fractions. The energy loss per unit path length due to electronic exchange processes is also evaluated. Our calculations show that the relative contribution to the stopping power from capture and loss processes is of the order of 15% for the case of protons moving in aluminum. Good agreement with experimental data is found.