The current theoretical and experimental status of angular distributions of inelastically scattered nucleons and succeeding $\gamma$ radiations on the basis of a compound-nucleus mechanism is reviewed, with special reference to symmetry, isotropy, and identity characteristics. Results of investigations using a fast computer to ascertain the influence of higher partial waves, multipole mixing, unobserved intermediate transitions, and the presence of additional exit channels are presented, together with an over-all survey of distribution systematics and tabulations of numerical parameters to assist in evaluation of differential cross sections by hand. The predictions for both proton and neutron inelastic scattering are discussed in detail and illustrated by analyses of experimental data for many nuclear spin sequences. In particular, it is shown for $\gamma$ distributions that the effect of cascades from higher levels upon the distribution structure and magnitude can be very appreciable. Also, the examination of the predicted behavior of ($n, n^{\prime }\gamma$) distributions near threshold has disclosed features deserving of further experimental and theoretical study. A set of recently measured ($n, n^{\prime }\gamma$) distributions for several heavy nuclei involving transitions between nuclear states of relatively high integer or half-integer spin is shown to compare well with the theoretical predictions when suitable account is taken of cascade and exit-channel contributions. It is concluded that there is a wide range of application of this theoretical approach to energy-averaged distributions, much of which remains yet to be exploited.

Quasi-free processes in nuclei are reviewed both from a theoretical and an experimental point of view. The discussion is limited to nuclei with mass number≥4 and to incident energies larger than 100 MeV for quasi-free proton-proton and 300 MeV for electron-proton scattering. The reactions are discussed qualitatively, and their relevance for the investigation of nuclear shells, in particular of the strongly bound ones, is shown. The cross section for quasi-free scattering is then derived in the distorted wave impulse approximation, and some special cases are considered. Through a few examples the main features of the experimental results are presented and compared with calculated ones. Measurements on several $1p$, $2s-1d$, and $2p-1f$ shell nuclei are discussed.

This review includes a compilation and critical evaluation of absolute cross sections for ionization of atoms and diatomic molecules by electron impact. Experimental techniques used for ionization are surveyed. Selected relative cross sections for production of multiply charged ions and a brief discussion of relative cross-section data near threshold are presented. Absolute limits are not set on the size of probable systematic errors in the various experiments.

The irreversible equations of evolution of classical gases, as obtained by Prigogine and Résibois from a study of the Liouville equation, in the limit of the system being very large, are examined, and the structure of the Markovian equation of evolution of the velocity distribution function is studied for homogeneous systems. It is then shown that the Markovian equations completely contain the Bogoliubov theory.

Further support is provided for a model of the stimulation process in inorganic phosphors recently proposed by Luchner, Kallmann, Kramer, and Wachter. A reasonable identification of the center responsible for the absorption of stimulating radiation (the main feature of this model) is made for zinc sulfide phosphors containing copper, but it is shown that no identification can be made as yet of the absorbing centers responsible for most of the peaks of stimulation spectra so far observed. Many of the apparently incompatible published observations can be reconciled with the aid of previously unpublished work.

The physical effects created by strong shock waves propagating in hydrogen are reviewed and theoretically studied for speeds up to relativistic conditions. In the progression from weak to relativistic shock speeds, various physical phenomena affect the shock wave. Dissociation, ionization, and the presence of an upstream electric field cause several important effects for slow (sub-Alfvénic speed) normal ionizing shock waves. Switch-on shock behavior is extended to slow ionizing waves. The effect of radiation is investigated for both the optically thick and thin cases. Relativistic shock jump equations are solved for wave speeds approaching the speed of light. Thermonuclear shock solutions are examined. The theory of the electromagnetically driven shock tube is reviewed and the corresponding shock tube problem is explored. Wave stability is reviewed. Experimental results on strong ionizing shock waves are reviewed and discussed.

It is shown that an earlier study by Hamilton and Woolcock of fixed momentum-transfer dispersion relations may be complemented by a study of fixed energy dispersion relations. Two main results are obtained. First, by demanding that the two types of relation give the same value for the amplitude, nontrivial restrictions are obtained on the amplitude (the $f_0-N-N$ coupling constants and the values of certain integrals over the high-energy $\pi N$ amplitude are obtained). Secondly, the fixed energy relation enables one to discuss quantitatively the validity of the "CGLN" approximate method which Hamilton and Woolcock had used to calculate the partial-wave amplitudes at low energies from the fixed momentum-transfer dispersion relation alone. The terms neglected by this approximation are evaluated, and found to be large except at low energies (the authors had themselves suggested that this might be the case). Even when these terms are included, undesirable cancellations occur, and the conclusion in fact is that fixed variable relations are not suitable for calculating the partial-wave amplitudes (except at low energies), but only for providing sum rules.

The formalism of the coupled-channel analysis of the scattering of nuclear projectiles by nuclei is presented in detail. Since the necessity for coupled-channel calculations increases with the degree of collectivity exhibited by the target nucleus, the presentation is particularly suited to collective nuclei, with the target states described by phenomenological collective coordinates. Within this restriction the formalism given here is quite general so that the following cases can be considered: The target can be any (collective) nucleus, even-$A$ or odd-$A$, vibrational or rotational; the projectile can be either charged or uncharged, and can have any spin; either or both the projectile and the target can be polarized; finally, the energy of the projectile can be very low since the contribution of the compound-state formation to the cross section can be included. Using a computer program which was written following the above formalism (which can be used to do any of the calculations enumerated above) scattering cross sections for several typical cases were obtained and are presented to show their contrasting behavior when different targets (and different coupling schemes) and different projectiles are chosen. Realistic calculations were also made in order to fit a large number of existing experimental data. Good fits were obtained in most cases which indicates that the coupled-channel calculation is a very powerful tool in explaining various complicated scattering data, and further in extracting useful spectroscopic informations about the target nucleus. Possible future developments of the present analyses are discussed.

This review is concerned with the application of dispersion relation methods to direct nuclear reactions. We begin with a discussion of the assumptions required to relate analyticity properties to the conventional descriptions of direct-reaction amplitudes. This leads naturally to a description of phenomenological methods such as extrapolation to poles and similar topics. The use of the unitarity condition provides a framework for the discussion of the distorted wave Born approximation from the $S$-matrix point of view Finally we call attention to some dynamical calculations of relevance to our discussion.

Elementary particle physics has demonstrated the complete symmetry between particles and antiparticles. From this follows the equivalence between matter and antimatter. It is very unsatisfactory that current cosmological theories are not symmetric with respect to matter and antimatter.

It is postulated that a cosmological theory should be matter-antimatter symmetric, and introduce no ad hoc laws of nature. These postulates form part of Klein's theory, but are not satisfied by the "expanding universe" or "continuous creation" theories.

Essential properties of an "ambiplasma" consisting of matter and antimatter are studied. It is shown that it emits radio waves but no detectable $\gamma$ rays. If initially the plasma contains equal amounts of matter and antimatter, the two ingredients can be separated by electromagnetic and gravitational forces. In the present state of the universe there may be coexisting regions of matter and antimatter, separated by thin "Leidenfrost" layers.

Klein's theory of the metagalaxy is reviewed and developed. The "initial condition" is supposed to be an extremely thin plasma of matter and antimatter which contracts under the action of gravitation. When the density has reached about ${10}^{-2\mathrm{}}$ particles ${\mathrm{cm}}^{-3\mathrm{}}$, annihilation produces a radiation pressure which transfers the contraction to the present expansion. The theory leads to a relation between the average density and the Hubble parameter which is in satisfactory agreement with observations.

Different ways of detecting antimatter are discussed. It is possible that radio stars consist of ambiplasma. The enormous energy quantities emitted from some celestial objects may be supplied by annihilation.

Outside our metagalaxy there may exist other similar systems. The possibility of observing them is discussed.

Data and references on properties of particles and resonances are compiled, tested for consistency, and summarized in tables and wallet cards. This is an updating of the Reviews of Modern Physics article of October 1964, and some new quantities have been included in the tables.

Invariance principles are used, in physics, in two distinct manners. First, they are used as superlaws of nature in that, once their validity has been suggested by their consistency with the known laws of nature, they serve as guides in our search for as yet unknown laws of nature. Second, they can serve as tools for obtaining properties of the solutions of the equations provided by the laws of nature. It is desirable for the first use to give a formulation of invariances directly in terms of the primitive concepts of physical theory, i.e., in terms of observations, or measurements, and their results. Invariances which can be so formulated are called geometric invariances. The present paper contains an attempt at such a formulation of geometric invariances. This formulation is then applied, in detail, to the classical mechanics of point particles, to a relativistic mechanics of interacting point particles, and to quantum theory. With the exception of the relativistic mechanics of point particles, these applications form a review, from a single point of view, of earlier work on this subject. The last part of the paper contains a review of the second use of invariances.

Experimental data bearing on the precision determination of the numerical values of the fundamental physical constants are reviewed, with particular emphasis being placed on the identification and isolation of discrepancies and inconsistencies. The purpose of the analysis is to present a consistent set of values of the fundamental constants and to present a careful and complete description of the steps taken to reach this end. The Introduction discusses the significance of such an analysis and indicates the general method of approach. The indispensability of local unit systems and conversion factors connecting them, in order to avoid a sacrifice of precision peculiar to different metrological techniques, is emphasized. The point is stressed that conversion constants introduce the danger of ignoring error-statistical correlations between physically measured quantities, and the effects of such correlations on the assignment of errors is discussed. All available sources of experimental information relative to the necessary input data are presented, and changes in definitions of units since our last review are discussed. After the available stochastic input data have been reviewed and the less reliable items eliminated, the third section examines the remainder for mutual compatibility by means of an analysis of variance in which special criteria for recognizing the incompatibility of a datum are developed, using the analogy of the energy of internal strain introduced in overdetermined mechanical structures. Tables of least-squares adjusted values of fundamental constants and conversion factors of physics and chemistry based on the 1963 adjustment are given. Research pertinent to the constants which has been completed or published subsequent to the 1963 "recommended" adjustment is discussed, and the effect of these on our knowledge of the numerical values of the fundamental constants is presented.