Showing papers in "Reports on Progress in Physics in 1972"

Semiclassical approximations in wave mechanics

Abstract: We review various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions). To start with we treat one-dimensional problems and discuss the derivation of WKB connection formulae (and their reversibility), reflection coefficients, phase shifts, bound state criteria and resonance formulae, employing first the complex method in which the classical turning points are avoided, and secondly the method of comparison equations with the aid of which uniform approximations are derived, which are valid right through the turningpoint regions. The special problems associated with radial equations are also considered. Next we examine semiclassical potential scattering, both for its own sake and also as an example of the three-stage approximation method which must generally be employed when dealing with eigenfunction expansions under semiclassical conditions, when they converge very slowly. Finally, we discuss the derivation of semiclassical expressions for Green functions and energy level densities in very general cases, employing Feynman's path-integral technique and emphasizing the limitations of the results obtained. Throughout the article we stress the fact that all the expressions obtained involve quantities characterizing the families of orbits in the corresponding purely classical problems, while the analytic forms of the quantal expressions depend on the topological properties of these families. This review was completed in February 1972.

Polarization transfer and spin correlation experiments in nuclear physics.

Abstract: This review is concerned with nuclear reactions and nuclear elastic scattering in which the spin polarization of more than one of the reactants is measured. If both of the particles whose polarization is known are in the initial channel, or both in the final channel, we refer to a `spin correlation' experiment; if one polarized particle is in the initial and one is in the final channel, we refer to a `polarization transfer' experiment. We consider mainly particles with spin ? and with spin 1; to a minor extent higher spins are included. The state of the art with respect to the production of polarized beams and targets and with respect to polarization analysing devices is briefly reviewed. A considerable amount of space is devoted to the definitions of cartesian polarization transfer and spin correlation coefficients which are suitable for the description of reactions involving spin ? and spin 1 particles. These parameters are generalizations of the triple scattering and spin correlation parameters introduced by Wolfenstein for a description of nucleon-nucleon scattering. Finally, the experiments of these types so far performed are reviewed. Reactions involving photons are excluded, and the nucleon-nucleon problem is only briefly mentioned. This review was completed in March 1972.

The dynamics of disordered lattices

Abstract: This article reviews the theory of atomic vibrations in disordered solids, ranging from almost perfect crystal lattices to glassy materials where geometrical regularity is entirely absent. As a preliminary, the basic notations and equations of conventional lattice dynamics are briefly outlined; the essential equivalence of quantal and classical formulations within the harmonic approximation is indicated, as in the considerable simplification which occurs for periodic systems. The classical time-independent Green's function formalism is then introduced and applied to lattices with isolated defects. Extension of the Green's function method to more grossly disordered systems is described, together with other relevant analytical techniques, such as the phase theory and the Anderson approach. Next, the time-independent numerical method, based on the negative eigenvalue theorem, is introduced and applied to two-component mass disordered lattices; here the numerical calculations are related, where possible, to existing analytical results. The most recent applications of the negative eigenvalue approach concern glasses, polymers and orientationally disordered crystals, and the calculated properties of these systems are reviewed in some detail. Finally, attention is drawn to several areas of the vibrational problem which seem ripe for further detailed study.

The theory of charge exchange

Abstract: This report describes the development of the theory of charge exchange in collisions of ions with atoms or ions, paying particular attention to the work of the last decade. The successful approximations based on the impact parameter and classical path methods, suitable for low energy collisions, are treated in detail. For high energies, approximations that are completely satisfactory from a theoretical viewpoint do not exist, but both the Born approximation and the classical models of Gryzinski and Thomas are found empirically to reproduce many features of the observed cross sections and a discussion is given of the successes and limitations of these and related models. This review was completed in March 1972.

Applications of algebraic manipulation programs in physics

Abstract: This paper describes the application to three areas of physics of computer programs that carry out formal algebraic manipulation. The application areas discussed are celestial mechanics, general relativity and quantum electrodynamics. The paper describes typical problems from each of these disciplines which can be solved using algebraic manipulative systems and presents sample programs for the solution of these problems using several algebra systems. For each discipline a review of published work acknowledging the use of algebra programs is presented and the most advanced applications are discussed in detail. In particular the Lie transform, Petrov classification and Kahane's simplification procedure are reviewed from the standpoint of algebra programs. A number of simple examples are used to introduce the reader to the capabilities of an algebra program and a brief review of the technical problems of algebraic manipulation is given. Further applications of such systems to mathematics, chemistry and engineering are briefly mentioned in the text and relevant work is referenced in the bibliography but the main emphasis is placed on applications in theoretical physics. However, the simple examples indicate, and the applications in the physical sciences confirm, that algebra systems are capable of exploitation over a much wider area than is covered in the present review. This review was completed in December 1971.

Earth's field magnetometry

Abstract: In the last decade a vast expansion has been experienced in the use of observations and measurements of the Earth's magnetic field. The type and quality of the observations required by newly developed geomagnetic research interests, in themselves partly stimulated by the possibilities offered by new types of magnetometers, greatly increased the amount of effort which has been applied to further developing the instruments and devising new ones. The demand arose from two main sources. The first was the evolution, with the advent of satellite experimentation, of magnetospheric physics, and the second derived from the eventual acceptance of reversed magnetization in rocks as being due to reversal of the Earth's field itself. This paved the way to the chronological interpretation of alternating positive and negative anomalies, and stimulated vigorous research into ocean floor spreading and crustal movements. It is not possible in a single review article to describe all the variants of sensors and detection systems which have been developed to meet the very wide range of observations currently required, for example for survey by land, sea and air, measurement of minute magnetization of rock samples in paleo and archeo-magnetism and for rocket, satellite and space probe applications. Recent excellent reviews of the objectives of including magnetometers in spacecraft experimentation, of the instruments used and of the special techniques which have been developed to overcome the operational and interpretational difficulties of that branch of geomagnetism are given by Heppner (1967) and Ness (1970). The subject of aeromagnetic surveying is discussed in depth by Hood and Ward (1969). This review is, therefore, limited to the generalities of the devices currently in use for ground-based magnetic measurements. The operating principles of each detection system are explained in simple physical terms. Any important developments or extensions of basic technique which are of particular significance are discussed, together with their essential characteristics and limitations. Details of electronic detection systems are not described except where appropriate reference cannot be included. The instruments described are in the following main classifications: magnetometers using nuclear and atomic resonance, saturable cores, suspended magnets, induction coils and superconducting devices. In addition, the magnetometer systems which use artificially created fields to allow vector measurements to be made by total field sensors are described. Their operation performance is assessed and the use of bias and backing-off fields are discussed. The use of the proton gyromagnetic ratio as the absolute standard of geomagnetic field measurement is summarized. There follows a discussion of the requirement for routine ground-based geomagnetic data to be supplied to the scientific community in digital form for direct machine read-in, and some speculation about practicable automatically recording observatory systems. This review was completed in April 1972.

Electrodeless methods for conductivity measurement in metals

Abstract: The bulk of the article is concerned with a critical discussion of inductive, electrodeless techniques that enable the resistivity of a metal to be investigated, especially by the use of massive samples, with or without the presence of a strong magnetic field. The principal methods are the following: modification of the inductance of a coil by a metal core, eddy current decay, `hard' helicons in a rigidly mounted sample, `soft' helicons in an elastically mounted sample and torque on a sphere turning in a steady transverse field. The theory underlying the methods is expounded, but greatest attention is paid to the variety of disturbing effects that can introduce significant errors, and to the refinements of technique and analysis needed to minimize them. Although the literature is reviewed in some detail, much of the material is new. In an introduction the problems of conventional measurements, by four-terminal methods, in the presence of strong magnetic fields are outlined, particularly the `current-jetting' effects that can cause disastrous errors. This review was completed in January 1972.

Recent work on interstellar grains

Abstract: Observational data accumulated over the past decade have considerably narrowed down the choice of proposals for grain models. Mixtures of particles composed of refractory species such as graphite, silicates, quartz and iron appear likely. Such particles may form in a wide range of astronomical situations, for example, cool stars, protostars and supernovae explosions. Dust grains are responsible for infrared radiation in galactic sources, and also play an important role in the synthesis of interstellar molecules.

The interaction of two nucleons

Abstract: Research on the two-nucleon problem during the period 1959-1971 is reviewed and the status of this field is assessed. An attempt is also made to give a complete bibliography covering this period. This review was completed in August 1972.

Far infrared spectra of magnetic ions in crystals

Abstract: The absorption spectra of magnetic ions in crystalline solids, observed in the spectral range between approximately 5 and 200 cm−1, are surveyed. The electronic excitations of single ions are considered first. The measurements of line positions, intensities and widths are discussed in terms of both static and dynamic crystal electric field models. The second half of the review deals with the excitation of coupled ions both in dilute and concentrated materials. The spectra observed are discussed in terms of current models of the various interactions which can occur. In both areas there are obvious gaps between the experimental data and their theoretical interpretation. For pairs of interacting ions the theory is well advanced but as yet there is little data available for interpretation; while for many effects in single ion spectra the difficulties inherent in the theory limit our understanding. Progress towards the elimination of these problems is likely to aid our understanding of the behaviour of ions in crystals.

Data analysis techniques in high energy physics

Abstract: An account is given of the reduction and analysis of data from bubble chambers. Initially, the principles of operation and the important advances in the bubble chamber technique are briefly described. Since the discovery of the bubble chamber principle, chamber volumes have increased in two decades by a factor of 106. The development in the chambers themselves has been accompanied by a parallel development in the techniques used to analyse the data. The development of film measuring machines is then outlined and the construction and performance of some of these machines are discussed. In the late 1950's manual machines such as Franckenstein were highly automated and they were operating on-line to computers by the second half of the 1960's with program assistance and error detection. Fully automatic machines, proposed in the early 1960's, did not live up to their early promise. Evidently automatic event recognition is a very sophisticated task and the crude methods at present available require far too much computer time. Problems with precision CRT's were resolved in the mid 1960's, and their advantages over mechanical scanning systems have been successfully exploited. At the present time semi-automatic CRT machines such as POLLY are proving most successful. Specialized processor hardware such as BRUSH and SATR may eventually offer the solution to complete automation. The rest of the article describes the geometrical reconstruction, kinematical fitting and statistical analysis of bubble chamber events. The problems of geometrical reconstruction in the present generation of chambers caused by the use of wide angle photography are discussed. A description of the common methods of presenting bubble chamber data and some of the mathematical techniques used in the analysis are also given.

Spatial filtering in optical data-processing

Abstract: Optical data-processing is generally considered to have begun with Abbe's theory of image formation in the microscope. Since then the subject has expanded greatly until at this point in time it includes a plethora of techniques ranging from the simplest one-lens Fourier analysers and multipliers through coherently and incoherently illuminated correlators and processors to electro-optic devices and computer processing of optically logged data. To review the complete range of techniques and applications adequately is not possible within this article which is restricted, therefore, to a discussion of optical imaging techniques employing coherent illumination that are designed to process the input signal by the inclusion of masks and spatial frequency filters that control the system transfer function. Emphasis will be put on the characteristics of those spatial frequency filters and the processed images produced with them. The article will introduce the basic theory of coherently illuminated optical systems in terms of the Fourier transform relationships that exist between specific planes of those systems, including a discussion in general terms of the influence of masks and filters on the imaging characteristics of those systems. The major portion of the article will present a detailed examination of the properties of specific spatial frequency filters. They will be discussed firstly under a classification of filter types where their individual data processing characteristics will be elaborated and then, in summary, they will be reviewed within a classification of data processing function. Finally an appendix is included which further elaborates the theory of coherently illuminated optical systems, detailing the exact relationships between the complex amplitude distributions occurring in the principle and other planes of such optical systems.

Semi-empirical band structure theory

Abstract: The development of semi-empirical band structure theory over the last decade is surveyed. Methods are described that are based on the use of pseudopotentials and ad hoc potentials taken from atomic calculations. Self-consistent calculations are excluded. Stress is laid upon a generalized view, showing interrelationships between different methods. The connection with experiment is made explicit and a survey of results is given that is representative of the state of the art.

Stellar evolution toward the main sequence

Abstract: This review describes the evolution of stars during the period that starts just after formation in interstellar clouds and ends at the point of stabilization on the main sequence where nuclear reactions begin to provide the entire energy supply. During this pre-main-sequence phase the star shines at the expense of its gravitational potential energy. At the earlier stages this energy is released rapidly as the star experiences hydrodynamic collapse; later on the star contracts slowly through a series of states of quasihydrostatic equilibrium. The initial-boundary-value problem that must be solved to obtain the structure of a star as a function of time is discussed. The equations have been solved numerically for a wide range of stellar masses during both the hydrostatic and hydrodynamic phases, under the assumption of spherical symmetry with neglect of rotational or magnetic effects. The character of these solutions is described, with particular attention given to the effect upon the results of the assumed initial conditions. Mass loss has been investigated in theoretical calculations; its short-term effects are undoubtedly important but observational evidence indicates that a star ejects a negligible fraction of its total mass during pre-main-sequence evolution. The theoretical results are subject to a number of observational tests. The observations which are discussed include (i) the properties of T Tauri stars, (ii) the colour-magnitude diagrams of young clusters, (iii) the abundances of the rare light nuclei, particularly lithium, and (iv) the properties of the `infrared' stars. Calculations of evolution during the quasistatic contraction are found to be generally consistent with the observational results. However, information about stars in the hydrodynamic phase of evolution is difficult to obtain and is controversial. The observations of a number of objects which have been identified as protostars are reviewed. Inclusion of the effects of rotation in calculations of pre-main-sequence evolution presents a difficult numerical problem, and relevant observational material is very scarce. Some recent progress has been made; in particular, numerical work has strengthened the hypothesis that close binary systems are formed by fission of a rapidly rotating single star. Rotation must be of dominant importance during the earliest phases of evolution just after star formation. Future work on this problem is essential to an understanding of the formation of the solar system. This review was completed in January 1972.

Quantum metrology - standards of measurement based on atomic and quantum phenomena

Abstract: The past quarter of a century has seen a great change in ideas about units and standards of measurement. The system based on mechanical standards such as the metre bar is being replaced by one based on atomic and quantum phenomena such as a wavelength of light. The new system is now, in part, internationally accepted through definitions of the metre based on a wavelength of light of krypton and of the second based on a hyperfine transition in caesium. The advantages of the new system are in part conceptual, but principally they are practical since the new standards are more generally available and allow more accurate and more convenient measurements in science and engineering. The possibilities of the new approach to metrology go much further than length and time measurements. Ways of relating the electrical units, in particular, to measurements of frequency are being explored and it can be foreseen that in the near future it will be possible to relate most measurements to a measurement of frequency, with the great practical advantage that standards of frequency are immediately available from radio broadcasts. Emphasis is placed in this review on the importance of precise measurements in gaining new knowledge of the physical world and in applying it in engineering and it is argued that the most important property of a system of measurement is that it should be widely and easily available. The physical principles of atomic standards of frequency and length are explained, the ways in which they are realized at present are described and the possibility of a unified system of units of length and time based on frequency is discussed. The present basis of the electrical units is explained and an account is given of work in progress whereby it may be replaced by a system related to frequency through such phenomena as the Josephson effect between superconductors and the precession of protons in a magnetic field. The relation of the fundamental constants of physics to metrology is discussed, examples of current work on their determination being given. Finally, the possible structure of a system of units and standards based on frequency is considered and some examples of modern demands on metrology are given.

Accelerators for nuclear physics

Abstract: This article describes the principal charged particle accelerators being used today for research in nuclear physics in the energy range up to about 1000 MeV. The accelerators include Van de Graaffs, sector cyclotrons and linear accelerators for both positive ions and electrons. For each type of accelerator a brief treatment is given of the recent history, operating principles, some special techniques, a typical facility, and some examples of experimental data from that type of accelerator. Descriptions are also given of new types of machines under construction, such as pelletrons, frequency modulated sector cyclotrons, separated sector cyclotrons and superconducting linear accelerators. New ideas for the future are mentioned, including multistage tandem cyclotrons and the electron ring accelerator. The reader is assumed to have no experience in accelerators or nuclear physics, and many references are given to more detailed treatments of the topics covered.

Ten years of accelerator physics.

Abstract: In the last ten years high energy physics has made many discoveries. Coulomb's law has been shown to hold at distances down to less than 10−14 cm - smaller than the size of the proton. Since parity violation was first observed in 1957, weak interactions have become an enormous field. From the simple Fermi theory of beta decay we now have shown the existence of two neutrinos and have demonstrated the exact form of the interaction. The superweak interaction has been found, a thousand times weaker than the Fermi interaction and violating time reversal invariance. This is beautifully demonstrated by precise experiments with neutral K mesons. The many hundreds of elementary particles have been shown to be grouped in mass and quantum numbers according to a symmetry scheme SU3. There are many beautiful tests of this symmetry. The description of it in terms of a quark of charge e/3 has not yet had experimental confirmation. The nucleon is yielding to study. Inelastic electron scattering shows that a nucleon consists of internal objects called partons. Whether these are the quarks of the symmetry rules is not yet known. It is likely that the next ten years will be more exciting still. At higher energies weak interactions will reach the unitary limit and the theory will break down; with smaller wavelength probes the inside of the nucleon will yield its secrets. This review was completed in November 1971.