Showing papers in "Reviews of Modern Physics in 1976"

General Relativity with Spin and Torsion: Foundations and Prospects

Abstract: A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the ${U}_{4}$ theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the ${U}_{4}$ theory arises as a local gauge theory for the Poincar\'e group in space-time. The deviations of the ${U}_{4}$ theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed.

What is "liquid"? Understanding the states of matter

Abstract: Liquids exist in a relatively small part of the enormous range of temperatures and pressures existing in the universe. Nevertheless, they are of vital importance for physics and chemistry, for technology, and for life itself. A century of effort since the pioneering work of van der Waals has led to a fairly complete basic understanding of the static and dynamic physicochemical properties of liquids. Advances in statistical mechanics (the fundamental formulations of Gibbs and Boltzmann, integral equations and perturbation theories, computer simulations), in knowledge of intermolecular forces, and in experimental techniques; have all contributed to this. Thirty years ago the very existence of liquids seemed a little mysterious; today one can make fairly precise predictions of the solid-liquid-gas phase diagram and of the microscopic and macroscopic static and dynamic properties of liquids. This paper is a survey, with particular emphasis on equilibrium properties, of the theory which underlies that basic understanding, which is now at least comparable with our understanding of the physics of solids.

Theory of plasma transport in toroidal confinement systems

Abstract: The dissipation induced by coulomb-collisional scattering provides an irreducible minimum, and thus a useful standard for comparison, for transport processes in a hot, magnetically confined plasma. The kinetic description of this dissipation is provided by an equation of the Fokker-Planck form. As in the standard transport theory for a neutral gas, approximate solution of the Fokker-Planck equation permits the calculation of transport coefficients, which linearly relate the fluxes of particles, energy, and electric charge, to the density and temperature gradients, and to the electric field. The transport relations are useful in studying the confinement properties of present and future experimental devices for research in controlled thermonuclear fusion. The transport theory for a magnetized plasma (in which the Larmor radius is much smaller than gradient scale lengths describing the plasma fluid) departs from the theory for a neutral gas in several fundamental ways. Thus, transport coefficients for a magnetized plasma can be calculated even when the collisional mean free path is much longer than the gradient scale length (as would pertain in thermonuclear regimes). Such transport coefficients are generally nonlocal, being defined in terms of averages over surfaces with macroscopic dimensions. Furthermore, when the mean free path is long, the magnetized-plasma transport coefficients depend crucially upon the magnetic field geometry, the effects of which must be treated at the kinetic level of the Fokker-Planck equation. The results display several novel couplings between collisional dissipation and the electromagnetic field. The present review of magnetized-plasma transport theory is intended to be as widely accessible as possible. Thus the relevant features of magnetic confinement in closed (toroidal) systems, and of charged particles in spatially varying fields, are derived, at least in outline, from first principles. Although consideration is given to "classical" transport in which most field geometric effects are omitted, major emphasis is placed on the "neoclassical" theory which has been developed over the last decade. Neoclassical transport coefficients are specifically relevant to a magnetically confined plasma, rather than to just a magnetized plasma; their unusual features, such as nonlocality and geometry dependence, become particularly important in the high temperature regime of proposed thermonuclear reactors. The area of neoclassical theory which seems most complete---its application to axisymmetric tokamak-type confinement systems---is correspondingly stressed.

Network theory of microscopic and macroscopic behavior of master equation systems

Abstract: A general microscopic and macroscopic theory is developed for systems which are governed by a (linear) master equation. The theory is based on a network representation of the master equation, and the results are obtained mostly by application of some basic theorems of mathematical graph theory. In the microscopic part of the theory, the construction of a steady state solution of the master equation in terms of graph theoretical elements is described (Kirchhoff's theorem), and it is shown that the master equation satisfies a global asymptotic Liapunov stability criterion with respect to this state. The Glansdorff-Prigogine criterion turns out to be the differential version and thus a special case of the global criterion. In the macroscopic part of the theory, a general prescription is given describing macrostates of the systems arbitrarily far from equilibrium in the language of generalized forces and fluxes of nonlinear irreversible thermodynamics. As a particular result, Onsager's reciprocity relations for the phenomenological coefficients are obtained as coinciding with the reciprocity relations of a near-to-equilibrium network.

Mixed-valence compounds

Abstract: In a number of rare-earth compounds, the atomic-like $f$ levels and the wide $s\ensuremath{-}d$ band coexist at the Fermi level. Such compounds are being referred to as mixed-valence compounds. These compounds have a variety of unique thermal and magnetic properties. In this article, we review some salient experimental results in such compounds and discuss a theoretical framework in which they may be understood. Special emphasis is given to the Samarium chalcogenides, on which extensive experimental results are available. The review is not meant to be a comprehensive survey of theoretical and experimental results. Rather it reflects the interests of the author. The hope is that the basic unresolved issues in the theory of mixed-valence compounds are pointed out so as to stimulate further experimental and theoretical work.

The stability of matter

Abstract: A fundamental paradox of classical physics is why matter, which is held together by Coulomb forces, does not collapse. The resolution is given here in three steps. First, the stability of atom is demonstrated, in the framework of nonrelativistic quantum mechanics. Next the Pauli principle, together with some facts about Thomas-Fermi theory, is shown, to account for the stability (i.e., saturation) of bulk matter. Thomas-Fermi theory is developed in some detail because, as is also pointed out, it is the asymptotically correct picture of heavy atoms and molecules (in the Z→∞ limit). Finally, a rigorous version of screening is introduced to account for thermodynamic stability.

Interstellar molecule reactions

Abstract: Considerable progress has been made during the past five years toward a quantitative understanding of the formation and destruction processes for interstellar molecules. Two areas have been most successful---investigations of the formation process for molecular hydrogen on the surfaces of dust grains and studies of reactions involving positive ions in the gas. Laboratory measurements for ion-molecule reaction rates have provided strong support for the latter. Extensive studies at ultraviolet wavelengths from the Copernicus satellite make possible detailed comparisons between predictions and observations for ${\mathrm{H}}_{2}$ and other species in the diffuse interstellar gas. These confirm that a hydrogen atom is converted into an ${\mathrm{H}}_{2}$ molecule at approximately every collision with an interstellar dust grain. In the more dense interstellar gas, observations with radio telescopes provide vast data on complex molecules and have recently identified a number of reactive intermediate species---HC${\mathrm{O}}^{+}$, ${\mathrm{N}}_{2}$${\mathrm{H}}^{+}$, HNC, CCH---whose presence strongly supports the proposed reaction processes. The quite recent development of laboratory methods to measure the microwave frequencies of reactive molecules and molecular ions has been an essential contribution to these identifications. Observed fractionation of (deuterium/hydrogen) and possibly (carbon-13/carbon-12) in certain interstellar molecules provide additional challenges and information for studies of reactions. Although there is semiquantitative agreement between predictions and observed abundances for a wide range of small molecular species, the tests are sufficiently precise in only a few cases to reach reasonably definitive conclusions. To a large degree this is due to poor knowledge of the physical conditions in the gas where the molecules are located. Certain laboratory data are needed---especially, photodissociation cross sections and radiative lifetimes in the ultraviolet, as well as some charge-transfer and reaction rate coefficients under low temperature/density conditions. Information on surface reactions applicable to the astrophysical situation is also desirable. At present the chief problems for interstellar molecule reactions are understanding the formation of larger molecules (larger than triatomic), and the role of surface reactions on dust grains for molecules other than ${\mathrm{H}}_{2}$. A lengthy introduction to the interstellar medium is provided for the nonastronomer. The status of information on the basic surface and gas phase processes is reviewed. Finally, the reaction schemes which seem to be of most importance for the major species of small interstellar molecules are discussed and quantitatively compared with observations when possible. Reactions that produce isotope fractionation are treated in some detail.

Cross sections for ionization of inner-shell electrons by electrons

Abstract: A survey is given of the available cross-section data for ionization of inner-shell electrons by incident electrons in the range of interest for electron-probe microanalysis and for Auger-electron spectroscopy of solid surfaces. Owing to the paucity of data, the bulk of the discussion is limited to $K$-shell and $L$-shell ionization of light atoms. Calculated, semiempirical, and experimental cross-section data have been intercompared graphically and through fits to the linearized Bethe equation for inner-shell ionization (the Fano plot). Almost all of the data could be satisfactorily fitted over the range $4\ensuremath{\lesssim}{U}_{\mathrm{nl}}\ensuremath{\lesssim}30$, where ${U}_{\mathrm{nl}}=\frac{{E}_{0}}{{E}_{\mathrm{nl}}}$, ${E}_{0}$ is the incident electron energy, and ${E}_{\mathrm{nl}}$ the binding energy of electrons in the $\mathrm{nl}$ shell. From these fits, values could be obtained of the "effective" Bethe parameters ${b}_{\mathrm{nl}}$ and ${c}_{\mathrm{nl}}$. Values of the parameter ${b}_{\mathrm{nl}}$ have also been derived from photoabsorption data and were found to be generally consistent with the ionization data if account was taken of the distribution of differential oscillator strength with respect to excitation energy and the consequent expected variation of ${b}_{\mathrm{nl}}$ with incident electron energy. The derived "effective" Bethe parameters should not therefore be used outside the range of each fit.

Eckart vectors, Eckart frames, and polyatomic molecules

Abstract: The fundamental role of Eckart vectors and Eckart frames is demonstrated in the theort of the vibration--rotation Hamiltonian for a polyatomic molecule. (AIP)

The effective interaction between nucleons deduced from nuclear spectra

Abstract: Two-body matrix elements of the residual nucleon-nucleon interaction are extracted from experimental data throughout the periodic table and are used to determine the ranges and well depths of various components of a local interaction. The $T=1$ even and odd components of the central interaction both definitely require two wells with different ranges; a shorter-range attractive well with a longer-range repulsive one. The need for a tensor interaction and a two-body spin-orbit interaction is also explored and their inclusion improves the fit slightly.

On the Origin of Cosmic Rays: Some Problems in High-Energy Astrophysics

Abstract: This paper reviews the present state of the problem of the origin of cosmic rays Primary attention is paid to galactic diffusion models with a halo, and questions of cosmic-ray chemical composition, electron component, and synchrotron galactic radioemission The authors' conclusion is that models with a large halo with a characteristic cosmic-ray age ${T}_{\mathrm{cr}}\ensuremath{\sim}{10}^{8}$ years are confirmed by radio data, and at least do not contradict the information on cosmic-ray chemical composition The paper also deals with the problems of anisotropy, plasma phenomena in cosmic rays, and the prospects of gamma-ray astronomy

The electronic structure of solid surfaces

Abstract: We present a short review of the current status of electronic structure calculations for ordered solid surfaces. For the s--p bonded metal surfaces, emphasis is centered entirely on self-consistent field (SCF) calculations employing a local density approximation for exchange and correlation. For semiconductor surfaces both SCF and empirical tight-binding methods are discussed, while for transition metal surfaces, where no SCF calculations have been carried out, a number of different schemes for solving Schrodinger's equation at a surface are reviewed that use plausible but not self-consistent forms for the surface potential. Finally, calculations for chemisorbed systems are briefly covered, with emphasis on ordered monolayers on semiconductor and transition metal surfaces. (AIP)

On Understanding Spin-Flip Synchrotron Radiation and the Transverse Polarization of Electrons in Storage Rings

Abstract: A mainly didactic discussion is given of the mechanism for the gradual build up of transverse polarization of electrons and positrons in storage rings. The history and basic results are reviewed briefly. Then an intuitive explanation of the polarization in terms of spontaneous emission via a nonrelativistic magnetic dipole transition in a moving inertial frame is presented and criticized. This simple treatment contains a large part of the essential physics, but not all. It is surprisingly successful for electrons and positrons ($g=2$), becomes exact for large $g$ factors of either sign, but fails badly for particles with $g$ factors of the range $0\ensuremath{\lesssim}g\ensuremath{\lesssim}1.5$. The failure occurs because here the spin-magnetic-moment system cannot be treated even approximately in isolation from the orbital motion. A correct semiclassical description of radiation by a spin system is then given, in direct analogy with semiclassical radiation theory for charged particles ignoring spin. The classical equation of motion for a spin in relativistic motion, derived originally by Thomas, is used to obtain an effective Hamiltonian of interaction of a spin with electromagnetic fields. Emission and absorption of radiation is then described by replacing the classical electromagnetic fields with the appropriately normalized photon fields. The resulting formulas are applicable to charged particles of arbitrary $g$ factor. Expressions are given for the differential spectra in angle and in frequency for numbers of photons and for radiated power, as well as the previously known results for the total transition rates. These results seem of physical interest only for $g=2$ but serve useful pedagogic purposes, refuting some of the expectations of the naive explanation. The various differential spectra are treated in detail for $g=2$ and compared with the corresponding spectra for ordinary synchrotron radiation.

Rotational motion in nuclei

Abstract: A review is given of the historical development of the study and interpretation of rotational states in nuclei. The explanation provided by the Bohr-Mottelson model of observed spectra and moments of inertia is emphasized. (AIP)

The origin of galaxies: A review of recent theoretical developments and their confrontation with observation

Abstract: The subject of Galaxy Formation has advanced considerably during the past decade. On the theoretical side two theories in particular have been developed to the point where confrontation with observation will be possible; these are the "Gravitational Instability Picture" and the "Cosmic Turbulence Theory." These theories are discussed at some length here, with particular attention to the question of the origin of cosmic angular momentum and the nature of the initial conditions. There is now a considerable body of data on galaxies; the problem is in deciding which kind of observation is most relevant to understanding the origin of galaxies. Throughout the review an attempt is made both to put the present research in its historical perspective and to stress the possibilities for future advances towards the goal of understanding the origin of cosmic structure.

An interpretation of two-body hadron reactions

Abstract: This is a review and study of the absorption model approach to two-body hadron reactions. The basic view is that reactions proceed by Reggeized particle exchange, modified by (mainly) absorptive initial and final state interactions. Our approach is pedagogical in two respects. First, the conceptual basis of the approach is discussed in detail, and considerable emphasis is put on spin properties and relating amplitudes and observables. We attempt to explain the procedures in sufficient detail that the interested reader can apply them. Limitations and theoretical weaknesses of the approach are discussed. Second, by approaching the whole field of two-body hadron reactions from one viewpoint, we can give unified treatments of some areas, such as polarizations, and of many observables and regularities, and unified explanations of why the data behave as they do from the viewpoint of the model. Because our purpose is primarily pedagogical, we consider representative reactions and amplitudes rather than exhaustively discuss data. At least one example of every major kind of amplitude is discussed, so the extension to additional reactions is often qualitatively possible without further calculation.

Electron-optical properties of atomic fields

Abstract: We present a unified discussion and illustrations of the electron-optical aspects of electron penetration into, or escape from, the inner region of atoms Both processes may focus or defocus the amplitudes of wavefunctions and shift their phases, as manifested in countless phenomena ranging from level shifts to $\ensuremath{\beta}$-decay rates A background survey begins by discussing the Fermi-Segr\`e formula for hyperfine splittings and emphasizes the interplay of hydrogenic and WKB approximations The Phase-Amplitude Method, which determines amplitude ratios and phase shifts directly, proves useful for interpreting the systematics of these parameters along the Periodic System We present results of survey calculations, carried through the Periodic System using Hartree-Slater potential fields, of: (a) $\frac{{\ensuremath{\alpha}}_{l}(0)}{{\ensuremath{\alpha}}_{l}(\ensuremath{\infty})}$, the ratio of the wavefunction's amplitude at $r=0$ to that outside the atom; (b) ${\ensuremath{\delta}}_{l}(E=0)$ and ${\frac{d{\ensuremath{\delta}}_{l}}{\mathrm{dE}}|}_{E=0}$, the phase shift and its energy derivative at $E=0$, and (c) the changes in ${\ensuremath{\delta}}_{l}(E=0)$ and $\frac{{\ensuremath{\alpha}}_{l}(0)}{{\ensuremath{\alpha}}_{l}(\ensuremath{\infty})}$ induced by either a unit perturbation localized near $r=0$ or a relativistic correction Thus we provide a broad mapping of certain fundamental parameters based on rather crude but realistic calculations These results are meant to serve as a bench mark in surveying problems and in checking new results, while standard methods are preferable for working out specific applications accurately

Elementary modes of excitation in the nucleus

Abstract: In the field of nuclear dynamics a central theme has been the struggle to find the proper place for the complementary concepts referring to the independent motion of the individual nucleons and the collective behaviour of the nuccleus as a whole. This development has been a continuing process involving the interplay of ideas and discoveries relating to all different aspects of nuclear phenomena. The multi-dimensionality of this development makes it tempting to go directly to a description of our present understanding and to the problems and perspectives as they appear today. However, an attempt to follow the evolution of some of the principal ideas may be instructive in illustrating the struggle for understanding of many-body systems, which have continued to inspire the development of fundamental new concepts, even in cases where the basic equations of motion are well established. Concepts appropriate for describing the wealth of nuclear phenomena have been derived from a combination of many different approaches, including the exploration of general relations following from considerations of symmetry, the study of model systems, sometimes of a grossly oversimplified nature, and, of course, the clues provided by the experimental discoveries which have again and again given the development entirely new directions.

Colliding heavy-ions - nuclei as dynamical fluids

Abstract: Heavy ion experiments are already enriching nuclear science with a tapestry of new phenomena which require explanation. In response, theoretical nuclear physics is rapidly expanding its insights to encompass these new observations, especially those concerned with the macroscopic aspects. Preliminary theoretical studies already suggest that the dynamical nuclear fluid must sometimes be considered viscous, compressible, and/or rotational, if its microscopic properties are to be encompassed. These and some threads already well placed in the picture will be discussed. Other reasons will be cited to support the expectation that theoretical nulear macroscopists may more and more come to be fluid dynamicists who specialize in those few thousand fluids called nuclei. Three such reasons are (a) the promised richness of their structure as dynamical fluids, (b) their unique prospect, among all the objects of modern physical science, of allowing a complete microscopic, as well as a phenomenological macroscopic, description, and (c) the possible overflow of such nuclear implications into classical fluid theory, from the viewpoint of which the nuclear heavy ion data are a significant novelty.

Diffraction Scattering of Hadrons: The Theoretical Outlook

Abstract: This is a review of the salient features of high energy diffraction scattering of hadrons. It begins with a summary of the experimental situation for those processes which persist at very high energies: the diffractive processess: and defines the underlying exchange mechanism called the Pomeron. A review is made of the key features of the multiperipheral model, since it lies at the beginning of all studies of diffraction. Its virtues and blemishes are exposed. Then we turn to various models which attempt to add unitarity to the multiperipheral model. From the point of view of the direct channel we consider absorptive models, eikonal models, and the multiperipheral bootstrap. The t channel is taken next, and an exposition of the formulation and major results of Reggeon field theory is given. (AIP)