Showing papers in "Reviews of Modern Physics in 1969"

Shapes of Inhomogeneously Broadened Resonance Lines in Solids

Abstract: Inhomogeneous broadening has been observed in resonance lines in solids over the wide range of energies spanned by nuclear magnetic resonance, electron spin resonance, optical, and M\"ossbauer methods. The broadening arises from random strains, electric fields, and other perturbations from the defects in the lattice containing the centre whose transitions are studied. This paper reviews the calculation of the shapes of such resonance lines. The most important method used is the so-called statistical method. This method determines the line shape as a function of the distribution of the defects with respect to the centres studied, the density of the defects, and the perturbation fields of the individual defects. Emphasis is laid on the physical assumptions and approximations in this method and on its relation to other approaches. The theory is applied to a variety of broadening mechanisms, both in the widely used continuum approximation for the lattice containing the defects and in the more realistic discrete-lattice model. Two classes of experimental work are reviewed. The first deals with the ways in which resonance lines are recognised as being inhomogeneously broadened. These methods show that a wide range of phenomena can be used to check the theory of the line shapes. The second discussion of the experimental work compares theory and experiment for each of the various broadening mechanisms. These mechanisms include broadening by the strains from dislocations and point defects, by the electric fields and field gradients from charged defects, and by unresolved hyperfine structure. In each case theory and experiment are compared in detail for the system for which the most complete data are available. The conclusion is that the statistical method provides a satisfactory approach in all cases for which there are adequate data.

Radiative Corrections to Elastic and Inelastic ep and up Scattering

Abstract: We have investigated and improved the reliability of many formulas used in the radiative corrections to elastic and inelastic electron scatterings when only the scattered electrons are detected. The radiative corrections to muon scattering are also investigated. A practical and reliable recipe for unfolding the entire inelastic spectra, including effects due to virtual photons, internal and external bremsstrahlungs, is given. Examples of actually unfolding the inelastic electron spectra are given using the experimental data obtained by the electron-scattering group at the Stanford Linear Accelerator Center.

Survey of Vibrational Relaxation Data for Processes Important in the C O 2 - N 2 Laser System

Abstract: Vibrational relaxation data are surveyed in order to provide the rates of vibrational energy transfer for processes important in the C${\mathrm{O}}_{2}$-${\mathrm{N}}_{2}$ laser A kinetic model is assumed for the vibrational energy transfer into and within the various vibrational modes of the molecules that make up a C${\mathrm{O}}_{2}$-${\mathrm{N}}_{2}$ laser, including the species ${\mathrm{H}}_{2}$O, ${\mathrm{O}}_{2}$, He, and ${\mathrm{H}}_{2}$ Experimental data are assembled and interpreted for the rate constants and the probabilities per collision for the various kinetic processes of the assumed mechanism as a function of temperature For certain processes, the experimental data are reinterpreted in terms of more recent knowledge of vibrational energy transfer The data are compared with theoretical calculations and various anomalies in those comparisons are discussed The significance of the various vibrational energy transfer processes for understanding the operation of the C${\mathrm{O}}_{2}$-${\mathrm{N}}_{2}$ laser are contrasted with the state of knowledge of the rate information

Effective lagrangians and field algebras with chiral symmetry.

Abstract: This paper reviews recent developments of effective Lagrangians and field algebras as means of treating chiral symmetry and partially conserved axial current (PCAC) for the study of elementary particle physics. The techniques employed are developed in considerable detail. As examples, we concentrate primarily on spin 0 and 1, linear and nonlinear realizations of $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ and $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ and some of the significant predictions of the theory are derived. The paper contains an extensive discussion of an effective Lagrangian with nonets of real scalar, pseudoscalar, vector, and axial-vector mesons that illustrate the problems of broken $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$.

Review of particle properties

Abstract: This review of the properties of leptons, mesons, and baryons is an updating of Review of Particle Properties, Particle Data Group [Phys. Letters 50B, No. 1 (1974), and Supplement, Rev. Mod. Phys. 47 (1975) 535]. Data are evaluated, listed, averaged, and summarized in tables. Numerous tables, figures, and formulae of interest to particle physicists are also included. A data booklet is available.

Set of Nuclear-Mass Relations and a Resultant Mass Table

Abstract: Two new independent mass relations are derived and are shown to be consistent with several existing nuclear models. The most general functional dependence on proton number, neutron number, and mass number (or isospin value) of masses which satisfy these relations exactly is discussed, and a procedure for determining the values of these functions which give a best least-squares fit to the body of known masses is developed. The functions which give the best over-all fit are listed together with the resulting theoretical mass table which shows the discrepancies to known masses and the theoretical values for proton, neutron, and alpha-particle decay energies.

Review of Some Experimental and Analytical Equations of State

Abstract: Four different polynomial equations and seven nonlinear equations, all applicable to both solids and liquids, are compared theoretically and statistically. Detailed curve-fitting results are presented for recent water and Hg isothermal data. Uncommonly used methods of statistical analysis and comparison, including generalized least squares, are described, justified compared to usual methods, and applied. In general, certain polynomial equations are found to yield significantly better fits of many different water and Hg data sets than any nonlinear equation considered. The Tait and Murnaghan equations, in particular, lead to strong systematic behavior of all residuals calculated herein with them, showing that they are inadequate models for all the data considered. Even a nonlinear equation derived from a second-order expansion of the bulk modulus $K$ in powers of the pressure, which is shown to include several frequently used equations as special cases, is inferior to selected polynomial equations but is still the best equation examined when appreciable extrapolation is necessary. The method of volume normalization almost always used heretofore in statistical fitting of equations of state to $P\ensuremath{-}V$ data is shown to be inadequate and two alternative approaches are proposed and employed herein. Critical comparison of previous analyses of water and Hg data is made with the results of the present, more refined approach. The likelihood of important systematic errors in $P\ensuremath{-}V$ data, particularly data derived from ultrasonic measurements on liquids under pressure, is pointed out and high probability of their occurrence in some of the data analyzed is demonstrated. Even the combination of the best data apparently available and the use of better statistical-analysis methods than have been employed before does not yet allow one to obtain highly accurate values of the ${{K}_{0}}^{\ensuremath{'}}$ parameter of water or Hg, and only an order-of-magnitude estimate of the ${{K}_{0}}^{\ensuremath{'}\ensuremath{'}}$ parameter seems currently possible. Nevertheless, it appears that near room temperature ${{K}_{0}}^{\ensuremath{'}\ensuremath{'}}$ is positive for water and probably negative for Hg and that its appreciable magnitude for both materials renders a second-order expansion of $K$ inadequate.

Pair production by photons

Abstract: This paper reviews, analyzes, and integrates the various quantitative results that have been obtained for the process of pair production by photons. Included in this summary is a detailed review of total and differential cross sections for pair production in an atomic and in an electron field, with a critical evaluation of the conditions of validity and the accuracy of the results. In addition, a summary is given of the important kinematic relations, theoretical considerations, and the polarization effects that occur in pair production. The paper does not include a treatment of radiative corrections to pair production, thick-target pair production, or pair production by electrons in the field of a nucleus (trident production). Otherwise, the review is intended to include results on pair production available up to January 1969.

Scattering of Polarized Leptons at High Energy

Abstract: A unified treatment is given of the high-energy elastic and inelastic electromagnetic scattering of electrons and muons by hadrons in terms of the polarization density matrix of the virtual photon exchanged. It is shown that when the leptons are longitudinally polarized, the virtual photon is in a pure polarization state which is a coherent superposition of an elliptically polarized transverse state and a longitudinal state. Experiments utilizing these features are suggested and the formulas for the cross sections are obtained. The limit in which the virtual photon is almost real is investigated carefully. Finally, it is shown that the formalism is immediately applicable to neutrino scattering.

Effective Potential Model for Calculating Nuclear Corrections to the Energy Levels of Hydrogen

Abstract: The present work is an attempt to re-evaluate the nuclear corrections to the energy levels of hydrogen by using an effective potential approach. The basic idea is to infer from electron-proton scattering a potential which may then be applied to the bound-state problem. In lowest order, the potential is chosen from the first-order Feynman diagram for the scattering. With this choice the Breit equation is obtained. It is then solved in an approximate way, in the non-relativistic limit of the proton, to obtain wave functions which are accurate enough for use in evaluating the effects of perturbations of the potential. The reduced mass corrections to the fine structure and the hyperfine structure levels are readily found. The effect on the hyperfine splitting of the distribution of the proton charge and magnetic moment is obtained by correcting the lowest-order potential to include the proton form factors. A further modification is needed in evaluating additional recoil corrections, of relative order $\frac{\ensuremath{\alpha}m}{M}$, to the fs and the hfs. This additional term accounts for the failure of the iteration of the lowest-order potential to reproduce the scattering obtained from the second-order Feynman diagrams. The $\frac{{\ensuremath{\alpha}}^{2}m}{M}$ contribution to the state-dependent mass corrections to the hfs is also analyzed within the context of this approach. All the corrections found are in complete agreement with previous results obtained by the Bethe-Salpeter (BS) equation, but the present method has the virtue of conceptual simplicity.

Systematic Survey of the α − α Interaction

Abstract: A systematic survey of the subject of the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ interaction is made. The early observations of $\ensuremath{\alpha}$ emission and resulting theoretical descriptions, especially the $\ensuremath{\alpha}$-particle model of nuclei, are described, as are more recent $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ scattering experiments. The latter were designed to obtain information about the nature of the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ interaction and about the energy levels of $^{8}\mathrm{Be}$ by studying the resonance behavior of the phase shifts. The phenomenological approach, i.e., the attempt to construct the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ potential which reproduces the experimental phase shifts, is described as are detailed theoretical constructions of the repulsive inner part and attactive outer part of the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ interaction. Studies of how the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ interaction provides better understanding of the structure of $\ensuremath{\alpha}$-clustered nuclei and also of the fundamental forces between the constituents of these nuclei are discussed. Suggestions for the direction of further efforts are made.

Electron Spin Polarization by Low-Energy Scattering from Unpolarized Targets

Abstract: The status of theory and experiment of electron polarization resulting from spin-orbit interaction in low-energy scattering from unpolarized targets is reviewed. Polarization effects in scattering from free atoms, molecules, and solid targets at energies between a few electron volts and a few thousand electron volts are discussed. Apart from a survey of the problems which have been solved, a perspective is given of the work which would be interesting to pursue in this rapidly developing field of research.

Low-Energy Electron-Diffraction Dispersion Surfaces and Band Structure in Three-Dimensional Mixed Laue and Bragg Reflections

Abstract: Although the theory of the propagation of electron waves in periodic solids and the theory of the elastic diffraction of electron waves by periodic solids have developed independently into band theory and dynamical electron-diffraction theory, respectively, they are in fact formally identical. The electron wave functions which can exist in the crystal are determined by a seven-dimensional hypersurface in energy-complex K space which defines the totality of solutions to the wave equation in the infinite crystal. In the diffraction problem, the introduction of the crystal surface together with the magnitude and direction of the external electron wave vector selects the particular set of eigenfunctions which are excited during a given experiment and which correspond to the allowed electron states in the crystal. This set constitutes the wave field in the self-consistent multiple-scattering approach. It is demonstrated that the energy band diagram of band theory and the constant energy dispersion surface of dynamical theory are in fact sections of the same hypersurface. The complex nature of the dispersion surface leads to the excitation of evanescent waves both in the crystal and in the vacuum. The diffraction boundary conditions, notably conservation of total energy and of momentum parallel to the crystal surface, can easily be introduced, geometrically, by means of a constraint surface which contains the crystal normal. In a given experiment the excited wave functions are determined by the intersection of the hypersurface with the appropriate constraint surface. It is shown that the most useful constraint surfaces are those at constant energy and furthermore that the dispersion hypersurface is an ameniable method for the discussion of low-energy electron-diffraction (LEED) cases of high order and high symmetry, several of which are outlined in detail. The variation of the reflected intensities observed in electron-diffraction experiments is discussed in terms of the changes in the allowed electron wave functions as calculated by three-dimensional band-structure and/or dynamical diffraction theory. In particular, we predict zeros in the reflected Bragg intensities for certain special geometries in the case of two simultaneous reflections (mixed Bragg-Laue case).

Nonforward Scattering of Hadrons and High-Energy Phenomenology

Abstract: This review is divided into three parts. First, we survey the general features of nonforward scattering. We comment on two large-angle scattering models (the statistical model and the proposal for explaining the "breaks" in the differential cross section in terms of production cross sections) and discuss the axiomatic results on lower bounds and the asymptotic angular dependence. Second, we review the motivation and the general formalism of the multiple-scattering model and the qualitative success of the model\char22{}in particular, its application to the nonforward scattering. Third, we discuss the impact of the multiple-scattering model on high-energy phenomenology. Here, we emphasize that, in addition to providing a concrete model for large $|t|$ scattering, the multiple-scattering model contains virtues from both the optical model and the Regge-pole model. Similar to the absorption model, it helps to explain problems encountered in a pure Regge-pole model. On the other hand, it preserves the past success of the Regge-pole model and opens new possibilities for it.

Whither Axiomatic Field Theory

Abstract: We survey some recent progress in constructing models of local, relativistic quantum mechanics. These field-theory models have nontrivial scattering.