Hadronic multiparticle reactions at very high energies are reviewed with emphasis on current theoretical pictures and models.

The past three years have seen new measurements of the $g$-factor anomalies of the free leptons ($e^{\pm }, {\mu }^{\pm }$). At the same time there have been several major theoretical advances including a quantum electrodynamic calculation of the sixth-order coefficient of the electron anomaly. In this article we review these recent developments in detail, however we also: (1) present a historical overview of $g$-factor measurements and their interpretation since the early days of quantum theory, (2) discuss several experiments which are currently being attempted but which have not yet yielded results of high precision, (3) attempt to predict the most likely course of $g$-factor research in the near future. An extensive Bibliography and Tables summarizing both historical events and current work are included.

Optical pumping of ground-state and metastable atoms and ions is reviewed. We present a critical survey of the literature on pumping mechanisms, light propagation, relaxation mechanisms, spin exchange, and experimental details on the various atomic species which have been successfully pumped.

A review is presented of the direct numerical approach to the study of the atomic vibrational properties of disordered systems. The basis and details of the numerical methods employed are first described. This is followed by a review of applications of the approach to two-component disordered lattices, glasses, mixed-crystal systems, orientationally disordered crystals, and random polymers.

A theory of analog resonances is reviewed which makes use of projection operators. The Hilbert space is divided into three parts: a continuum or open-channel space, an analog-state space, and a compound space. The phenomena are discussed in terms of the dynamical coupling of these spaces. The parameterization of the $T$ matrix is discussed in detail, and equations are presented for various cross sections. The commutator [$H$, $T_{-}$], where $T_{-}$ is the isospin-lowering operator, plays an important role in the theory, and the various terms which contribute to this commutator are discussed. The energy splitting of the isospin multiplet, i.e., the Coulomb displacement energy, is discussed in detail. The importance of the analog resonance phenomena for the extraction of spectroscopic information is stressed, and it is shown how such information may be obtained. Various processes which contribute to the escape amplitude of the analog state are classified, and some numerical estimates are given. For several regions of the Periodic Table, graphs are presented for the various theoretical escape amplitudes, continuum energy shifts, asymmetry phases, and optical phase shifts, etc. Spectroscopic factors are calculated and compared with those obtained in other experiments.

The paper begins with a tutorial introduction to the theory of inelastic light scattering by polaritons in dielectric crystals. The treatment is based on a simple two-oscillator model which represents the ionic and electronic motions of a crystal. The model contains a third-order anharmonicity which allows an incident laser beam to mix with the oscillator fluctuations and produce scattered light of frequency different from the incident frequency. The magnitude of the oscillator fluctuations is determined by an application of the Nyquist of fluctuation-dissipation theorem, using the response functions of the oscillators for externally applied forces. The simple model gives results for light scattering cross sections which agree with more rigorous derivations in the existing literature. The response function approach is generalized to apply to crystals having many ionic resonances and of uniaxial or orthorhombic structure. The general formulas reduce in appropriate special cases to results already published. Experimental and theoretical work on light scattering by polaritons and by pure phonons is reviewed in the context of both the two-oscillator model and the general theory. Particular attention is given to resonance scattering in an attempt to achieve consistency between the differing theoretical treatments in the literature. The subject matter of the review overlaps some topics in nonlinear optics, and contact is made with the theories of the electrooptic effect and stimulated Raman scattering.

The available experimental data on energy spectra of electrons ejected in ion-atom collisions are reviewed against the background of modern theoretical concepts.

The various experimental techniques used to obtain differential, total, and momentum-transfer electron-molecule scattering cross sections at low electron energies are reviewed, and observations are compared with theory, especially with theoretical calculations of rotational excitation cross sections for slow electrons incident on homonuclear diatomic molecules. A detailed discussion of the theory of rotational excitation by slow electrons is given, with particular attention to the merits and deficiencies of recent attempts to improve on the lowest-order Born approximation predictions, via the so-called rotational close coupling and adiabatic-nuclei approximations.

Experiments relating to measurements of total and momentum-transfer cross sections for the scattering of low-energy electrons by atoms and diatomic molecules are critically reviewed. Principal emphasis is placed upon the Ramsauer method, dc swarms, and crossed-beams experiments, which account for the bulk of the reliable data in the literature although other techniques including differential measurements are also discussed. The theories of the various methods and possible sources of error are discussed. The case of low-energy electron scattering by helium is exhaustively reviewed since this system has been most intensively studied experimentally and is particularly amenable as well to theoretical calculations. The best available cross section values, along with comments on individual experiments, are presented in several tables.

This article gives a systematic review of the many NMR experiments in solid helium to date, emphasizing the view-point that the results may be interpreted primarily in terms of the effects of three fundamental excitations in the solid: the vacancy waves; the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ tunneling interaction or exchange; and the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ tunneling interaction or mass fluctuation waves.

Calculational procedures are developed for the ground-state energy of a many-fermion system. The entire theory is developed from the many-body Schrödinger equation via perturbation theory. The linked cluster expansion is derived by elementary methods. The analytic singularities of the energy function are analyzed, and procedures designed to avoid or overcome them. Results for the calculation of the energy in the presence of a purely repulsive two-body force are reviewed, and the situation is found to be reasonably satisfactory, though good results are restricted to weak potentials when the system is not dilute. Results for an attractive potential surrounding a strongly repulsive core are reviewed, and procedures discribed for calculations in this case. A sample calculation with an assessment of the probable errors is reviewed.

The application of the single-particle model to nonspherical nuclei is reviewed. The band-head ($I=K$) energy data for intrinsic states of predominantly one-quasiparticle character are compiled for odd-A nuclides in the region $150<A<\mathrm{}190\mathrm{}$. The data are analyzed in two steps: first, the rotational and vibrational contributions to the energies are subtracted to give quasiparticle excitation energies; second, single-particle level schemes are fitted to the quasiparticle energies by BCS blocking calculations. The resulting schemes are presented graphically. The single-particle energies and the pairing calculation parameters are made available so that they can be utilized for various purposes in nuclear structure work. As a result of the analysis, we find indications that the zero-point rotational contributions to the band-head energies may have appreciable variations. The level systematics is compared with various single-particle model calculations, assuming local, axially symmetric potentials, and the potential and shape parameters entering are discussed. The potentials used offer satisfactory interpretation of the relevant features of the systematics. The use of a diffuse potential well with proper parameter choices is of significance, particularly for the single-neutron levels. The values of the deformation parameters ${\epsilon }_2$ and ${\epsilon }_4$ (or ${\beta }_2$ and ${\beta }_4$) preferred by the level systematics are compatible with other evidence concerning the nuclear surface shapes.

The configuration assignments for the known energy levels of the odd-$A$ deformed nuclei in the mass range $150<A<\mathrm{}190\mathrm{}$ have been systematically reviewed. For each nucleus, a summary is given of the intrinsic states that are considered well identified, and the main arguments that support particular assignments are outlined. A discussion is presented of the theoretical framework used in the analysis which is basically the Nilsson single-particle model with pairing correlations and Coriolis coupling taken into account, and with appropriate consideration given to vibrational excitations and their mixing with the one-quasiparticle states. Energy systematics are shown for the one-quasiparticle excitations and for the gamma-vibrational excitations (most of which have significant one-quasiparticle admixtures), and these systematics are discussed in terms of current theory.

The current understanding is summarized from a unified point of view, which Bethe initiated four decades ago and which enables one to put a variety of theoretical and experimental data into a coherent picture. Properties of the generalized oscillator strength, which plays the central role in the theory, are treated in detail. The integrated cross section for inelastic scattering and related quantities at the high-velocity limit also are discussed. The theory provides a series of criteria for testing the compatibility of cross-section data and atomic (or molecular) properties that may be obtained from theory or independent experiments.

We give a review of methods used to set a limit on the mass $\mu$ of the photon. Direct tests for frequency dependence of the speed of light are discussed, along with more sensitive techniques which test Coulomb's Law and its analog in magnetostatics. The link between dynamic and static implications of finite $\mu$ is deduced from a set of postulates that make Proca's equations the unique generalization of Maxwell's. We note one hallowed postulate, that of energy conservation, which may be tested severely using pulsar signals. We present the merits of the old methods and of possible new experiments, and discuss other physical implications of finite $\mu$. A simple theorem is proved: For an experiment confined in dimensions D, effects of finite $\mu$ are of order ${\left(\mu \mathrm{D}\right)}^2$—there is no "resonance" as the oscillation frequency $\omega$ approaches $\mu$ ($\hslash =c=1\mathrm{}$). The best results from past experiments are (a) terrestrial measurements of $c$ at different frequencies $\mu \le 2\times {10}^{-43\mathrm{}}\mathrm{g}\equiv 7\times {10}^{-6\mathrm{}}{\mathrm{cm}}^{-1\mathrm{}}\equiv {10}^{-10\mathrm{}} \mathrm{eV}$ (b) measurements of radio dispersion in pulsar signals (whistler effect) $\mu \le {10}^{-44\mathrm{}}\mathrm{g}\equiv 3\times {10}^{-7\mathrm{}}{\mathrm{cm}}^{-1\mathrm{}}\equiv 6\times {10}^{-12\mathrm{}} \mathrm{eV}$ (c) laboratory tests of Coulomb's law $\mu \le 2\times {10}^{-47\mathrm{}}\mathrm{g}\equiv 6\times {10}^{-10\mathrm{}}{\mathrm{cm}}^{-1\mathrm{}}\equiv {10}^{-14\mathrm{}} \mathrm{eV}$ (d) limits on a constant "external" magnetic field at the earth's surface $\mu \le 4\times {10}^{-48\mathrm{}}\mathrm{g}\equiv {10}^{-10\mathrm{}}{\mathrm{cm}}^{-1\mathrm{}}\equiv 3\times {10}^{-15\mathrm{}} \mathrm{eV}.$ Observations of the Galactic magnetic field could improve the limit dramatically.

This review of the properties of leptons, mesons, and baryons is an updating of Review of Particle Properties, Particle Data Group [Phys. Letters 33B, 1 (1970)]. Data are evaluated, listed, averaged, and summarized in Tables. A data booklet is also available.