Multiscattering effects in the far-field region for two small particles on a flat conducting substrate

Abstract

The scattered field in the far-field region for two small metallic particles on a conducting substrate is analysed as a function of both their separation and the angle of incidence. Special attention is paid to multiple scattering, which appears when the particles are very close, as well as to its related effects such as its influence on the enhanced backscattering phenomenon and depolarization of the incident beam in the plane of incidence.     

Chaotic scattering and acceleration of particles by waves

Relativistic charged particles in a uniform magnetic field and traveling waves of large amplitude can be accelerated limitlessly. Since much of phase space is chaotic the process can be viewed as chaotic scattering on waves. For multiple waves an explicit map arises with unusual properties. It contains infinite island chains around nonperiodic orbits and it is also an example of transient chaos in a Hamiltonian system.     

A possible mechanism for acceleration of heavy charged particles

A law of motion for a charged particle in a variable magnetic field is found. It is shown that the parametric effect of the magnetic field can be used for acceleration of heavy charged particles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 30–33, February, 1972.     

Magnetic reconnection and acceleration of particles on the sun

The present-day state of the problem regarding the acceleration of high-energy particles in solar flares is reviewed briefly. It is shown that an analytical solution to the equation of charged-particle motion in a reconnecting current layer with a 3D magnetic field and the electric field caused by magnetic reconnection allows us to offer an explanation for the acceleration of electrons and protons to relativistic energies over very short time intervals. The theoretical results are compared to recent observations of accelerated particles in solar flares.     

Electrodynamic metanuclei

A relativistic system of electrically charged fermions and oppositely charged massive scalars with no self-interactions, is argued to have a long-lived collective state with a net charge. The charge is residing near the surface of the spherically-symmetric state, while the interior consists of the condensed scalars, that are neutralized by the fermions. The metastability is achieved by competition of the negative pressure of the scalar condensate, against the positive pressure, mainly due to the fermions. We consider such metanuclei made of helium-4 nuclei and electrons, below nuclear but above atomic densities. Typical metanuclei represent charged balls of the atomic size, colossal mass, electric charge and excess energy. Unlike an ordinary nucleus, the charge of a metanucleus scales proportionately to its radius. The quantum mechanical decay through tunneling, and vacuum instability via pair-creation, are both suppressed for large values of the electric charge. Similar states could also be composed of other charged (pseudo)scalars, such as the pions, scalar supersymmetric partners, or in general, spin-0 states of new physics.     

Light within small particles

We calculate the energy density distribution in the ultraviolet within small spheres containing concentric cavities, aimed at simulating interstellar dust grains. We explore the dependence on chemical composition by progressively changing, in an arbitrary way, the refractive index of the sphere material. We conclude that a significant fraction of the energy of the impinging radiation is trapped throughout the particle interior.     

Structure of small metallic particles

This is a short review of some crystallographical anomalies or specific behaviour in thin metallic films. We give information about the structure of microparticles which do not have bulk-like symmetries. Their structure has been investigated by electron diffraction and electron microscopy. It is concluded that for the early stage of growth, the particles have five-fold symmetries and icosahedral structure. The growth mechanism is discussed and evidence for a layer- by-layer growth with respect to the pentagonal symmetry is emphasized. It is suggested that the substrate has much influence on the very early stages of growth of icosahedral particles. Beyond a certain size (about 80 Å), icosahedral particles transform into polytetrahedral particles which growth with the same shape and with a pseudo-pentagonal structure.     

Reactivity of small supported particles

Transition metals are frequently used in heterogeneous catalytic reactions. In many cases catalysts have specific properties related to crystallographic structure and morphology. One point of actual interest concerns the reactivity of specific sites as steps and kinks. These low co-ordination sites are characteristic for surfaces of small supported particles ranging from 1 to 10 nm. The structure sensitivity for CO chemisorption on supported Pd particles is explained by formation of (100)×(111) surface steps.     

Magnetization of small lead particles

The magnetization of an ensemble of isolated lead grains of sizes ranging from 4 to 1000 nm is measured. A sharp disappearance of the Meissner effect with a lowering of the grain size is observed for the smaller grains. This is a direct observation by magnetization measurement of the occurrence of a critical particle size for superconductivity, which is consistent with Anderson's criterion.     

Fraunhofer holography of small particles

The reconstruction of an in-line Fraunhofer (far-field) hologram is re-examined, and an analytical solution of the intensity distribution throughout the entire reconstructed image is presented. The solution bridges the gap between previously documented solutions which are limited to the plane-of-focus image and distant out-of-focus images. The analysis is motivated by a particle velocity measurement technique which attempts to distinguish the focussed image by photographic thresholding. The general methodology is presented for objects of one- and two-dimensional cross-section. Specific results are presented for the single exposure holograms of a long wire and a small particle of circular cross-section. The one-dimensional solution is verified experimentally. The results show precisely how the Fresnel diffraction term creates peaks in the intensity distribution, both upstream and downstream of the focussed image. This characteristic limits the resolution of methods which use thresholding as a means of distinguishing focussed images from their out-of-focus neighbors.     

Diamagnetism in small metal particles

We investigate the diamagnetic response of small metal particles using a quadratic confinement potential. We find that the dependence of the susceptibility on the magnetic field is rather sensitive to the symmetry of the applied confinement, while the dependence on the system size is similar to that of the bulk limit.     

Phase instabilities in small particles

In this review we consider the existing theories for the structure of small particles and the nature of morphological instabilities as the size is reduced. The various electron microscopic observations confirming the stability of a new phase, the so called ‘Multiply twinned structure’, in small particles is discussed. A theoretical model is presented to calculate the free energy surfaces for a series of asymmetric and single crystal structures using a modified Curie-Wulff construction for the surface energy, and a disclination model for the elastic strain energy. Depending on the activation barrier heights and the Boltzmann occupancy factors for the various local minima on the energy surface, the idea of ‘quasi-melting’ is introduced and compared with the structural instabilities in molecular clusters seen recently by various authors using computer simulations. A phase diagram for small particles as a function of size and temperature is presented and the effect of statistical fluctuations on stability is discussed. Finally a phenomenological discussion relating the phase instabilities to various melting and related phase transitions is given.     

Inhomogeneous strains in small particles

This paper considers the evidence for strains in small particles. Firstly, the dynamical electron diffraction theory for dark field imaging of small particles is briefly reviewed, considering primarily the effects of strain on wedge crystals and identifying the fingerprint of strain contrast effects under strong beam conditions. Evidence included herein and from published papers by other authors clearly shows inhomogeneous strain effects in both multiply twinned particles and single crystals. Considering these results and earlier reports of lattice parameter changes, there are problems with the uniqueness of these analyses, and the strains in the small single crystals are thought more likely to be due to interfacial stresses or contaminants than any intrinsic particle effect; there are so many different origins of this type of strain that we cannot with confidence isolate a unique source. It is emphasised that the uniqueness of any interpretation of experimental results from small particles must be very carefully considered.     

On acceleration of charged particles in intensity minima of laser fields

Using Klíma-Bogoliubov-Zubarev method, the acceleration of charged particles (electrons) in moving intensity minima of interference laser fields is investigated. The electromagnetic field intensity threshold for a prospective slipping-through of the particle through the potential barrier is found both analytically and numerically. Millimetre and submillimetre electromagnetic waves should be emitted because of forced electron oscillations in potential wells.This work has been initiated by gratefully acknowledged discussions with Professor H. Hora during the author's stay at the University of N. S. W., Sydney. The author thanks this University for the kind hospitality.     

Electron microscope investigation of small particles

In this review paper some possibilities to investigate small particles (1–1000 nm) with the electron microscope are treated. The transmission electron microscope is a unique tool to obtain information from small particles. This information covers the important area where atomic and bulk properties meet. The emphasis is focused on observations in connection with gas evaporation, adhesion between particles, possible vibration at contact, particle twinning, dynamical effects, martensitic transformation and superlattice crystals.     

Electronic properties of small metallic particles

Metallic particles with linear dimensions d small compared with other characteristic lengths (like the wavelength of electromagnetic radiation, the de Broglie wavelength of the conduction electrons, the coherence length or the penetration depth in the superconducting state, etc.) show interesting effects which are usually unobservable in bulk metals. The electronic properties of these particles with diameters of a few nm can be analysed by considering the microcrystals not as “giant molecules” but as “small solids”, i.e. by using the familiar methods of solid state physics with some properly defined boundary conditions. Due to the smallness of the particles, the customary quasi-continuous electronic excitation spectrum splits up into discrete energy levels with an average energy splitting δ of a few meV. If then the relevant energies (like the thermal energy kT, the Zeeman energy μ₀μ_BH, the electrostatic energy edE, the photon energy $\text{h}\text{?}\text{ω}$, the condensation energy for the superconducting state Δ, etc.) are comparable with δ, novel effects are to be expected, called “quantum size effects” (QSE). In an ensemble of small particles, it is expected that the discrete energy levels are statistically distributed; therefore, methods of level statistics can be employed to calculate the different electronic properties of small particles.In this report, the more phenomenological aspects of the physics of small particles are discussed, where e.g. the interaction of the electromagnetic radiation with the particle is described by a dielectric constant, also characteristic for the bulk metal. The more microscopic quantum size effects in small particles are then analysed theoretically, mainly from the point of view of the statistics of discrete energy levels, and the existing experimental results are discussed. Superconductivity in small metallic particles is reviewed with emphasis on the critical fields in small particles, the magnetic field dependence of their microscopic properties (e.g. density of states), the problem of a lower size limit of a superconductor, and fluctuations in small superconductors. Finally, the most commonly used experimental methods to produce small particles are described.