New results are presented for absorption cross sections of nine possible detectors of solar neutrinos (${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$, ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$, ${}_{}{}^{81}{}_{}{}^{}\mathrm{Br}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$, and ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$). Special attention is given to nuclear physics uncertainties. The calculated cross sections are used (with the aid of illustrative solar models and ad hoc assumptions about neutrino propagation) to discuss what can be learned about the sun or weak interactions from each of the nine suggested solar neutrino experiments. An experimental program for neutrino spectroscopy of the solar interior is outlined. It is shown in addition that stellar collapses can be detected to typical distances of several kpc (kiloparsecs) by the proposed ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$, and ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$ solar neutrino detectors (provided that electron neutrinos do not decay or oscillate).

Observations of extensive air showers generated by interactions of cosmic rays high in the atmosphere provide our only source of information about hadronic interactions above 1000 TeV. We review the current status of such experiments, discuss their implications for particle physics, and also note the astrophysical implications of the results. We place considerable emphasis on a description of the experiments and of the calculations required for their interpretation. We are motivated particularly by the relevance of existing air shower data both to the proposed new generation of accelerators, which will explore the region up to ∼1000 TeV, and to a new generation of air shower experiments, which has the potential to observe longitudinal development of individual showers with energies up to ${10}^{21}$ eV.

A review is presented of the various theoretical methods that have thus far been developed for the study of states introduced by impurities and other point defects in semiconductors. The main body of the paper is prefaced with brief sections on the role of impurities and defects in semiconductors and on the general aspects of experimental techniques, as an appropriate setting for the theoretical discourse. Theoretical methods, including those of the effective-mass type, and a wide range of methods appropriate to deep levels are then presented. Applications of these methods are discussed critically. Finally, the relative merits of the various approaches are compared and the prospects for future work are assessed.

The rich nonlinear phenomena that occur in plasmas are reviewed in a systematic way. The foundations of turbulence theory (both weak and strong) and experiments performed in the past decade to verify such theories are presented. The aim is to emphasize those experiments that demonstrate clearly the validity (or failure) of some of the theories. In particular, we discuss experiments that demonstrate the validity and/or limits of weak turbulence theory, strong turbulence theory, parametric instabilities, echoes, trapping of particles in large-amplitude waves, and electrostatic ion acoustic shocks. We present concluding remarks in each section regarding the present status of each of these phenomenon.

Three problems in hypothetical unified theories of electromagnetic, weak, and strong interactions are discussed here. First, the problem of embedding color in any simple gauge group is solved, and a complete classification of theories where the fermion color is restricted to $1^c$, $3^c$, and ${\overline{3}}^c$ of $\mathrm{S}{\mathrm{U}}_3^c$ is given. Generalizations are also indicated. Second, an unbroken ${\mathrm{U}}_1$ generated by electric charge is embedded into each of the above theories and the charge assignments analyzed. Third, the general problem of stabilizing the proton by a suitable atomic mass number $A$ is studied for the same set of theories. It is always possible to define $A$ if the gauge group is not too small. In many of these theories there must be fermions with weird values of $A$: leptons with $A\ne 0$ and quarks with $\mathrm{A}\ne \frac{1}{3}$. Examples are discussed. Some future directions of research are indicated.

The present state of the theory of volume effects in a polymer chain is reviewed. The theory of coils (i.e., chains with predominately repulsive volume interaction of monomers) and the analogy between the excluded volume problem and the theory of second-order phase transitions are briefly described. The theory of globules, formed by attractive interaction of monomers or by external attractive fields, is considered in greater detail. The coil-globule transition under various conditions is analyzed. A theory is constructed for the simplest model of the polymer chain—the model of "interacting beads on a flexible string." The connection of this model with more realistic ones is discussed. This review is based on the approach proposed by I. M. Lifshitz in 1968. While attention is focused on the physical aspects of the problems, some questions concerning biological applications are discussed in the conclusion.

Interaction of atoms with two intense coherent time-delayed short pulsed standing waves produces quantum interference effects in the atomic fluorescence. This type of quantum interference effect applied to Doppler-free two-photon spectroscopy (an extension of the Ramsey method of separated r.f. or microwave fields in atomic beam experiments) offers a number of important improvements in the presently available techniques of ultra-high-resolution spectroscopy of atoms, molecules, and crystals.

With well-defined coherent light pulses of several ${10}^{-12\mathrm{}}$ sec duration we are in a position to investigate a variety of ultrafast vibrational processes in liquids and solids. Several new experimental techniques have been devised to study directly the dynamics of different vibrational modes and molecules in the electronic ground state. A first light pulse excites the vibrational system via stimulated Raman scattering or by resonant infrared absorption. A second interrogating pulse allows one to determine the instantaneous state of the excited system. Using a coherent probing technique one can measure the dephasing time of homogeneously broadened vibrational transitions and a collective beating of multiple isotope levels. In addition, one can investigate inhomogeneously broadened vibrational modes and observe the dephasing time of a small molecular subgroup. Different information is obtained when the coherent anti-Stokes Raman scattering of the probe pulse is measured. The population lifetime of known vibrational modes can be investigated and evidence for inter- and intra-molecular interactions is obtained. In a third probing technique, the vibrationally excited jolecules are promoted to the first electronic state by a second pulse and the fluorescence is measured. In this way it is possible to see the very rapid change of population of the primary excited vibrational mode. The article gives a detailed theoretical treatment of different excitation and probing processes. Several experimental techniques successfully applied in the authors investigations are outlined and a variety of results is presented and discussed. New information, not available from other experimental methods, is obtained.

A current algebra formulation of the radiative corrections in gauge theories, with special applications to the analysis of the universality of the weak interactions, is developed in the framework of quantum chromodynamics. For definiteness, we work in the SU(2)×U(1) model with four quark flavors, but the methods are quite general and can be applied to other theories. The explicit cancellation of ultraviolet divergences for arbitrary semileptonic processes is achieved relying solely on the Ward identities and general considerations, both in the $W$ and Higgs sectors. The finite parts of order $G_F\alpha$ are then evaluated in the case of the superallowed Fermi transitions, including small effects proportional to $g_s^{-2\mathrm{}}\left({\kappa }^2\right)$, which are induced by the strong interactions in the asymptotic domain. We consider here both the simplest version of the Weinberg-Salam model in which the Higgs scalars transform as a single isospinor, as well as the case of general symmetry breaking. Except for the small effects proportional to $g_s^{-2\mathrm{}}\left({\kappa }^2\right)$, the results are identical to the answers previously found on the basis of heuristic arguments. The phenomenological verification of Cabibbo universality on the basis of these corrections and the superallowed Fermi transitions has been discussed before and found to be in very good agreement with present experimental evidence. The analogous calculation for the transition rate of pion $\beta$ decay is given. Theoretical alternatives to quantum chromodynamics as a framework for the evaluation of the radiative corrections are briefly discussed. The appendixes contain a generalization of an important result in the theory of radiative corrections due to L. S. Brown, G. Preparata, and W. I. Weisberger, an analysis of the hadronic contributions to the $W$ and $\phi$ propagators, mathematical methods for evaluating the $g_s^{-2\mathrm{}}\left({\kappa }^2\right)$ corrections, and discussions of quark mass renormalization and the absence of operator "seagulls" in the hadronic correlation functions. Some of the methods discussed in this paper can also be applied to the study of radiative corrections of order $G_F\alpha$ to other processes affected by the strong interactions.

We use functional techniques to give a simple derivation of Wilson's Feynman rules for strongly coupled gauge theory formulated on a lattice. Coupling sources to the various degrees of freedom, we obtain a compact formal expression for the Green's functions of the theory. The theory is rewritten in terms of creation and annihilation operators for quarks and "string bits" in a new space called "string space." This formulation emphasizes the close analogy with a lattice version of the string model. We also give a systematic diagrammatic procedure to evaluate all group integrations arising in the strong coupling expansion.

A review of several new or very active areas of research in the field of intermediate-and high-energy proton-nucleus research is presented. Theoretical advances used in treating the data are described. The areas covered include: $p$—${}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering and polarization; elastic and inelastic scattering, $A\ge 4$; the neutron pickup reaction; and particle production and elastic scattering near 180°.

The current state of nuclear matter calculations is described with special reference to the present disagreement between the variational and Brueckner-Bethe methods. The system is assumed to consist of point nucleons with a nonrelativistic Hamiltonian containing the kinetic energy and two-body potentials. The physical ideas of the variational method, especially of its hypernetted-chain version, and of the Brueckner—Bethe method are outlined. Practical ways of testing the validity of these methods are discussed and are illustrated by numerical results taken from the literature. It is found for central forces that the hypernetted-chain variational method, if properly used, gives reliable upper bounds to the ground-state energy. Lowest-order Brueckner-Bethe results lie well above these upper bounds, and it is both important and feasible to check whether higher-order corrections will bring the Brueckner-Bethe results into agreement with the variational ones. For realistic nuclear potentials, which have tensor forces, spin-orbit forces, etc., the situation is much less clear. An adequate calculation has not yet been done by either the variational or Brueckner-Bethe method. For the Reid potential, with the presently available numerical results, the variational calculation predicts a much higher saturation density than the Brueckner-Bethe calculation. Feasible calculations that will help to resolve this discrepancy are discussed.

The fundamental physical ideas underlying the dynamical behavior of globular star clusters are reviewed. The results of detailed numerical experiments involving large $N$-body stellar systems are summarized and compared with observations. Intuitive arguments and crude, analytic derivations of many of the major results are provided. The topics treated represent, in effect, a chronological history of the dynamical life of a globular cluster—from its birth in the early universe through core contraction to a compact state, to ultimate dissolution in the galactic tidal field. The approach is nonrigorous and pedagogical rather than mathematical and the paper is intended as an introduction to recent developments in stellar dynamical theory.

High-energy photon interactions are discussed in terms of the hadronic structure of the photon, which is expressed by means of a formulation which is akin to, but somewhat more general than, vector-meson-dominance or specific generalized vector-dominance models. Experiments which demonstrate and yield information about this hadronic structure are discussed critically, and the resulting information is carefully evaluated. Special attention is paid to diffractive processes such as the photoproduction of vector mesons and to photon shadowing effects on nuclei. Relationships to other views of photon interactions, such as the parton model and the space-time description, are also discussed; these views are seen to complement the hadronic structure picture rather than to be in conflict. The general overview is that there is ample evidence which shows that the photon's hadronic structure plays a significant role in its interactions. What further work would most significantly enhance the understanding of the hadronic structure of the photon is also pointed out.

It is rather paradoxical that, although entropy is one of the most important quantities in physics, its main properties are rarely listed in the usual textbooks on statistical mechanics. In this paper we try to fill this gap by discussing these properties, as, for instance, invariance, additivity, concavity, subadditivity, strong subadditivity, continuity, etc., in detail, with reference to their implications in statistical mechanics. In addition, we consider related concepts such as relative entropy, skew entropy, dynamical entropy, etc. Taking into account that statistical mechanics deals with large, essentially infinite systems, we finally will get a glimpse of systems with infinitely many degrees of freedom.

This paper surveys the characteristics of threshold switching systems and examines the evidence for threshold switching as an electronic process. A semiquantitative model is proposed for the nature of the ON—state. The OFF—ON transition is also discussed in the light of recent experimentation, as are the principal aspects of the problem still in need of furthur clarification.

Utilization of nuclear fuels and management of nuclear wastes have become major topics of public discussion. Under the auspices of the American Physical Society this study was undertaken as an independent evaluation of technical issues in the use of fissionable materials in nuclear fuel cycles, together with their principal economic, environmental, health and safety implications. Reprocessing and recycling in light water reactors were examined, along with technical measures proposed as possible safeguards; advanced reactor fuel cycles were also studied for their resource and safeguards implications. Much of the work of the group centered on the principal alternatives for disposal of radioactive wastes and control of effluents. The group examined the research and development programs sponsored by government agencies along with associated relationships among agencies and between government and private industry. Available information was also considered on nuclear fuel resources, and on important economic and environmental aspects of the various fuel cycles in order to strive for a balanced comparative study. The report presents many conclusions on various aspects of the nuclear fuel cycles and also provides recommendations concerning present utilization and future improvement of fuel cycle technology.