The authors review the Keldysh method of obtaining kinetic equations for normal and superconducting metals. The use of the method is illustrated by examples involving electron-impurity, electron-phonon, and electron-electron scattering, both within and beyond the quasiclassical approximation.

A single charged particle in a Penning trap is a bound system that rivals the hydrogen atom in its simplicity and provides similar opportunities to calculate and measure physical quantities at very high precision. We review the theory of this bound system, beginning with the simple first-order orbits and progressively dealing with small corrections which must be considered owing to the experimental precision that is being achieved. Much of the discussion will also be useful for experiments with more particles in the trap, and several of the mathematical techniques have a wider applicability.

A comprehensive review is given of investigations, both theoretical and experimental, that demonstrate interference to take place even when the fields involved are produced by independent sources. The physical situation is rather different for coherent and incoherent fields. In the first case, where the sources are lasers, a conventional interference pattern can be observed which is adequately described by the classical theory. In the present paper, special attention is paid to the question of whether this interference persists when the two laser beams become strongly attenuated. In the second case, the sources are individual atoms excited by a pumping mechanism, that emit spontaneously and, hence, independently from each other. In those circumstances, no interference pattern can show up. However, it becomes evident from both the classical and the quantum-mechanical theory that interference effects can still be established by observing intensity correlations rather than the intensity itself. This point is discussed in greater detail. The pioneering experiments of Forrester, Gudmundson and Johnson, and Brown and Twiss are reviewed in this context. Especially interesting from the theoretical point of view is the case of two emitting atoms, since then the classical and the quantum-mechanical description differ significantly, the quantum theory predicting the intensity correlations to be distinctly stronger than those following from classical considerations. This specific quantum-mechanical feature is shown to be intimately connected with the corpuscular aspect of light.

The linear and nonlinear theory of resistive magnetohydrodynamic modes is reviewed, with particular emphasis on aspects figuring prominently in the behavior of magnetic confinement fusion devices.

This review on some aspects of waves in gases concentrates first (Part I) on modern research in the acoustics of fluids at rest or in steady or turbulent motion, in free space, in the presence of obstacles, or in ducts. The study of sound, for which the sole restoring force is pressure, will be extended in a later paper (Part II) to include the other three restoring forces, namely, gravity, electromagnetic, and Coriolis forces, leading to current research on internal, magnetic, and inertial waves and their couplings. The Introduction at the beginning of Part I, and the discussion at the end of Part II, concern all four types of waves in gases, and their relevance in physics and engineering. In Part I, the following areas of acoustics are addressed: the generation of noise by turbulence, inhomogeneities or bubbles, in natural and engineering flows, e.g., wind or jets; the scattering of sound by interfaces and diffraction by turbulence, and their effects on spectral and directional redistribution of energy; propagation in ducts, without or with mean flow, e.g., the horns of musical instruments and loudspeakers, and inlets and exhausts of engines; the effects of dissipation and nonlinearity on waves, e.g., in laboratory and engineering shock tubes, and in geophysical and astrophysical conditions. Underlying these topics is the interaction of acoustics with manking, ranging from the processes of human hearing and speech to the reproduction of desirable sounds (music) and reduction of undesirable sounds (noise).

Clusters of galaxies are gravitationally bound configurations containing typically hundreds of galaxies in a region about ${10}^{25}$ cm in size. They range from irregular clusters, with strong subclustering, no strong central concentration, and mainly spiral galaxies, to regular clusters, with smooth and centrally condensed galaxy distributions containing few spiral galaxies. Observations of these clusters of galaxies show that they are bright x-ray sources, with luminosities of ${10}^{43-45}$ ergs/sec. It is now established that the emission mechanism is thermal bremsstrahlung from hot (∼${10}^8$ K), low-density (∼${10}^{-3\mathrm{}}$ atoms/${\mathrm{cm}}^{-3\mathrm{}}$) gas. This intracluster gas has a distribution similar to that of the galaxies in the cluster and fills the space between the galaxies. Remarkably, the total mass of hot gas in a typical cluster is similar to the total mass in all the stars in all the galaxies in the cluster. The x-ray spectra of clusters show strong x-ray line emission from iron and other heavy elements; this indicates that a significant portion of the intracluster gas must have been ejected from galaxies in the cluster. Recent x-ray observations from the Einstein x-ray satellite show that intracluster gas is cooling in some clusters and being accreted onto large, central galaxies. X-ray images from Einstein also suggest that the morphology of the gas mirrors the dynamical state of the cluster. In this paper the x-ray observations of clusters of galaxies are reviewed. Related optical and radio measurements of clusters are also summarized. Theories for the physical state, distribution, origin, and evolution of the intracluster medium are extensively discussed. Finally, the author comments on the prospects for future x-ray observations.

In slow heavy-ion—atom collisions, inner-shell electrons with velocities larger than the projectile velocity form diatomic molecular orbitals around the projectile and target nuclei. If a vacancy exists in one of these orbitals, it can decay at some point during collision, emitting an x ray characteristic of the molecular transition energy at that internuclear distance. Since the projectile-target internuclear distance varies during the collision, x-ray continua are seen, which for $1s\sigma$ molecular-orbital x rays (transitions to vacancies in the lowest $1s\sigma$ orbital) stretch toward the united-atom $K$-shell binding energy. This paper reviews the theory of and the experimental evidence for molecular-orbital x-ray emission. A historical overview of the development of these studies is given, showing how the theory of quasimolecular x-ray emission has evolved from a semiclassical quasistatic model to a general dynamic theory, including the Coriolis coupling between molecular orbitals making up the initial and final states. X-ray cross section, angular distribution, and other measurements are discussed, and their impact on the development of the theory of molecular-orbital x-ray emission is illustrated.

Existing data on the ionization of neutral atoms and molecules by proton impact are reviewed, and electron production cross-section data are collected. The three major experimental methods are discussed and possible sources of error identified. Some theoretical cross sections are discussed, and well-established methods of relating them to measured cross sections are reviewed. A mathematical equation is fitted to the weighted experimental data for each target, and these fits are adjusted to be consistent with appropriate theoretical calculations and with electron impact and photoionization data. Recommended values of total cross sections for proton-impact ionization are given.

This paper gives a survey of the alpha-nucleon interaction and then describes experimental work on angular distributions of differential scattering cross sections and polarizations in proton-alpha and neutron-alpha scattering. The phenomenological approach, which includes the study of both local and nonlocal potentials reproducing the experimental alpha-nucleon scattering data, is discussed. Basic studies of the alpha-nucleon interaction attempting to build an interaction between an alpha particle and a nucleon from first principles are then described. The authors then present a critical discussion of the results with some concluding remarks suggesting the direction for further investigation.

A summary of the current understanding of nuclear magnetic ordering in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is presented. The main emphasis is a critical review of what is known from the experiments along with a critique of various theoretical models. Unanswered questions are raised about both the macroscopic phenomena and the microscopic origins of the magnetism. Several experiments are proposed which should help advance our understanding of the magnetic behavior of solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.

Photon-assisted tunneling of electrons through an insulating barrier may be used to detect long-wavelength radiation with a sensitivity approaching the limit imposed by the Heisenberg uncertainty principle. A new generation of ultra-low-noise millimeter-wave receivers, currently being developed for astronomical observation, utilizes the extremely sharp nonlinearity produced by single-electron quasiparticle tunneling between two superconductors in a superconductor-insulator-superconductor (SIS) tunnel junction. At millimeter wavelengths, the quantum energy $\frac{\hslash \omega }{e}$ may be larger than the voltage width for onset of quasiparticle tunneling in a SIS junction; and under these conditions the absorption of a single photon can cause one additional electron to tunnel through the barrier. Several newly discovered quantum effects become possible in this regime, including power amplification of an incoming signal during the process of frequency down-conversion in a heterodyne receiver. The experimental development of SIS millimeter-wave receivers is reviewed, along with the quantum theory of mixing which predicts their performance.

The wetting of solids by liquids is connected to physical chemistry (wettability), to statistical physics (pinning of the contact line, wetting transitions, etc.), to long-range forces (van der Waals, double layers), and to fluid dynamics. The present review represents an attempt towards a unified picture with special emphasis on certain features of "dry spreading": (a) the final state of a spreading droplet need not be a monomolecular film; (b) the spreading drop is surrounded by a precursor film, where most of the available free energy is spent; and (c) polymer melts may slip on the solid and belong to a separate dynamical class, conceptually related to the spreading of superfluids.

In 1978 it was discovered, largely through the work of Fleischmann, Van Duyne, Creighton, and their coworkers that molecules adsorbed on specially prepared silver surfaces produce a Raman spectrum that is at times a millionfold more intense than expected. This effect was dubbed surface-enhanced Raman scattering (SERS). Since then the effect has been demonstrated with many molecules and with a number of metals, including Cu, Ag, Au, Li, Na, K, In, Pt, and Rh. In addition, related phenomena such as surface-enhanced second-harmonic generation, four-wave mixing, absorption, and fluorescence have been observed. Although not all fine points of the enhancement mechanism have been clarified, the majority view is that the largest contributor to the intensity amplification results from the electric field enhancement that occurs in the vicinity of small, interacting metal particles that are illuminated with light resonant or near resonant with the localized surface-plasmon frequency of the metal structure. Small in this context is gauged in relation to the wavelength of light. The special preparations required to produce the effect, which include among other techniques electrochemical oxidation-reduction cycling, deposition of metal on very cold substrates, and the generation of metal-island films and colloids, is now understood to be necessary as a means of producing surfaces with appropriate electromagnetic resonances that may couple to electromagnetic fields either by generating rough films (as in the case of the former two examples) or by placing small metal particles in close proximity to one another (as in the case of the latter two). For molecules chemisorbed on SERS-active surface there exists a "chemical enhancement" in addition to the electromagnetic effect. Although difficult to measure accurately, the magnitude of this effect rarely exceeds a factor of 10 and is best thought to arise from the modification of the Raman polarizability tensor of the adsorbate resulting from the formation of a complex between the adsorbate and the metal. Rather than an enhancement mechanism, the chemical effect is more logically to be regarded as a change in the nature and identity of the adsorbate.

The authors give a general discussion of the derivation from field theory of a formalism for the perturbative solution of the relativistic two-body problem. The lowest-order expression for the four-point function is given in terms of a two-particle three-dimensional propagator in a static potential. It is obtained by fixing the loop energy in the four-dimensional formalism at a point which is independent of the loop momentum and is symmetric in the two particle variables. This method avoids awkward positive- and negative-energy projectors, with their attendant energy square roots, and allows one to recover the Dirac equation straightforwardly in the nonrecoil limit. The perturbations appear as a variety of four-dimensional kernels which are rearranged and regrouped into convenient sets. In particular, they are transformed from the Coulomb to the Feynman gauge, which greatly simplifies the expressions that must be evaluated. Although the approach is particularly convenient for the precision analysis of QED bound states, it is not limited to such applications. The authors use it to give the first unified treatment of all presently known recoil corrections to the muonium hyperfine structure and also to verify the corresponding contributions through order ${\alpha }^2\ln \alpha E_F$ in positronium. The required integrals are evaluated analytically.

Recent advances in the understanding of Rayleigh-Bénard convection and turbulence are reviewed in light of work using liquid helium. The discussion includes both experiments which have probed the steady flows preceding time dependence and experiments which have been directed toward understanding the ways in which turbulence evolves. Comparison is made where appropriate to the many important contributions which have been obtained using room-temperature fluids, and a discussion is given explaining the advantages of cryogenic techniques. Brief reviews are given for recent experimental investigations of convection in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures—in both the superfluid and the normal states—and investigations of convection in rotating layers of liquid helium.

Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the geometric theory of differentiable dynamical systems, moderately excited chaotic systems require new tools, which are provided by the ergodic theory of dynamical systems. This theory has reached a stage where fruitful contact and exchange with physical experiments has become widespread. The present review is an account of the main mathematical ideas and their concrete implementation in analyzing experiments. The main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions). The relations between these quantities, as well as their experimental determination, are discussed. The systematic investigation of these quantities provides us for the first time with a reasonable understanding of dynamical systems, excited well beyond the quasiperiodic regimes. This is another step towards understanding highly turbulent fluids.