Table of contents

Progress in the application of quantum mechanics to study the electronic structure of molecules has, until recently, been disappointing and slow. Many difficulties, both of mathematical method and of numerical analysis, arise when there is a large number of particles in the quantum mechanical system. In this review the different ways of applying quantum mechanics to chemical problems are discussed. The accuracy expected and attained by each method is illustrated, but applications to individual molecules are not reviewed.

The coming of electronic computers has already produced great changes in this subject. In particular, it is now possible to calculate highly accurate wave functions from first principles for a range of molecules. Direct calculations of this kind are not possible for large molecules and, for these, the problem has been to find suitable parameters which remain constant for a series of molecules and can be used to describe their properties. This problem is intimately connected with the problem of interpreting quantum mechanical calculations in a chemically significant way. Quantum mechanics can also be applied to molecules by setting up models which simplify the quantum mechanical equations but retain those features which are most significant for a series of related molecules.

Finally, some of the objectives of current research are briefly reviewed. The wider significance of the subject and its importance for chemistry and the theories of the solid state and the nucleus are also discussed.

This article is concerned with advances in vacuum technology during the last two decades, although the achievements of the second half of this period have received most emphasis. The account is written from the point of view of the physicist and does not refer specifically to the considerable progress in the applications of vacuum technology to such specializations as metallurgy or chemical engineering.

In dealing with mechanical pumps some of the more recent improvements in rotary backing pumps are described, and the advent of the positive displacement rotary compressor is noted and its advantages discussed. The controversial subject of condensation pump theory receives brief attention, and sections on both oil and mercury condensation pumps give the more salient points of the advances leading to the present capabilities of these pumps. Ejector type vapour pumps have been in use for a long period but the use of ejector principles at lower pressures is mentioned as a more recent development.

Trap design has kept reasonably in step with progress in vapour pumps, but unsolved physical problems bearing on the efficiency of traps are shown to remain.

New methods of pumping are challenging the established position of the vapour pump, and the achievements of various types of ionization and gettering type pumps are reviewed, as is some of the work on the mechanism of pumping in devices of this nature. This subject emerges as one holding many interesting problems, both theoretical and practical, and the progress in recent years is an encouraging pointer to the future.

Comparison of pumping speeds quoted by different workers has been difficult, due not only to differing definitions but to large errors inherent in many methods of speed measurement. Progress in understanding and resolving this problem is described.

In a section on pressure measurement progress in various types of gauges is assessed. Recently long-standing obstacles to measuring very low pressures have been overcome; the methods which have been developed, including some still in the laboratory stage, are discussed. The whole new subject of very low pressure techniques is one in which there has been rapid advance; this is surveyed and future trends are suggested.

Conventional deflection-type mass spectrometers have been omitted, but newer types which have found application as convenient tools in vacuum systems are described in principle. These include the omegatron, the linear r.f. types and the time-of-flight types.

The growth of leak detection as a branch of vacuum technology is discussed and a brief review of some methods is given. Reasons are advanced for the present difficulty of quantitative comparison of methods, and suggestions for progress are given.

The general principles governing the behaviour of plane elastic waves in aeolotropic media are developed and the significance of the velocity, slowness and wave surfaces is indicated. Sections of these surfaces for media of hexagonal and cubic symmetry are illustrated and discussed from a theoretical and an experimental standpoint.

The general problem of reflection and refraction which arises when a plane wave is incident upon a plane interface between two arbitrarily oriented aeolotropic media is discussed and exemplified by a simple case involving two copper crystals.

The conditions under which surface waves of Rayleigh and Love types may be propagated are discussed.

Problems of elastic wave propagation in anisotropic aggregates are mentioned and briefly examined.

The article concludes with a consideration of the main assumptions relating theory and experiment.

The laws of relativity corresponding to Newtonian dynamics are discussed and contrasted with those suited to Maxwell's equations. Einstein's principle of relativity is inferred, and some of its consequences are briefly examined.

The peculiar features of Newtonian gravitational theory are described and are shown to lead to the principle of equivalence. The roles of this principle and of the general principle of relativity in the foundations of Einstein's general theory of relativity are critically discussed, and the theory is formulated. Modern developments in the theory are summarized.

The phenomenon of double beta decay is discussed rather fully both from the experimental and from the theoretical point of view, the relation between double beta decay and the possible kinds of inverse beta decay being also briefly treated. A summary of the available experimental data is given, all methods of detection of the various double beta decay processes being considered. The theory of double beta decay, both in the no-neutrino and in the two-neutrino cases, is worked out, ab initio, on the basis of a nucleon-lepton interaction without conservation of parity. It is particularly emphasized that, with a ` two-component neutrino ' type nucleon-lepton interaction without conservation of parity, absence of no-neutrino ββ decay does not by itself uniquely imply that neutrino and anti-neutrino are distinguishable and that the total lepton charge is conserved.

Comparison of the experimental limits on the double beta decay half-lives with the corresponding theoretical values indicates that two neutrinos are emitted together with two electrons in each double beta decay process - this conclusion is, however, not yet certain and must be confirmed by further experimental work. A treatment is given of the implications of the actual occurrence of two-neutrino rather than no-neutrino double beta decay for the problems of neutrino-anti-neutrino identity and conservation of total lepton charge. It is concluded, on the basis of (i) the available double beta decay, inverse beta decay and muon decay experimental data and (ii) the provisional assumption of the universal applicability of ` two-component neutrino ' type coupling, that a verdict may be tentatively reached in favour of a ` Dirac ' neutrino, operationally distinguishable from a ` Dirac ' anti-neutrino, and with conservation of total lepton charge valid in all neutrino interactions.

The interest in thermoelectric phenomena and in their practical applications led to an investigation of semiconductors with high electric conductivities σ and low thermal conductivities κ. The requirement of the highest possible ratio of the mobility U to κ directed our attention to solid solutions. κ could be decreased to values corresponding to a free path of phonons of a few interatomic distances.

The replacement of positive ions in a compound by analogous ions (for instance Bi by Sb in Bi₂Te₃ or Pb by Sn in PbTe) decreases many times the mobility of electrons, while the mobility of holes remains unaltered. A distortion of the sub-lattice of negative ions leads to a decrease of the mobility of holes.

The influence of impurities on the free path of phonons and of free charge carriers reveals the scattering cross section of defects. Crystal lattices with a proportion of unfilled sites have exceptionally short free paths which, calculated in the usual way, are smaller than the periods of the lattice. Accordingly the mobility increases with rising temperature.

Using degenerate systems of free charge carriers it became possible to separate the influence, on the mechanism of scattering, of the velocity of electrons on one hand, and of the thermal motion of the lattice on the other.

The onset of intrinsic conduction introduces an additional thermal conductivity due to the diffusion of electron-hole pairs. Excitons, with small excitation energies, have an analogous effect.

The high transparency of pure semiconductors to radiation with hv<E₀ brings into action a heat conduction mechanism, due to the transmission of infra-red radiation, as long as absorption by impurities or by free charges does not stop the radiation.

The dragging of phonons and electrons increases both the thermal conductivity and the thermoelectric power at low temperatures.

The materials selected for thermoelectric devices are investigated in detail.

A table of experimental paramagnetic resonance data is presented. Its purpose is to bring up to date (to the end of 1958) the results given in an earlier Progress Report (1955) by Bowers and Owen, and it follows closely the form of this Report. Results are given, in the form of values for the parameters in the spin Hamiltonian, for transition group ions in solids, F centres, V centres and other damage centres. No results on paramagnetic resonance in liquids or free radicals are included.

This paper discusses the recent information gained about the E-layer of the ionosphere by various experimental techniques. The basic information is provided by penetration-frequency measurements made from routine pulse soundings, giving a general picture of the variation of the ionization during the day, with season and with latitude, as well as the effect of changing solar activity and of the magnetic current system. Special radio-reflection experiments to measure height changes have yielded important results, particularly concerning tidal movements. The detailed structure of the layer has also been deduced from high-resolution pulse soundings. Independent information about the structure of the layer has been determined directly using rockets, and shows marked differences from the structure deduced from ground observations.

Observations with high-resolution ionosondes reveal that the reflections from the E-region are often very complex, and this introduces uncertainties in the identification of the characteristics of the normal E-layer. A brief discussion is given of observations of fine-structure in the layer.

Rocket measurements of solar radiations and of the atmospheric composition have made it possible to predict the distribution of ionization in the E-layer; this prediction is in quite good agreement with the distribution determined from accurate soundings.

Observations of changes in the ionization during solar flares and radio fade-outs are described.

Radio-frequency and optical spectroscopy are compared. Standard results in the theory of hyperfine structure are quoted. The excitation of atoms and the detection of radio-frequency resonances are discussed quantitatively. Experiments are described in which the techniques of `double resonance', electron impact, and atomic beams are used. A table of measurements is given.

The review gives the general theory of an isotropic Fermi liquid constructed by L. D. Landau, and continued by the authors of the present article. The results of the theory are compared with the experimental data on the properties of liquid helium 3 at low temperatures.

The contents of the review are set out in the following order. After a short introduction (§ 1), § 2 gives the basic premises of L. D. Landau's theory, and in particular the energy of excitations and the interaction function f are derived. § 3 gives the derivation from Galileo's principle of a relation which expresses the effective mass of the excitations in terms of the mass of the atoms and the zeroth harmonic of the function f.

§ 4 is devoted to the derivation of the specific heat of a Fermi liquid, and an expression for the magnetic susceptibility is deduced in § 5. The exchange interaction of the excitations plays a considerable role in this expression. § 6 gives the kinetic equation for the excitations and this is used to find expressions for the momentum and energy flux. The results of § 6 are applied in § 7 to the calculation of the coefficient of viscosity, and in § 8 the coefficient of thermal conductivity is found by an analogous method. § 9 is concerned with the problem of the velocity of sound. In particular, this section contains the result obtained by L. D. Landau concerning the possibility of propagating the so-called `zero sound' in a Fermi liquid at sufficiently low temperatures. § 10 considers the problem of dispersion and absorption of sound. § 11 deduces the average fluctuations of the distribution function and this result is used to calculate the scattering of light. An expression is given for the total intensity of scattered light, and the frequency and angular distributions are also given.

The Appendix shows how the basic premises of the theory of a Fermi liquid can be derived from microscopic considerations.

§ A1 considers the properties of a rarefied Fermi gas. § A2 gives the microscopic basis of the energy spectrum of a Fermi liquid in the general case, and also gives a relation between the function f and the scattering amplitude of excitations.

An account, as non-technical as possible, is given of the invariance properties that have important applications in elementary particle physics. These can be classified in several ways. Firstly some are related to continuous groups (rotations), others to discrete groups (inversions). Secondly some are related to groups of well-known geometrical or kinematical significance (ordinary space time), others are not and are peculiar to elementary particle physics (isobaric space). Finally some are, it appears, rigorously valid while others are of approximate nature. The discussion aims to cover all cases and their interpretation. In as far as possible explicit use of quantum field theory techniques is avoided.

This article is concerned with nuclear magnetic resonance effects in pure liquids which result directly or indirectly from the interactions of electrons with nuclei in diamagnetic molecules. Magnetic shielding and indirect spin-spin coupling are discussed in detail both experimentally and theoretically for steady state spectra and for transient measurements. Experimental techniques as such are not treated. The structure and behaviour of liquids is only dealt with in so far as it affects the interactions referred to above. The emphasis is placed on the description and explanation of physical effects rather than any detailed survey of their application to chemical and specifically molecular structure problems. There are some two hundred and fifty references and it is hoped that all the relevant ones have been included up to those available in London at August 1958.

The report describes all aspects of experimental work on ³He: methods of extracting ³He from a mixture of isotopes and the sources from which it is obtained, details of the most efficient methods and apparatus, experiments on saturated vapour pressure and the critical point, the equation of state of gaseous ³He, thermomolecular pressure rates, melting curve and α-β transition in solid ³He, experiments and data on the density of liquid, gaseous and solid ³He, the thermal properties of ³He - latent heat, specific heat and entropy - the magnetic properties of ³He, and the phenomena of viscosity and thermal conductivity, results of experiments on the temperature discontinuities at the boundary between ³He and a solid, the velocity of sound, the compressibility of ³He and adsorption on activated charcoal, the construction and specifications of the work of cryostats, which enable us to obtain and maintain temperatures to 0·3°K by pumping off ³He vapour.

The possibility is discussed of obtaining and maintaining temperatures below 0·3°K by adiabatic crystallization of ³He. The article reviews with brief critical comments practically all published experimental work on the investigation of ³He, and gives tables and graphs for all known properties of ³He.

In recent years there have been great advances in understanding the interaction of two nucleons, both phenomenologically and in terms of a fundamental meson-nucleon coupling. The present report describes the methods and achievements of phenomenology and meson field theory in this subject.