Allowed beta decay is studied using the elementary particle approach including all second forbidden terms. Model independent forms are given for various spectrum and correlation effects with parent polarization and/or orientation and for delayed particle emission correlations. The restrictions due to various symmetry assumptions are analyzed, as well as the problem of Coulomb corrections. We comment on past and future experiments in this realm.

The experimental evidence supporting the double-humped character of the fission barrier in actinide nuclei is reviewed and compared to theoretical predictions. The discussion covers the existence and half-life systematics of spontaneously fissioning isomers, shape-isomeric gamma decay, rotational transitions and the moment of inertia of isomers, fragment angular distributions in isomeric fission, intermediate structure in fission cross sections, and finally the systematics of barrier heights as deduced from fission probability measurements. The implications of a possible octupole deformation at the second barrier for fragment mass distributions are also discussed, including the size of the mass asymmetry and recent experiments on the competition between symmetric and asymmetric fission as a function of excitation energy.

We discuss the types of thermonuclear reactions that are of importance to stellar evolution and nucleosynthesis, with particular attention to the explosive ejection of shells of He, C, O, and Si. We present tables of the reactions important in the various burning phases, including the reason for their importance and an estimate of the value of a carefully measured rate. This format is chosen for dual purpose: (1) to clarify the nuclear needs by evaluating the importance of specific reactions within the astronomical settings and (2) by assigning a value scale for cross-section measurements.

A unified description of systems with a condensed phase in terms of hydrodynamic equations of motion is given. These equations are of two kinds: First those equations obeyed by the thermal excitations (the "first fluid") typically are local conservation equations of mass, energy and momentum. Second the equation obeyed by the condensed phase (the "second fluid") is an equation of motion related to the order parameter of the broken symmetry. These equations are established on phenomenological grounds making use of irreversible thermodynamics. The eigenmodes of the linearized form of these equations, typically first and second sound, are discussed in particular with respect to their manifestation in inelastic light and neutron scattering. The systems considered are homogenous superfluids, superconductors, dielectric crystals and magnetic systems. Except for superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ the critical behavior at the phase transition to the ordered state is not systematically discussed.

This review discusses the physical properties of nematic, cholesteric, and smectic liquid crystals. Molecular theories of the liquid crystal phases are discussed and the molecular field theories of the phase transitions between the various liquid crystal phases are presented. The elastic theory and hydrodynamics of liquid crystals is developed. A wide variety of phenomena in liquid crystals, including elastic distortions, disclinations, flow properties, fluctuations, light scattering, wave propagation, nuclear magnetic resonance, effects of magnetic and electric fields, electrohydrodynamics, and optical properties, is discussed.

The renormalization group approach to the theory of critical behavior is reviewed at an introductory level with emphasis on magnetic systems. Among recent results reported are the dependence of critical exponents above $T_c$ on dimensionality $d=4-\epsilon$; on the symmetry index or number of spin components, $n$; on the range and anisotropy of exchange couplings; and on dipolar interactions and lattice anisotropies, in ferro- and antiferromagnets. Calculations of the scaling functions for the equation of state and critical scattering are summarized.

The London-Ginzburg-Landau concept of superconductivity as a macroscopic quantum state is reviewed. Experimental measurements are then discussed of resistance below $T_c$, and of enhanced diamagnetism above $T_c$, both caused by thermodynamic fluctuations away from the Ginzburg-Landau state of lowest free energy. Next the limitations on superconductivity at nonzero frequencies are reviewed: normal electron dissipation $\propto {\omega }^2$, and strong absorption above the energy gap frequency. Sum rule arguments relate the superfluid response at low frequencies to the gap; effects of strong electron-phonon coupling are also found. Finally, results of recent work on the resistive state of superconducting filaments above the critical current are summarized.

Chiral symmetries are discussed in considerable detail, and their importance and consequences for the study of elementary particle physics are reviewed. For the study of broken symmetries we concentrate mainly on meson-nucleon sigma terms, $\pi \pi$ scattering, and $K_{l3\mathrm{}}$ decays. In addition to giving a critical and detailed review of most of the "experimental" estimates for pion-nucleon and kaon-nucleon sigma terms done so far, we also outline the most common chiral symmetry-breaking schemes at present, such as $(3,\overline{3})+(\overline{3},3)$, $(6,\overline{6})+(\overline{6},6)$, (8,8) and (1, 8) + (8, 1) representations of SU(3) × SU(3) and possible mixtures of them, and discuss and compare their predictions with experiment. Nonlinear effective Lagrangians are briefly discussed, and the connection between broken scale invariance and chiral symmetry breaking is outlined, with emphasis on our present knowledge of meson-nucleon sigma terms.

We review the methods which have been developed over the past several years to determine the behavior of solids whose properties vary randomly at the microscopic level, with principal attention to systems having composition variation on a well-defined structure (random "alloys"). We begin with a survey of the various elementary excitations and put the dynamics of electrons, phonons, magnons, and excitons into one common descriptive Hamiltonian; we then review the use of double-time thermodynamic Green's functions to determine the experimental properties of systems. Next we discuss these aspects of the problem which derive from the statistical specification of the microscopic parameters; we examine what information can and cannot be obtained from averaged Green's functions. The central portion of the review concerns methods for calculating the averaged Green's function to successively better approximation, including various self-consistent methods, and higher-order cluster effects. The last part of the review presents a comparison of theory with the experimental results of a variety of properties—optical, electronic, magnetic, and neutron scattering. An epilogue calls attention to the similarity between these problems and those of other fields where random material heterogeneity has played an essential role.

Electrons at the surface of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are potentially valuable probes of both static and dynamic properties of the interface. Two species of surface state are discussed. One of these is localized just above the interface, weakly bound by the image force. The existence of this state has been confirmed by direct spectroscopic observation. Measurements of parallel field mobility and life-time on the surface are discussed and compared with predictions. The other surface state is an electron bubble held below the interface with an applied field. A resonance experiment in this geometry determines an effective mass different from the bulk liquid value. Studies of field emission from the bubbles lead to an evaluation of other bubble properties.

Systematic neutron scattering studies on phase transitions have been carried out at Brookhaven in recent years. A consistent picture has now emerged from these investigations of "how" certain structural phase transitions take place. These are caused by a lattice dynamical instability; namely, the frequency of a particular lattice vibrational mode tends toward zero as the transition temperature is approached from above. At the transition these displacements are incorporated into the new atomic positions of the low-temperature phase. Modes of this type have become known as "soft" modes. This concept of soft modes was first emphasized by Cochran in 1960 for the special case of the BaTi${\mathrm{O}}_3$-type ferroelectrics. We have demonstrated that the generalized concept applies to many other types of structural phase transitions such as SrTi${\mathrm{O}}_3$(110°K), ${\mathrm{Nb}}_3$Sn, Si${\mathrm{O}}_2$ and N${\mathrm{D}}_4$Br. The neutron scattering technique has been particularly useful in obtaining detailed knowledge of dynamical properties near the phase transition. This is due to a fortunate combination of the wavelength of typical thermal neutrons (2.5Å) and their energy (13 meV). The phase transition studies, in turn, have contributed to considerable improvement of the inelastic neutron scattering technique, which may offer many future applications.

The proceedings of the International Conference on Magnetic Structures in Superconductors held at Argonne National Laboratory, Argonne, Illinois on 5-8 September 1973 are reviewed and summarized. Recent experimental and theoretical developments in the field of magnetic flux structures in both type-I and type-II superconductors are described, current research directions are discussed, and expected future developments are outlined.

This paper reviews the success of the quark model in describing deep-inelastic lepton scattering. The neutral current predictions of a variety of unified gauge models are given and it is shown how experiment may distinguish among them. All the models involve new hadronic quantum numbers (charm or fancy). Their effects at high energy are explored.

Solutions of the inverse problem of scattering are reviewed. Quantum mechanical, semiclassical, and classical methods in the high-energy limit are discussed for both the step from the cross section to the phase shifts or the deflection function and the step from these functions to the potential. The emphasis is on the practical applicability of such procedures in molecular physics rather than on the question of existence and uniqueness. The procedures which had been applied to the determination of spherically symmetric, interatomic potentials by the inversion of actual scattering data are critically surveyed and illustrated by approprite examples.

The use of intense laser light to bring about thermonuclear reactions in a plasma is of considerable current interest. We present detailed analytical and computational studies which show the feasibility of laser-driven fusion. The required laser technology and the presently anticipated practical difficulties are discussed in outline.

The problem of quantum collisions involving several particle systems is reviewed within the framework of multiple scattering theory. The basic apparatus of collision theory for nonrelativistic potential problems is first developed, and the Born and eikonal series are introduced. A general analysis is then given of multiple scattering expansions for several particle problems. We discuss in particular the Born developments, the Faddeev-Watson expansions, the Glauber method, and various multiple scattering approaches to the determination of the optical potential. Applications to atomic collision problems and to high-energy hadron-deuteron scattering are discussed at length.

A review is presented of progress since mid-1972 in the development of gauge theories of the weak, electromagnetic, and strong interactions. A brief introduction to the history and the fundamentals of the subject is also provided.