Within the nonrelativistic approximation the authors discuss three different mechanisms for the capture of a light particle from a bare heavy nucleus by another bare heavy nucleus which is incident with a very high relative velocity. The emphasis is on physical interpretation. For each mechanism a "physical" (i.e., more readily comprehensible) derivation is given of the asymptotic form of the total cross section, and a comparison is made of the relative importance of the different mechanisms in the case of electron capture from hydrogenlike "atoms." (Electron capture is normally referred to as charge transfer). The first mechanism is knock-on capture, where the two nuclei have equal masses and simply switch places. The second mechanism is radiative capture, which occurs with the emission of a photon. The third mechanism, which is perhaps the most interesting one, is double scattering, first suggested within the framework of classical mechanics by Thomas in 1927. In this mechanism the light particle undergoes two collisions, the first with the incident nucleus, and the second with the target nucleus; the light particle finally has almost the same velocity as the incident nucleus and therefore has a reasonable probability of being captured. The capture process in the asymptotic domain is a fascinating one theoretically since radiative capture can dominate over nonradiative capture; what is perhaps more remarkable is that for nonradiative capture integrated over the forward direction the second Born contribution dominates over the first in the asymptotic limit. For the capture of an electron bound in a high Rydberg state, capture via the knock-on the double scattering mechanisms are describable classically (Thomas' result becomes exact!) and (near the forward direction) the second Born(Born again) term dominates over the first at much lower energy. (Changing only the notation and the kinematics, the results can be used to study mass transfer processes in which one of a massive gravitationally pound pair of astrophysical objects is captured by a third massive object). A number of results for capture into a true bound state can be readily carried over to "capture to the continuum," with the electron emerging with a small positive energy relative to the incident nucleus. An understanding of the asymptotic form of the capture cross section is of considerable interest in its own right; it may also be helpful in understanding the dynamics of the capture process in the medium velocity range where applications are important. At medium velocities electron capture is of interest in many areas of physics such as astrophysics, chemical physics, plasma physics, and atomic physics; it is also of practical interest, having applications in laser and fusion research.

The propagation theory of multimode and single-mode optical waveguide fibers is reviewed. The subjects reviewed include basic propagation theory, the influence of the glass medium on attenuation and pulse dispersion, and the effects of perturbations of the waveguide's geometry and index profile.

The inverse scattering method (ISM) as applied to self-induced transparency (SIT) is reviewed. The linear scattering equations (Zakharov-Shabat equations) that are the basis of the inverse scattering method applied to SIT are physically interpreted. They in turn are solved by establishing an analogy with the equations are shown to follow from application of the principle of causality of the parametric amplifier analog.

The effects of dephasing due to spatial inhomogenelty on the space-time evolution (two-dimensional steady state) of nonlinear three-wave interactions are described. After summarizing previous work on the inhomogeneous-medium three-wave equations, the authors describe an inverse scattering transform for these equations. They then use this transform along with numerical integration of the equations to determine the effects of inhomogeneity on the nonlinear evolution of decay, backscatter, and explosive interactions. The effects include modified threshold conditions for explosive instabilities and modified conditions for optimal energy transfer in two-pump interactions. Energy transfer in both absolute and convective decay interactions in an inhomogeneous medium is found to plateau and then decrease with increasing pump width, in striking contrast to homogeneous-medium interactions. A suppression of the nonlinear modulation in stimulated backscatter is described. A time-asymptotic solution for the spatial profiles of daughter waves is given for the absolute instability.

The authors describe the evolution in time and one spatial dimension (steady-state in two spatial dimensions) of coherent three-wave interactions in a lossless homogeneous medium. They obtain their results by a complementary use of inverse scattering methods and numerical integration of the equations. The nonlinear saturation by pump depletion of instabilities which are absolute in the pump reference frame is found to involve only soliton transfer, thus allowing a complete solution in terms of an $N$-soliton formula. Threshold formulas for explosive instabilities, and conditions for optimal energy transfer in two-pump interactions, are presented. Nonlinear collisions of wave packets are found to give rise to upconverted packets which are sharply spiked. A nonlinear modulation is described in stimulated backscatter.

The author presents a perspective on possible future projects at Fermilab.

The presence of a gravitational field leads to both practical and fundamental limits of the resolution in critical phenomena experiments in fluids near the gas-liquid critical point. We present equations that yield estimates of the gravitational limitations in a variety of critical phenomena experiments for a large number of fluids and as a function of the magnitude of the gravitational field. Various strategies for improving the resolution of such experiments are discussed, including procedures that remove a fluid from thermodynamic equilibrium (e.g., stirring). A comparison is made between the gravitational limitations in earth-bound experiments and those at the microgravitational levels that may become accessible in an orbiting laboratory.

The authors discuss the coherence properties of neutron scattering from perfect crystals and apply them to the splitting and coherent recombination of a neutron beam in a Laue-type interferometer. They also point out the difference between neutron and x-ray scattering in such devices and discuss the effect of a relative displacement of the various interferometer slabs on the fringe pattern. All this can be done without using the detailed dynamical theory of x-ray scattering. Various experiments are discussed, especially the neutron-gravity experiment of Colella, Overhauser, and Werner, which is analyzed both in the laboratory frame and in a frame freely falling with the neutron beam. The older electron diffraction experiment of Marton et al., and its relevance to the Aharonov—Bohm effect, is also discussed and reinterpreted, because the standard interpretation is not consistent with the results of the neutron experiment. An Appendix presents a general discussion of the transformation to a uniformly accelerated reference frame, as a guide to help analyze future such experiments.

We present a phenomenological review of the weak hadronic decay processes $K\mu 2\pi$ and $K\to 3\pi$, primarily the $\mathrm{CP}$-conserving transitions. We have paid particular attention to consistency between different experimental measurements of the same quantity. We have performed a least-squares analysis of the data to determine transition amplitudes to various final states, and the dependence on final-state energy variables. Tests of isotopic spin selection rules have been made by applying various constraints to the least-squares analysis. Amplitudes for pure isotopic spin transitions to specific final states are presented. Current algebra predictions are remarkably well satisfied for the pure $\Delta I=\frac{1}{2}$ amplitude.

A graphical representation of angular momentum is used to evaluate relativistic matrix elements between antisymmetrized states of many- particle configurations having any number of open shells. The antisymmetrized matrix element is expanded as a sum of semisymmetrized matrix elements, which can be evaluated expediently in terms of radial integrals from easily constructed diagrams. The diagram representing a semisymmetrized matrix element is composed of four diagram blocks, namely, the bra block, the ket block, the spectator block, and the interaction block. The first three blocks indicate the couplings of the two interacting configurations while the last depends on the interaction and is the replaceable component. Interaction blocks for relativistic operators and commonly used potentials are summarized in ready-to-use forms. A simple step-by-step procedure is prescribed generally for calculating antisymmetrized matrix elements of one- and two-particle operators. A modified covarient 3-jm coeffecient is also introduced along with certain new graphical notations. Although we focus on the case of jj-coupled states, which comes naturally in relativistic formulation, the general procedure holds in any coupling scheme.

Correlations in the distribution of galaxies provide some important clues about the structure and evolution of the Universe on scales larger than individual galaxies. In recent years much effort has been devoted to estimating and interpreting galaxy correlations. This is a review of these efforts. It is meant to provide both an introductory overview of the subject and a critical assessment of some recent developments.

Electric field gradients present at the atomic nuclei in solids may be studied through the nuclear electric quadrupole interaction by several methods. In noncubic metallic systems, a large amount of data has become available and is critically testing our theoretical understanding of the sources of field gradients in these systems. After summarizing the relevant measurement techniques, we discuss the development of the existing experimental data base and the various theoretical approaches to explain it. Comprehensive coverage of the published literature extends through 1977.

The J. Robert Oppenheimer Lectures are given annually at the Institute for Advanced Study, Princeton, New Jersey, by a distinguished visiting scientist who has made outstanding research contributions in a field of current interest and who is recognized for his ability to communicate progress in his area of expertise to a broad spectrum of physical scientists. The lecturer summarizes the progress and significance of work in his field in a series of two talks. The lectures are named in honor of J. Robert Oppenheimer, former Professor in the School of Natural Sciences, Institute for Advanced Study, and the third Director of the Institute. This paper presents the text of the second lecture on the topic of singular layers and reconnection.

This review covers experimental results and theoretical ideas on the properties of superconducting weak links, i.e., weak electrical contacts between superconducting electrodes which exhibit direct (non-tunnel-type) conductivity. When the dimensions of such weak links are sufficiently small, the Josephson effect is observed in them, in other words, a single-valued and $2\pi$ -periodic relationship exists between the supercurrent $I_s$ and the phase difference $\sigma$ of the electrodes. With increasing dimensions, this relationship has a tendency to deviate gradually from the Josephson behavior. This deviation varies, depending on whether the weak link material is a superconductor or a normal metal. The various known types of weak links are described, and special mention is made of those weak links which are most suitable for physical investigations and have various practical applications. The data on the nonstationary (ac) processes in weak links, when the phase difference varies with time, are analyzed. In conclusion the existing concepts about the processes in weak links are briefly summarized and the most urgent outstanding problems are outlined.

The J. Robert Oppenheimer Lectures are given annually at the Institute for Advanced Study, Princeton, New Jersey, by a distinguished visiting scientist who has made outstanding research contributions in a field of current interest and who is recognized for his ability to communicate progress in his area of expertise to a broad spectrum of physical scientists. The lecturer summarizes the progress and significance of work in his field in a series of two talks. The lectures are named in honor of J. Robert Oppenheimer, former Professor in the School of Natural Sciences, Institute for Advanced Study, and the third Director of the Institute. This paper presents the text of the first lecture on the topic of turbulence and nonlinear waves.