This paper brings together, into a single unified notation, the multipole formalisms for gravitational radiation which various people have constructed. It also extends the results of previous workers. More specifically:

Part One of this paper reviews the various scalar, vector, and tensor spherical harmonics used in the general relativity literature—including the Regge-Wheeler harmonics, the symmetric, trace-free ("STF") tensors of Sachs and Pirani, the Newman-Penrose spin-weighted harmonics, and the Mathews-Zerilli Clebsch-Gordan-coupled harmonics—which include "pure-orbital" harmonics and "pure-spin" harmonics. The relationships between the various harmonics are presented. Part One then turns attention to gravitational radiation. The concept of "local wave zone" is introduced to facilitate a clean separation of "wave generation" from "wave propagation." The generic radiation field in the local wave zone is decomposed into multipole components. The energy, linear momentum, and angular momentum in the waves are expressed as infinite sums of multipole contributions. Attention is then restricted to sources that admit a nonsingular, spacetime-covering de Donder coordinate system. (This excludes black holes.) In such a coordinate system the multipole moments of the radiation field are expressed as volume integrals over the source. For slow-motion systems, these source integrals are re-expressed as infinite power series in $\frac{L}{\lambda }\equiv \frac{\left(\mathrm{size}\mathrm{of}\mathrm{source}\right)}{\left(\mathrm{reduced}\mathrm{wavelength}\mathrm{of}\mathrm{waves}\right)}$. The slow-motion source integrals are then specialized to systems with weak internal gravity to yield (i) the standard Newtonian formulas for the multipole moments, (ii) the post-Newtonian formulas of Epstein and Wagoner, and (iii) post-post-Newtonian formulas.

Part Two of this paper derives a multipole-moment wave-generation formalism for slow-motion systems with arbitrarily strong internal gravity, including systems that cannot be covered by de Donder coordinates. In this formalism one calculates, by any means, the source's instantaneous, near-zone, external gravitational field as a solution of the time-independent Einstein field equations. One then reads off of this near-zone field the source's instantaneous multipole moments; and one plugs those time-evolving moments into the standard radiation formulae given in Part One of this paper.

As building blocks for this formalism, Part Two also does the following things: (1) In the linearized theory of gravity, for the vacuum exterior of an isolated system, it derives the general solution of the field equations (a result due to Sachs, Bergmann, and Pirani). (2) In full nonlinear general relativity, for the vacuum near-zone exterior of an isolated system, it derives the structure of the general solution of the Einstein field equations. That structure is expressed as a sum of products of multipole contributions. It also matches this near-zone field onto an outgoing-wave radiation field. (3) In full nonlinear general relativity, for the vacuum exterior of a stationary isolated system, (a) it presents a definition of multipole moments which meshes naturally with gravitational-wave theory; (b) it introduces the concept of "asymptotically Cartesian and mass centered" (ACMC) coordinate systems; and (c) it shows how to deduce the multipole moments of a source from the form of its metric in an ACMC coordinate system. As an example, the lowest few ($l\le 3$) multipole moments of the Kerr metric are computed.

There is a reasonably good change that in the 1980s cosmic gravitational waves will be discovered and will become a powerful tool for astronomy. This prospect has stimulated a three-pronged research effort. First, relativity theorists are developing new mathematical tools for the analysis of gravitational radiation—including (i) methods of analyzing the generation of gravity waves by sources with strong selfgravity and large internal velocities (e.g., collisions of black holes), (ii) methods of computing radiation reaction in sources, and (iii) methods of analyzing how gravitational waves propagate through our lumpy curved-space Universe. Second, astrophysicists are attempting to identify the most promissing sources of gravitational waves, and are using the relativity theorists' mathematical tools to estimate the characteristics of the waves they emit. Third, with the estimated wave characteristics in mind, experimenters are designing and constructing a second generation of gravitational-wave detectors—detectors of three types: Doppler tracking of interplanetary spacecraft, Earth-based laser interferometers, and Earth-based Weber-type resonant bars. This article reviews, in brief, all three prongs of the research effort and gives references to more detailed articles about specialized aspects of gravitational-wave physics.

The current state of the theory and its application to low-energy electron-molecule collisions is reviewed. The emphasis is on elastic scattering and vibrational and rotational excitation of small diatomic and polyatomic molecules. New and traditional theoretical approaches are described, and the results of calculations are compared with existing experimental measurements.

The present status of quantum chromodynamics formalism for inclusive deep-inelastic scattering is reviewed. Leading-order and higher-order asymptotic freedom corrections are discussed in detail. Both the formal language of operator product expansion and renormalization group and the intuitive parton model picture are used. Systematic comparison of asymptotic freedom predictions with deep-inelastic data is presented. Extensions of asymptotic freedom ideas to other processes such as massive $\mu$-pair production, semi-inclusive deep-inelastic scattering, $e^{+}{e}^{-}$ annihilation, and photon-photon scattering are briefly discussed. The importance of higher-order corrections is emphasized.

The appropriate language for describing the pure Yang-Mills theories is introduced. An elementary but precise presentation of the mathematical tools which are necessary for a geometrical description of gauge fields is given. After recalling basic notions of differential geometry, it is shown in what sense a gauge potential is a connection in some fiber bundle, and the corresponding gauge field the associated curvature. It is also shown how the global aspects of the theory (e.g., boundary conditions) are coded into the structure of the bundle. Gauge transformations and equations of motion, as well as the selfduality equations, acquire then a global character, once they are defined in terms of operations in the bundle space. Finally the orbit space, that is to say, the set of gauge inequivalent potentials, is defined, and its is shown why there is no continuous gauge fixing in the non-Abelian case.

We review the theory of the electromagnetic interactions between rapidly moving charged particles and the matter through which they pass. The emphasis will be on very massive electric ($-100\mathrm{}\le Z_{1}100$) and magnetic ($\mathrm{}\left|g\right|=137e \mathrm{and} \frac{137e}{2}$) particles moving with relativistic velocities ($\beta >0.2\mathrm{}$, $\gamma <100\mathrm{}$). Consideration will be given to both the stopping power of the projectile and to the response of the absorbing medium to the excitation caused by the projectile.

Several common modes of crystal growth provide particularly simple and elegant examples of spontaneous pattern formation in nature. Phenomena of interest here are those in which an advancing nonfaceted solidification front suffers an instability and subsequently reorganizes itself into a more complex mode of behavior. The purpose of this essay is to examine several such situations and, in doing this, to identify a few new theoretical ideas and a larger number of outstanding problems. The systems studied are those in which solidification is controlled entirely by a single diffusion process, either the flow of latent heat away from a moving interface or the analogous redistribution of chemical constituents. Convective effects are ignored, as are most effects of crystalline anisotropy. The linear theory of the Mullins-Sekerka instability is reviewed for simple planar and spherical cases and also for a special model of directional solidification. These techniques are then extended to the case of a freely growing dendrite, and it is shown how this analysis leads to an understanding of sidebranching and tip-splitting instabilities. A marginal-stability hypothesis is introduced; and it is argued that this intrinsically nonlinear theory, if valid, permits aone to use results of linear-stability analysis to predict dendritic growth rates. The review concludes with a discussion of nonlinear effects in directional solidication. The nonplanar, cellular interfaces which emerge in this situation have much in common with convection patterns in hydrodynamics. The cellular stability problem is discussed briefly, and some preliminary attempts to do calculations in the strongly nonlinear regime are summarized.

This is an account of Einstein's work and thoughts on the quantum theory. The following topics will be discussed: The light-quantum hypothesis and its gradual evolution into the photon concept. Early history of the photoelectric effect. The theoretical and experimental reasons why the resistance to the photon was stronger and more protracted than for any other particle proposed to date. Einstein's position regarding the Bohr-Kramers-Slater suggestion, the last bastion of resistance to the photon. Einstein's analysis of fluctuations around thermal equilibrium and his proposal of a duality between particles and waves, in 1909 for electromagnetic radiation (the first time this duality was ever stated) and in January 1925 for matter (prior to quantum mechanics and for reasons independent of those given earlier by de Broglie). His demonstration that long-known specific heat anomalies are quantum effects. His role in the evolution of the third law of thermodynamics. His new derivation of Planck's law in 1917 which also marks the beginning of his concern with the failure of classical causality. His role as one of the founders of quantum statistics and his discovery of the first example of a phase transition derived by using purely statistical methods. His position as a critic of quantum mechanics. Initial doubts on the consistency of quantum mechanics (1926-1930). His view maintained from 1930 until the end of his life: quantum mechanics is logically consistent and quite successful but it is incomplete. His attitude toward success. His criterion of objective reality. Differences in the roles relativity and quantum theory played in Einstein's life. His vision regarding quantum theory in the context of a unified field theory. His last autobiographical sketch, written a few months before his death, concluding with a statement about the quantum theory, a subject to which (by his own account) he had given more thought than even to general relativity.

The authors review new techniques developed to apply the variational method to the nuclear matter problem. The variational wave function is taken to be ($S{\Pi }_{i<j}{\mathrm{F}}_{\mathrm{ij}}$) $\Phi$; the correlation operators ${\mathrm{F}}_{\mathrm{ij}}$ can in principle induce central, backflow, spin isospin, tensor, etc. correlations, and $\Phi$ is the ideal Fermi gas wave function. The application of diagrammatic cluster expansion and chain summation techniques to calculate expectation values with such wave functions is discussed in detail. The authors also give a brief overview of various other approaches to the calculation of the binding energies of quantum fluids, and a comparison of results for simple systems such ad helium liquids. Results obtained by various methods for simplified models of nuclear matter, which include central, spin, isospin, and tensor forces, have converged significantly in recent months. Results obtained with more realistic models which include the spin-orbit potentials are also discussed. The potential models considered so far either give too little binding or too high equilibrium density.

Resonance ionization spectroscopy, RIS, is a multistep photon absorption process in which the final state is the ionization continuum of an atom. The RIS process can be saturated with available pulsed lasers, so that one electron can be removed from each atom of the selected type. This method was first applied to the determination of the absolute number of He($2{}_{}{}^1{}_{}{}^{}S$) excited states produced when pulsed beams of protons interacted with helium gas. Laser schemes for RIS are classified into five basic types; with these, nearly all of the elements can be detected with commercially available lasers. A periodic table is included showing schemes applicable to all of the elements except He, Ne, F, and Ar. A compact theory of the RIS process is presented which delineates the conditions under which rate equations apply. Questions on the effects of collisional line broadening, laser coherence time, and nonresonant multiphoton ionization processes are discussed. The initial demonstration of one-atom detection of Cs is described. By using laser beams to saturate the RIS process and by using proportional counters as single-electron detectors, one-atom detection is made possible. With RIS, one-atom detection is highly selective, has the ultimate in sensitivity, and has excellent space and time resolution. Furthermore, a modification of the technique in which single electrons (or single ions) are detected with a channel electron multiplier permits single-atom detection in a vacuum. Resonance ionization spectroscopy has application to classical phenomena such as the diffusion of free atoms, the chemical reaction of free atoms with a gas, the measurement of concentration fluctuations in a dilute vapor, and a variety of other atomic fluctuation phenomena. The authors describe how RIS can be used for photophysics measurements such as far wing collisional line broadening, measurements of photoionization cross sections for excited states, and collisional redistribution among excited states. Modern applications include the detection of single atoms in individual ionization tracks, such as those created by the binary fission of a parent atom, and the extension of this technique to the detection of stable or unstable daughter atoms in time coincidence with the decay of a parent atom. These methods are beig developed for use in low-level counting to determine, for example, the flux of solar neutrinos on the earth.

Much of our information about quasars is derived from their emission-line spectra. The analysis of such spectra has become an intricate subject which differs considerably from traditional, low-density nebular astrophysics. This review is intended to explain our present understanding of the situation, including some aspects of galactic nuclei whose luminosities are more modest than quasars. Quasars' line-emitting regions are probably photoionized (even if supplementary heating processes also occur). So far, models have been constructed which include ionization and thermal equilibria, the transfer of resonance-line and related photons, and the likely effects of absorption and scattering by dust grains. From comparisons between emission-line intensities produced in these models and observed quasars' spectra, it appears that certain densities and pressures and size scales occur in or around quasars. The relative abundances of elements are not very far from solar values, although it is suspected that heavy elements—carbon, nitrogen, and oxygen in particular—are moderately "overabundant" in quasars. The emission-line intensities also provide indirect information about quasars' ultraviolet and soft-x-ray continua; there are hints that photons with energies between 20 and 300 eV—which are not directly observable—may even represent the peak of the luminous output of a typical quasar. Finally, some gas-dynamical questions, while extremely important, are very difficult to answer, because of a lack of observables.

This article is an interdisciplinary review of lattice gauge theory and spin systems. It discusses the fundamentals, both physics and formalism, of these related subjects. Spin systems are models of magnetism and phase transitions. Lattice gauge theories are cutoff formulations of gauge theories of strongly interacting particles. Statistical mechanics and field theory are closely related subjects, and the connections between them are developed here by using the transfer matrix. Phase diagrams and critical points of continuous transitions are stressed as the keys to understanding the character and continuum limits of lattice theories. Concepts such as duality, kink condensation, and the existence of a local, relativistic field theory at a critical point of a lattice theory are illustrated in a thorough discussion of the two-dimensional Ising model. Theories with exact local (gauge) symmetries are introduced following Wegner's Ising lattice gauge theory. Its gauge-invariant "loop" correlation function is discussed in detail. Three—dimensional Ising gauge theory is studied thoroughly. The renormalization group of the two dimensional planar model is presented as an illustration of a phase transition driven by the condensation of topological excitations. Parallels are drawn to Abelian lattice gauge theory in four dimensions. Non-Abelian gauge theories are introduced and the possibility of quark confinement is discussed. Asymptotic freedom of O(n) Heisenberg spin systems in two dimensions is verified for $n\ge$ and is explained in simple terms. The direction of present-day research is briefly reviewed.

Aspects of the theory of homotopy groups are described in a mathematical style closer to that of condensed matter physics than that of topology. The aim is to make more readily accessible to physicists the recent applications of homotopy theory to the study of defects in ordered media. Although many physical examples are woven into the development of the subject, the focus is on mathematical pedagogy rather than on a systematic review of applications.

Metal catalysts are technologically very important. Moreover, these materials are intriguing systems for scientific investigation. In general, metal catalysts are highly dispersed materials, i.e., materials with very high surface areas. The study of these materials with chemical probes including chemisorption and selected catalytic reactions, in conjunction with physical methods such as electron microscopy, x-ray diffraction, photoelectron spectroscopy, and extended x-ray absorption fine-structure spectroscopy, has contributed much to our knowledge of their structures. Metal catalysts considered in this article include systems consisting essentially of a single metal component (monometallic catalysts) and also bimetallic systems, this latter group including metal alloys as well as highly dispersed bimetallic clusters.

Electrons incident on a crystal surface can be temporarily trapped in surface states at energies above the vacuum level. These temporary or nonstationary surface states are observed as narrow fluctuations of elastic scattering intensity with respect to variation of electron energy and incidence direction. The scattering process is called electronic surface resonance scattering. The temporary surface states that are intermediate states in resonance scattering are called electronic surface resonances. The article surveys both experimental and theoretical research on electronic surface resonances as observed by scattering of low-energy (<1 keV) electrons. A critical account of experiments on A1(001), W(001), Ni(001), and oxygenated Ni(001) surfaces is offered together with theoretical commentary. Plots of the electronic surface resonance band structure $E\left({\mathrm{k}}_{\parallel }\right)$ ($E=\mathrm{resonance}\mathrm{energy}$, ${\mathrm{k}}_{\parallel }=\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}-\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{l}\mathrm{m}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{u}\mathrm{m}$) are compiled and the significance of $E\left({\mathrm{k}}_{\parallel }\right)$ plots for surface characterization is indicated.

The present experimental evidence on $T=\frac{3}{2}$ states in nuclei is presented with particular attention to quartets in which the properties of all four members are known. A relation between the masses of the quartet, the isobaric multiplet mass equation, is shown to hold extremely well. The significance of the coefficients of the equation is discussed, and a brief review of the present status of quintets is also presented.

A comprehensive review of the known classical solutions of $\mathrm{SU}\left(2\right)\mathrm{}$ gauge theories is presented. The author follows the historical development of this subject from its beginning (the first explicit solution found was an imbedded Abelian static Coulomb solution) up to the most recent work in the field (in particular the solutions which represent monopoles, instantons, and merons). As well as being a detailed survey, this article is intended to serve as a self-contained introduction to the subject.

Quantitative estimates are derived for three classes of phenomena that may occur in an open cosmological model of Friedmann type. (1) Normal physical processes taking place with very long time-scales. (2) Biological processes that will result if life adapts itself to low ambient temperatures according to a postulated scaling law. (3) Communication by radio between life forms existing in different parts of the universe. The general conclusion of the analysis is that an open universe need not evolve into a state of permanent quiescence. Life and communication can continue for ever, utilizing a finite store of energy, if the assumed scaling laws are valid.