Because many properties of a fluid are highly anomalous near a critical point, experimental situations that normally are very simple to describe become much more complicated. Thus the specific heat of a sample is different from bulk values because of large, gravity-induced density gradients. The problems of relaxation to equilibrium, free convection, Brownian motion of a particle, and the viscous damping of an oscillating cylinder or a rotating disk are all complicated by the large compressibility, and, in general, the need to solve the hydrodynamic equations in a nonlinear regime.

The theory of transformation relations between states of Born Oppenheimer and weak coupling approximations is developed for polyatomic molecules. The relations are a generalization of frame transformation relations used by Chang and Fano for symmetric-top molecules, and they lead to a more convenient symmetry labeling system than was previously available. A key internal symmetry label (named "soul") is defined so that it remains a constant label for frame transformation relations, and is conserved during vibronic transitions, ionization, and even dissociation provided the nuclear spin-rotation interaction is relatively small. Various nomograms, graphs, and tableaus associated with the soul label make it easy to predict and visualize the form of many types of complex high-resolution spectra. Simplified procedures are given for obtaining selection rules, statistical weights, and matrix elements of multipole operators for common molecules having various point symmetries. Simplifications of computational theory using the new level cluster bases for high $J$ are discussed.

Since the appearance of the title paper, a number of new developments have occurred which need to be included in that body of material. We present additional remarks and clarifications which supplement and update numerous aspects of the Bethe theory discussed in the earlier paper. We also bring the bibliography up to date. Plasma stopping power, the $z^3$ effect, and stopping power for particles at extreme relativistic energies are among the new topics included. We make several comments on Fano's earlier review article, Ann. Rev. Nucl. Sci. 13, 1 (1963).

The problem of double beta decay is reviewed with emphasis on its relevance to lepton number conservation. Recently, the ratio of the double beta-decay half-lives of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Te}$ and ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$ has been measured in a geological experiment and a limit for the ratio of the neutrinoless rate to the total rate for ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$ decay has been obtained from a direct-detection experiment. For the first time, these results show conclusively that double beta decay is not primarily a lepton-number-violating neutrinoless process. However, they also do not agree with calculations which assume that only lepton-number-conserving two-neutrino double beta decay occurs. The conclusion that lepton number conservation is violated is suggested by limited experimental information. By considering contributions to the total rate from both the two-neutrino and the neutrinoless channels, we obtain data which are consistent with a lepton nonconservation parameter of order $\eta =3.5\mathrm{}\times {10}^{-5\mathrm{}}$. Roughly the same value of $\eta$ is obtained by assuming that the decay occurs either via lepton emission from two nucleons or via emission from a resonance in the nucleus.

A comprehensive review is presented dealing with pion excitations and condensation in nucleon matter. A discussion of the behavior of bosons in scalar electric and nuclear fields is given along with a consideration of the possible existence of superdense and supercharged nuclei. The applications to nuclei and neutron stars are given.

A brief review is given of the development and current status of the theoretical descriptions of direct nuclear reactions.

The development of the theory of the interaction of electromagnetic radiation with atoms and molecules is outlined. A fully classical analysis of absorption and emission is formulated in which particular attention is paid to questions of detailed balance and to the sum rules obeyed by the susceptibility. Collision broadening is introduced through time-dependent dipole moment correlation functions, and brief discussions of interruption broadening and various frequency modulation models are given. The corresponding quantum mechanical analysis is presented with emphasis on the points in common with the classical approach. The importance of correspondence principles in bridging the gap between classical and quantum mechanical theories is stressed.

Since the discovery of radioactivity predates the birth of quantum mechanics by nearly thirty years, it was inevitable that the most fundamental aspect of radioactive processes, its spontaneity, was also the most baffling one to physicists during the first quarter of the twentieth century. The ensuing struggles in that period with regard to the origins of the radioactive energy release, and to the significance of the life time concept are discussed.

The main physical features of LMFBR safety are summarized with particular reference to the maximum possible mechanical energy release in a hypothetical core disruption accident. It is likely that such a postulated fuel melting accident would lead to a nonenergetic disassembly of the core. With pessimistic estimates of reactivity increaases, but not derived from any mechanistic point of view, mechanical energy impacts on the reactor vessel of 100 MJ have been calculated for the Clinch River Breeder Reactor. These are containable with the present design, and the increase should vary only linearly with increased power for future designs of similar concept. Various possible steps are discussed to increase the certainty of these conclusions.

A deformed single-particle potential mode, with residual interactions, is applied to an analysis of states in odd-mass nuclides with $A>\mathrm{}228\mathrm{}$, and configuration assignments are presented for many levels. The systematics of energy level spacings throughout the actinides are studied, and the values of the nuclear deformation parameters that are appropriate to these nuclides are discussed. Tables of occupation probabilities and single-particle matrix elements are provided to facilitate the comparison of future measurements with theoretical expectations.

In this tutorial-style article we discuss the time-independent perturbation formalism of Brandow for effective interactions and operators in a nonrigorous, intuitive way. The simple example of a 2×2 matrix is used to introduce the basic concepts, for instance the notion of folded diagrams. The same example is used subsequently in a discussion of the branch points arising from "level crossings" and the associated convergence difficulties with the perturbation series. Numerical calculations of the effective interaction and the effective charge are then reviewed, focussing, for the most part, on the ($1s0d$) shell. Whenever possible, simple physical models are used to illustrate the results. A fairly comprehensive summary of the calculations to date is given, and we attempt to synthesize and draw conclusions.

Recent developments in the field of large $p_T$ physics are reviewed. Special attention is paid to the explanation of the data offered by specific constituent models. Emphasis is placed on those data which tend to differentiate between the models. Prospects for better understanding of large $p_T$ events as the result of new experiments and further theoretical work are discussed.

All of the experimental evidence for and against the existence of free, physical quarks from cosmic rays, particle accelerators, and stable matter is reviewed. There is no evidence for the existence of free quarks of fractional charge save for one recent report of niobium pellets of third-integral residual charge. The related searches for quarks of integral charge, for free magnetic monopoles, tachyons, dyons, and other postulated, stable elementary objects are also reviewed. Although some puzzling observations are noted, there is no firm evidence for any of these particles.

Recent researches have shown that it is possible to obtain information about the physical content of nontrivial quantum field theories by semiclassical methods. This article reviews some of these investigations. We discuss how solutions to field equations, treated as classical, $c$-number nonlinear differential equations, expose unexpected states in the quantal Hilbert space with novel quantum numbers which arise from topological properties of the classical field configuration or from the mixing of internal and space-time symmetries. Also imaginary-time, $c$-number solutions are reviewed. It is shown that they provide nonperturbative information about the vacuum sector of the quantum theory.

The intersecting storage accelerator facility ISABELLE proposed for construction at the Brookhaven National Laboratory is reviewed. ISABELLE would permit the exploration of proton-proton collisions at center-of-mass energies continuously variable from 60 to 400 GeV and with luminosities of ${10}^{32}$-${10}^{33}$ ${\mathrm{cm}}^{-2\mathrm{}}$${\mathrm{s}}^{-1\mathrm{}}$ over the entire energy range. The facility would consist of two interlaced rings of superconducting magnets, operating at 40 kG, in a common tunnel about 2.6 km in circumference. The proton beams would collide at six intersection regions where particle detecting systems would be located. Protons of about 30 GeV from the AGS will be accumulated in each ring to obtain the design current of 10 A prior to their acceleration to the final energy. In this paper the design philosophy underlying the principal design choices, as well as a brief description of the major accelerator systems and the conventional structures, is presented. An overview of the physics potential provided by ISABELLE is then given. The large extension of the center-of-mass energy range combined with the very high luminosity would provide unique possibilities for the investigation of the questions of greatest current interest in particle physics. Arguments, based on the available data and reasonable theoretical concepts, are presented that suggest strongly that the intermediate vector bosons required for a unified weak and electromagnetic field theory should be discovered. They should be studied in detail. The hadron production at high transverse momentum, the energy dependence of the strong interactions, and the possible search for new, massive particles are also discussed. The paper concludes with a detailed beam analysis, the various limitations on beam current, the procedures followed in optimizing the luminosity, and a justification of the projected performance levels.

A number of apparently disparate problems from engineering, meteorology, geophysics, fluid mechanics and applied mathematics are considered under the unifying heading of natural convection. After a review of the mathematical framework that serves to delineate these problems, the heuristic approach to Bénard and Rayleigh convection is discussed with special attention to buoyancy and surface tension. Then consideration is given to some aspects of scaling, and the nondimensionalization of equations to a given problem. The thermohydrodynamic description of a Newtonian fluid is presented, and the Boussinesq-Oberbeck model. This is followed by a treatment of the linear stability problem, and a description of the basic ideas of Landau and Hopf concerning the bifurcation of secondary solutions. Quantitative, though approximate, estimations are given for quantities belonging to the nonlinear steady convective regime: flow velocity and temperature distribution. Higher-order, though steady, bifurcations are discussed, as well as the transition to turbulence, along with such time-dependent phenomena as relaxation oscillations. The paper concludes with an Appendix showing a simple application of the Leray-Schauder topological degree of a mapping.

First-order polymorphic, second-order, melting, and freezing transitions induced by shock-wave loading are reviewed. Comprehensive tabulations of the experimental observations are presented and materials that have been subjected to in-depth study are reviewed in more detail. Theories of the mechanics, thermodynamics, kinetics, and shear strength of shock-loaded materials are described and experimental techniques are briefly reviewed.

The principles of interaction of energetic electrons with atoms are reviewed with emphasis on effects due to the crystalline structure of the target. Computer "experiments" and analytic models that simulate the collision processes in a crystalline lattice are described and analyzed. The experimental part discusses, first, the techniques used for the investigation of point defects in single crystals. Then, the available experimental results on defect production and recovery in metal crystals are reviewed in detail, and basic information, such as threshold energies for displacement in the main crystallographic directions and electrical resistivities of Frenkel pairs, is extracted. Finally, it is shown how interatomic potentials can be deduced from the experimental results.