Image potential from a free electron metal

We calculate the response of a free electron metal to a static charge Q located outside of the metal surface. We derive the electrostatic potential outside of the surface, inside of the surface, and the frequency response. Our derivation uses standard quantum mechanics, and the results are found exactly in the random phase approximation. Unlike prior calculations, which made approximations, our results do not agree with classical image theory.     

Self-energy of a charge near a metal surface

A quantum mechanical expression for the self-energy of a charged particle near a metal surface has been derived. The expression incorporates the interaction of the charge with the surface and bulk plasmons including their dispersions in the hydrodynamic model. It is found that the inclusion of the plasmons dispersions gives result for the saturated value of the image potential for copper closer to experiment.     

A generalization of image theory to predict the interaction of multipole fields with plane surfaces

A derivation and computational scheme, based on exact image theory, for the field produced by the interaction of an outgoing vector wave harmonic with an infinite-extent plane surface is presented. The method represents the angular-dependent Fresnel reflection coefficients of the surface as Laplace transforms of a spatially dependent function, which results in the reflected field appearing as a superposition of image sources located at complex points along the normal axis within the surface medium. Exact, analytical formulas are given for the transformed reflection coefficients for arbitrary surface refractive index, and an efficient computation scheme for evaluation of the scattered field coupling between a particle and the surface is presented.     

Formation of charged defects during the nitridation of a metal particle

A model explaining and predicting generation of a temporal electric potential during nitridation of a single metal pellet has been developed. The model takes into account the kinetics of defects formation and assumes that the rate of the chemical reaction can be described by the shrinking-core process. The model simulations have shown that time scale of the generated electric potential depends on both the initial nitride shell thickness and heat removal from the particle surface. At thin initial shell and low rate of heat removal the maximum of the surface electric potential is attained before the temperature and surface nitrogen concentration have reached their maximums but after the maximum of nitridation has appeared. Quasi-neutral distributions of metal vacancies and electron holes are formed at the maximum temperature. At thick initial shell and/or high rates of heat removal from the particle surface the potential maximum may be observed much later: after the maximum temperature has been achieved. Correspondingly, non-equilibrium concentrations of the charged defects exist till the end of nitridation. In contrast to oxidation the nitrogen adsorption rate constants (the activation energy and pre-exponent) have negligible effect on the surface potential form and amplitude. At the ignition limit the rate of nitridation is proportional to the power of −1/2 for the ambient nitrogen pressure in the proposed scheme of defects formation. Metal vacancies and electron holes are the main charged defects in nitrides during nitrogen combustion. The nitride formation is limited by transfer of the vacancies in nitride.     

Van der Waals interaction between a molecule and a metal surface: Effect of spatial dispersion

In this paper the effect of spatial dispersion on the dielectric response of a semi-infinite metal is investigated in the hydrodynamic approximation, and the result is used to evaluate the van der Waals force between a molecule and a metal surface. It is shown that corrections to the image potential result arising out of spatial dispersion can be evaluated systematically.     

Dielectric response of arbitrary surfaces and size quantized metals

We propose a new, general method for obtaining closed form solutions of electrostatic response problems in solid bodies of arbitrary shape. The scheme is simple enough to be applied to problems with complicated geometries, yet it should be sufficiently reliable for most purposes. It is shown that its formulation in terms of boson pseudomodes provides a convenient generalization of a method proposed by Overhauser to treat electron correlation in metals. Explicit expressions are given for the image interaction between a point charge and a plane or spherical surface, and for the screening energies and the screened electric fields of impurities in size quantized metals. Several implications in the physical and chemical properties of small metal particles are briefly discussed. Quantum size effects are included by means of a suitable dielectric function, including quantum size, exchange and correlation effects, and are shown to be very significant when the particle radius is of the order of a few tens of angstroms.     

Small metal particles: Non-local optical properties and quantum-size effects

In this work we survey some recent results concerning non-local optical effects and particle-size dependence for the optical properties of individual metallic particles. We start by giving a historical overview and a conceptual discussion on the subject of small particles, underlining their potential applications. Simplified optical response functions for a metallic sphere are introduced and duly illustrated to bring out the physical content. Particular emphasis is given to optical absorption, resonance effects and far-infrared properties exhibited by simple and noble metal particles having less than 100 Å radii. A comparison between the traditional (Mie) approach and the proposed non-local scheme is made and it leads to an increased understanding of the various mechanisms a small particle exhibits when screening an external electromagnetic field.     

The electromagnetic two-body problem in special relativity

A system of two point charged particles is considered. Each particle moves in the electromagnetic field created by the other particle according to Maxwell's equations. A scheme of successive approximations is developed to study the field and the motion of the charges. The field (potentials and intensities) are exapanded in powers of c^?1 using a retarded time coordinate. The variables of the motion (position vectors, velocities, etc) are expanded in powers of c^?1 with coefficients depending on t only. The field is evaluated in the first three approximations. The equations of motion are derived in the same approximations and the corresponding conserved quantities are explicitly given. Thus, the usual assumption of an action-at-a-distance principle is avoided and the original nonlinear integrodifferential equations are reduced to a sequence of linear equations.     

New model of electron stimulated desorption from physisorbed monolayers application to Ar and N2O on Ru(001)

A new model of electron stimulated desorption from monolayers physisorbed on metal surfaces is proposed in which the excited surface state potential is due to a chemical rather than an image force acting on the adsorbed particle after the initial electronic excitation is completed. The equilibrium positions of the excited and the ground state potentials may nearly coincide and desorption is a purely quantum mechanical effect. It is demonstrated that, unlike for the commonly accepted Antoniewicz model, both, the kinetic energy distributions of desorbing neutral particles and the total desorption yields calculated in the model proposed here are consistent with the existing experimental data for Ar and N₂O physisorbed on Ru(001).     

Some remarks on the electronic configuration of a metal-adsorbate system

The screening parameter k(s) appearing in the potential energy of a massive point charge near a metal surface is calculated as a function of adatom-metal separation s. It is shown how the parameters needed for self-consistent determination of effective charge on adion near a metal surface change when k(s) and the approximate formula for the modified image potential energy of a unit point charge outside the metal are used, instead of the classical image potential.     

Surface plasmons and the image force in metals

It is shown that the classical image potential acting between a point classical charge and a metal surface may be regarded as originating in the shifted zero point energy of the surface plasmon field. The retardation correction to the image potential is studied using the electron gas model.     

Positrons in metals with voids,vacancies and surfaces

The behaviour of positrons near monovacancies and voids in a metal is discussed in terms of three contributions to the positron work function for the metal, namely the positron zero-point energy, the positron-electron correlation energy and the surface dipole barrier. The image potential when a positron comes near to a metal surface leads to a deep potential ‘trough’ just outside an exterior metal surface or just inside a void surface. Calculations indicate positron bound states localized at metal surfaces for most metals which should be manifested in a long lived positron lifetime component. The behaviour of positronium near metal surfaces is also discussed.     

Time dependent Thomas Fermi approach to atomic collisions II

Numerical solutions of the time dependent Thomas Fermi (TDTF) equations for central and noncentral proton-atom collisions are presented in the energy range between 27.5 and 900 keV. Different approximations to the TDTF equations are compared. A two step scheme is proposed for the reduction of the fluid dynamical time dependent Hartree Fock (TDHF) equations to an effective single particle problem.     

Transient response of a spherical shell in an acoustic medium—Comparison of exact and approximate solutions

The transient response of a spherical shell in an acoustic medium is studied. The exact solution is obtained by expressing the classical spherical wave equation in terms of a residual potential. Approximate solutions are obtained from the use of eight functions; namely, doubly asymptotic approximations, δ-sequence functions, and spherical wave approximations. The advantages and disadvantages of these approximate solutions are pointed out. The third member of the class of the modal doubly asymptotic approximations for a spherical surface and an improved spherical wave approximation are introduced.     

Thermionic field emission of electrons from metals and explosive electron emission from micropoints

We suggest a general approach to considering the thermionic, field, and thermionic field emissions of electrons from metals. For this purpose, based on the standard model of free electrons in a metal, we suggest a numerical method for determining the transmission coefficient through the potential barrier at the metal-vacuum interface suitable for an arbitrary barrier. This method is free both from the approximations based on the saddle-point approximation and characteristic of the analytical models for thermionic emission and from the approximations for the tunneling coefficient through the potential barrier characteristic of the models for field emission. Based on numerical simulations, we determine the thermal effect of the emission and ascertain that a very sharp transition from surface cooling by electron emission to heating occurs at certain electric field and temperature. We explain the triggering mechanism of the explosive electron emission observed during micropoint explosions by this phenomenon. The explosive emission is shown to begin when the level of the potential barrier at the micropoint tip drops below the Fermi level in the metal.     

Three-dimensional analysis of scattering by pressure-release plane surfaces and the validity of the image solution

Because of the complexity of the scattering integrals in three dimensions, numerous approximations are used to obtain closed-form solutions. By considering the scattering by an infinite, pressure-release plane surface, the effects of various phase approximations and source directivity approximations can be examined independently of the surface roughness. Calculations are carried out using the Fraunhofer and Fresnel phase approximations, and two directivity approximations. It has been shown experimentally that the image solution is valid for the reflection of an acoustic beam by an infinite, pressure-release plane surface if the plane is in the farfield of the source. Consequently, the image solution is used to compare analytical solutions obtained using various phase and directivity approximations, and it is found that both the Fresnel phase approximation and a realistic directivity approximation are required to achieve a good fit. The solution produced by the Fraunhofer phase approximation is obtained as an asymptotic limit of the modified Fresnel solution. Criteria for the validity of the Fraunhofer and Fresnel phase approximations are developed. The Fresnel phase approximation is valid under fairly broad conditions, but the Fraunhofer phase approximation is never valid for an infinite plane surface that must be in the farfield of the source.