A tensor equations-of-motion formalism for the excitation of a many-body system is presented, following the same general approach as the uncoupled formalism presented in a previous article. It is designed to take explicit account of the geometrical constraints imposed on excitation operators by the requirements that stationary states should have good angular momentum and, for a charge-independent nuclear Hamiltonian, good isospin. These developments are particularly relevant for application to molecular, atomic, and nuclear systems. By recognizing the geometrical constraints and exploiting the invariance properties of the excitation operators, the equations of motion become more readily applicable to nonscalar systems; i.e. to systems with nonzero angular momentum and/or isospin.

This paper presents a summary and evaluation of the experimental properties of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ as they were known in the fall of 1974. Subjects having thermodynamic significance, including specific heat, static magnetism, phase equilibria, and superfluid density, are discussed first. Then known flow properties are treated. After a brief discussion of the theoretical ideas which motivated some of the later experiments, the subject of dynamic magnetism is reviewed. Closely related work in a magnetic field in the immediate temperature region of the critical temperature is discussed, as are the propagation of ultrasound, the phenomena of supercooling and superheating, precise indication of the critical temperature, and the effects of certain restrictive geometries. The article concludes with a brief discussion of some new developments which appeared after the main text was finished. Appendices on thermometry and on parameters of the normal Fermi liquid are included.

This paper reviews the theory of anisotropic superfluid phases and its application to the new A and B phases of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. It is tutorial in nature and advanced formal techniques are avoided; even the formalism of second quantization is not required. After an initial discussion of the Fermi-liquid theory of Landau and its application to the normal phase of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, the idea of instability against formation of Cooper pairs is introduced. The effective interaction in liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is considered, with emphasis on the spin-dependent interaction arising from virtual spin polarization of the medium ("spin fluctuation exchange"). Next, a self-contained discussion of the "weak-coupling" BCS theory as applied to anisotropic superfluids is given, with special attention to the "Ginzburg-Landau" region close to the transition temperature. Formulas are derived for the specific heat, spin susceptibility, normal density tensor, and static spin-dependent correlation properties of superfluids with both singlet and triplet pairing: In the triplet case the ideas of "spin superfluid velocity" and "spin superfluid density" are also introduced. After a preliminary comparison of the weak-coupling theory with experiment, it is shown that feedback effects due to the modification, by formation of Cooper pairs, of the effective interaction connected with spin fluctuation exchange can produce results which are qualitatively different from those of the weak-coupling theory. An attempt is made to reformulate recent graph-theoretical treatments of this phenomenon in a more elementary language, and considerations based on possible invariant forms of the free energy are also introduced. The properties of the so-called Anderson-Brinkman-Morel and Balian-Werthamer states, which are commonly identified with ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-A and B, respectively, are studied in detail. Next, the effects which tend to orient the Cooper pair wave function in a given experimental situation are discussed; in this context the form of the free energy terms arising from spatial variation of the wave function is explored. A semiphenomenological theory of the nuclear magnetic resonance properties is developed and applied in particular to the case of unsaturated cw resonance; the analogy with the Josephson effect is emphasized. The question of relaxation and linewidths is also briefly discussed. A partial account is given of the theory of finite-wavelength collective oscillations, with particular reference to first, second, and fourth sound and spin waves. The splitting of the A-normal transition in a magnetic field is considered, with special attention to the possibility it offers of testing theories of the "spin fluctuation" type. Finally, a brief assessment is made of the extent to which the current experimental data support the conventional identification of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-A and B and the spin fluctuation theory, and some outstanding problems and possibilities are outlined. Subjects not discussed include "first-principles" theories of the effective interaction in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ collective excitations in the "collisionless" regime, and the problem of ultrasonic absorption, "orbit waves," and the theory of the kinetic coefficients.

The hadronic structure of photons is studied by treating the electromagnetic interaction in lowest order. General consequences of this picture and its connection with generalized vector meson dominance for diffractive processes are discussed. Emphasis is given to the dipion constituent which can be regarded approximately as a superposition of two parts: a ${\rho }^0$-meson core and a loose nonresonant two-pion structure. This modification of VMD increases the dipion contribution to the real photon cross section by 10%-20% (of the ${\rho }^0$ part) and to $\nu W_2$ by several percent. The internal spatial structure of this component is shown to shrink as the photon becomes more virtual. Various views of diffractive pion pair photoproduction are reconciled. The Drell process is interpreted in terms of the dipion component and some evidence is given for its presence in inclusive ${\pi }^{-}$-photoproduction data. Some speculations about the consequences of the spatial size of different photon constituents are given.

A systematic discussion of the phenomenology of charmed particles is presented with an eye to experimental searches for these states. We begin with an attempt to clarify the theoretical framework for charm. We then discuss the $SU\left(4\right)\mathrm{}$ spectroscopy of the lowest lying baryon and meson states, their masses, decay modes, lifetimes, and various production mechanisms. We also present a brief discussion of searches for short-lived tracks. Our discussion is largely based on intuition gained from the familiar—but not necessarily understood—phenomenology of known hadrons, and predictions must be interpreted only as guidelines for experimenters.

We examine the theoretical possibility that at high densities there may exist a new type of nuclear state in which the nucleon mass is either zero or nearly zero. The related phenomenon of vacuum excitation is also discussed.

The issue of light-water reactor (LWR) safety has been the subject of a part-time, year-long study sponsored by the American Physical Society. The goal of the study was the assessment of some of the technical aspects of the safety of large light-water nuclear power reactors typical of present commercial practice in the Unted States. The report examines issues related to safe operation of LWRs; the research and development program responsible for establishing and enhancing safety; and the consequences of accidents for public health and welfare. The report in no way deals with the need for nuclear power or its benefits, and should not be considered as a net assessment of the risks versus the benefits of nuclear reactors. Since the risks of ecological impacts of other energy technologies are not addressed, no recommendations are made concerning the specific reactor program which should be followed in the immediate future. Among the areas covered in the report are primary pressure-vessel integrity; quality assurance; accident initiation from operator error, transients, and sabotage; the adequacy of present emergency core-cooling system designs; the calculation of long-term consequences to health of one particular low-probability accidental release of radioactivity; and the experimental and calculational (computer-code-development) aspects of the present reactor safety research program. A number of recommendations are contained with the report, mainly addressed to ways in which the safety of the present LWRs can be improved or better understood.

Since approximately 1950 an increasing portion of experimental solid state physics research has been concerned with studying defects in crystals. This trend might appear to be a rather belated recognition that most of the materials we come into contact with have a random structure. In fact the theoretical understanding and controlled preparation of compounds with defects or random structure has been very slow in developing. The present paper examines and reviews our knowledge of the lattice vibrations associated with defects. The coverage is extremely broad, as shown by the table of contents. It includes localized and resonant modes of isolated defects as well as the modes in highly disordered mixed crystals and glasses. It is primarily a review of experimental work but theoretical results are included where the latter explain or predict significant features. In order to be self-contained several sections of the paper deal entirely with theoretical matters. There is a chapter on explicit solutions of the linear chain vibration problem and a short chapter on Green's function methods. The review emphasizes the infrared absorption and Raman scattering of defects. This is simply because other techniques have not yielded nearly so much information. Neutron scattering and electron tunneling are referred to only where they have shed light on certain systems. Extensive tables of defects and mode frequencies are included for each type of solid. The major solids which are reviewed include semiconductors, ionic compounds, organic compounds, and amorphous insulators.

In this review we consider deuterium-tritium (D-T) fusion reactors based on four different plasma-confinement and heating approaches: the tokamak, the theta-pinch, the magnetic-mirror, and the laser-pellet system. We begin with a discussion of the dynamics of reacting plasmas and basic considerations of reactor power balance. The essential plasma physical aspects of each system are summarized, and the main characteristics of the corresponding conceptual power plants are described. In tokamak reactors the plasma densities are about ${10}^{20}$ ${\mathrm{m}}^{-3\mathrm{}}$, and the $\beta$ values (ratio of plasma pressure to confining magnetic pressure) are approximately 5%. Plasma burning times are of the order of 100-1000 sec. Large superconducting dc magnets furnish the toroidal magnetic field, and 2-m thick blankets and shields prevent heat deposition in the superconductor. Radially diffusing plasma is diverted away from the first wall by means of null singularities in the poloidal (or transverse) component of the confining magnetic field. The toroidal theta-pinch reactor has a much smaller minor diameter and a much larger major diameter, and operates on a 10-sec cycle with 0.1-sec burning pulses. It utilizes shock heating from high-voltage sources and adabatic-compression heating powered by low-voltage, pulsed cryogenic magnetic or inertial energy stores, outside the reactor core. The plasma has a density of about ${10}^{22}$ ${\mathrm{m}}^{-3\mathrm{}}$ and $\beta$ values of nearly unity. In the power balance of the reactor, direct-conversion energy obtained by expansion of the burning high-$\beta$ plasma against the containing magnetic field is an important factor. No divertor is necessary since neutral-gas flow cools and replaces the "spent" plasma between pulses. The open-ended mirror reactor uses both thermal conversion of neutron energy and direct conversion of end-loss plasma energy to dc electrical power. A fraction of this direct-convertor power is then fed back to the ioninjection system to sustain the reaction and maintain the plasma. The average ion energy is 600 keV, plasma diameter 6 m, and the plasma beta 85%. The power levels of the three magnetic-confinement devices are in the 500-2000 MWe range, with the exception of the mirror reactor, for which the output is approximately 200 MWe. In Laser-Pellet reactors, frozen D-T pellets are ignited in a cavity which absorbs the electromagnetic, charged particle, and neutron energy from the fusion reaction. The confinement is "inertial," since the fusion reaction occurs during the disassembly of the heated pellet. A pellet-cavity unit would produce about 200 MWt in pulses with a repetition rate of the order of 10 ${\sec }^{-1\mathrm{}}$. Such units could be clustered to give power plants with outputs in the range of 1000 MWe.

This article consists of two parts. The first part presents a tutorial approach to cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems. Particular emphasis is placed on the question of how order and self-organization may arise. The following example is treated among others: the ordered phase of the laser giving rise to both coherently oscillating atomic dipole moments and coherent light emission. A complete analogy of the laser light distribution function to that of the Ginzburg-Landau theory of superconductivity is found mathematically which allows us to interpret the laser threshold as a quasi-second-order phase transition with soft modes, critical slowing down, etc. Similar phenomena, again closely resembling phase transitions, are found in tunnel diodes and in the nonlinear wave interaction which occurs, for example, in nonlinear optics. Remarkable analogies between the instability of the laser and those in hydro-dynamics are elaborated. While these phenomena show pronounced analogies to phase transitions in thermal equilibrium, there are further classes of instabilities and new phases which rather resemble hard excitations known in electrical engineering. Chemical oscillations are particularly important examples. In addition, the first part of this article contains the example of the cooperative behavior of neuron networks and shows the applicability of simple physical concepts, e.g., the Ising model, to the problem of the dynamics of social groups. All these above-mentioned examples demonstrate clearly that rather complex phenomena brought about by the cooperation of many subsystems can be understood and described by a few simple concepts. One of the main concepts is the order parameter; another is the adiabatic elimination of the variables of the subsystems, which is based upon a hierarchy of time constants present in most systems. The second part of this article gives a systematic account of the mathematical tools which allow us to deal with fluctuations. It contains the master equation, the Fokker-Planck equation, the generalized Fokker-Planck equation, and the Langevin equations, and gives several general methods for deriving the stationary and, in certain cases, the nonstationary solutions of master equations and the Fokker-Planck equations. Such general classes comprise those in which detailed balance is present or in which the coupling to the reservoirs is weak. In the quantum mechanical domain, the density matrix and the projection formalism for its reduction are presented. Finally, it is shown how the principle of quantum-classical correspondence allows us to translate quantum statistical problems completely into the classical domain.

The rapid progress in research on chemical lasers has led to increased interest in the development of theoretical models of molecular relaxation processes. In this review, recent applications of various theories of nonreactive collisions between diatomic molecules, from semiclassical to quantal, are surveyed in light of experimental data. The intention is to provide the theoretician with a back-ground of those features of the collision problems that require more accurate treatments, and to provide the experimentalist with a spectrum of models available for handling his data.

The framework of functional integrals in field theory is convenient for presenting a unified view of the perturbation expansion according to the number of loops. We review the calculation of the generating functional for irreducible Green functions and its renormalization properties. Calculations of the effective potential and $Z$-function are carried up to the order of two loops for the self-coupled scalar field. This is applied to compute the coefficients of the Callan-Symanzik equation which describes the short distance behavior of the theory. In conclusion, we present some speculations concerning the positivity of the coupling constant, and its relation to the on -shell two-particle scattering amplitude.

The theory of a free string is first presented classically and quantum mechanically both in a covariant and a nonexplicitly covariant treatment. Then the concepts and techniques obtained from the free string are used to build the operator formalism of dual models. Both the conventional Veneziano model and the Neveu-Schwarz-Ramond model are presented. The self-consistency of these models at the tree and loop levels is investigated, and the interpretation of the results obtained is given in terms of the string picture.

Photo pair productions of electrons, muons, and heavy leptons and bremsstrahlung of electrons and muons are reviewed. Atomic and nuclear form factors necessary for these calculations are discussed. Straggling of electrons in matter and other effects due to finite target thickness are considered. Tables of radiation lengths of all materials and the energy dependence of photon absorption coefficients of many materials are presented. Problems associated with production of particles by photon and electron beams are also discussed.