Table of contents

The exciting contributions made by radio astronomical observations over the last decade would not have been possible without the development of radio telescopes of increasing sensitivity and resolving power. In particular the study of the `radio galaxies' has depended very much on the availability of instruments capable of determining their positions with accuracy, investigating their detailed angular structure and their radio spectrum. These sources have a radio emission very much greater than that of our own Galaxy, and the mechanism by which this intense radiation is produced is of great astrophysical interest; the socalled `quasi-stellar' sources in which the whole radio emission originates in a region only about one hundredth of the dimensions of the galaxy, represent an extreme case involving unknown sources of energy.

By using radio telescopes of great sensitivity and angular resolving power, radio galaxies can be detected at very large distances; owing to the time taken for the radio waves to reach the earth, they are consequently observed as they were some thousands of millions of years ago, and such observations offer the possibility of exploring evolutionary changes in the Universe. In order to extend these types of observation, more powerful instruments became necessary, but the construction of larger steerable paraboloids of sufficient accuracy presents very great engineering difficulties. More economical instruments have been built by using fixed parabolic cr spherical reflectors, which can be supported from the ground at many points, but even with these instruments the cost becomes very great if an angular resolution better than five minutes of arc is sought.

Alternative methods of building large telescopes have been developed, in one of which advantage is taken of the fact that for most observations the sky can be regarded as unchanging over the period of observation; it is then not necessary to have the whole of the telescope present at the same time, and a large effective instrument may be `synthesized' by using two small elementary aerials arranged successively in all the positions present in the large area. The observations may be combined in a computer to produce a map of the sky having a resolution and signal-to-noise very much greater than that associated with the small elementary aerials.

Four large instruments have been built using this principle, two of which have been in use for six years. They have been particularly valuable both in enabling large resolving powers to be attained at long wavelengths in order to establish the radio spectra of the sources, and in extending the observations to the weakest sources yet observed.

A solution is proposed to e old problem of the asymptotic form of the radial distribution function g(r) for both quantal and classical liquids. For the quantal fluid helium 4 at absolute zero, Feynman's result that the structure factor S(k) = ℏk/2Mc for sufficiently small k is shown to yield g(r) ~ 1 - (ℏ/2π²n₀Mc)r^-4 where n₀ is the mean density and c is the sound velocity.

For classical liquid insulators, such as argon, where the long-range van der Waals interaction may be written as ϕ(r) ~ -Ar^-6, g(r) ~ 1 - (1/kT){S(0)}²ϕr in regions well away from the critical point. For simple liquid metals, such as sodium, neglecting Fermi surface blurring, ϕ(r) ~ Br^-3 cos 2k_fr and this gives g(r) ~ 1 - (1/kT){S(2k_f)}²ϕr where k_f is the magnitude of the Fermi wave vector.

This paper examines three types of inequalities for molecular integrals occurring in wave mechanical calculations.

e refractive index of helium for wavelengths longer than 600 Å is calculated by a variational method from the ground state representation of Hart and Herzberg. The results agree very well with the observations which refer to wavelengths between 2700 Å and 9000 Å.

A theory is presented of the recombination of electrons and positive ions in the presence of neutral atoms which act as third bodies, explicit account being taken of the effect of radiative transitions. Comparison is made with the theories of Thomson and of Pitaevsku. Detailed calculations are carried out on recombination in helium gas. It is found that the rate coefficient α is very great when the temperature theta is low and the number density N(He) is high: for example, that α for He⁺ is 5 × 10^-8 cm³ sec^-1 and for Na⁺ is 2 × 10^-8 cm³ sec^-1 when θ is 250 °K and N(He) is 3 × 10¹⁹ cm^-3.

Estimates are made of the rates for the de-excitation of (π^-, α) and (K^-, α) atoms in liquid helium. An estimate is also made of the rate of nuclear capture of K^- mesons from high s states. The calculated Auger and radiative rates give total cascade times which are roughly 5 times shorter than the experimental values. The approximations which are used are such that this is regarded as satisfactory agreement. For principal quantum number 21 ⩽ n ⩽ 24 the Auger rate for (K^-, α) atoms is approximately equal to the rate for nuclear absorption. The calculations indicate that the amount of K^- absorption from high s states may not be negligibly small.

From an analysis of charge exchange and elastic scattering of 35 MeV negative pions using a liquid hydrogen bubble chamber, the charge-exchange total cross section is found to be 5.61 ± 0.40 mbn and the s-wave scattering lengths a₁ = +0.187 ± 0.009 a₃ = -0.082 ± 0 011 in units of ℏ = c = m_π = 1. The quantity a₁ - a₃ is found by a method free from systematic error and independent of Coulomb corrections. It is compared with that of the analysis of pion-proton scattering data, using dispersion relations, by Hamilton and Woolcock. The agreement is reasonable.

e resonances observed in ⁶Li(d, α)α reactions have been fitted using the multi-level formalism of Wigner and Eisenbud's R-matrix theory. Three levels in ⁸Be around 22 MeV excitation are predicted at excitation energies of 22.542, 24.02 and 25.227 MeV having spins 2⁺, 0⁺ and 2⁺ respectively. The 0⁺ level has a large deuteron width which is about 75% of the Wigner limit while the two 2⁺ levels show smaller deuteron widths, about 25% and 3% of the Wigner limit for the lower and higher levels respectively. The alpha reduced widths for all these levels are small compared with the Wigner limit, the 0⁺ level having the maximum alpha width. The use of this reaction as a detector of polarized deuterons is discussed. Preliminary analysis of the ⁷Li(p, α)α resonances is also presented.

The ⁶Li(d, α)α reaction has been studied in the region between 4 MeV and 12 MeV deuteron energy. No new resonances have been found although the angular distributions show that the reaction mechanism is predominantly compound nuclear. No evidence was found for any direct interaction.

A method is presented by which the evaluation of the set of linear equations determining the local vibrations of defect lattices can be considerably simplified in the case of large imperfections. The treatment makes use of some theorems on partitioned matrices which permit the reduction in the matrix of these equations of the number of arising additional and encumbering terms, and the expression of these terms in a more convenient form for practical calculation. The method is illustrated in the case of five defect atoms in a two-dimensional lattice.

The time constants associated with the capture of hot electrons by gold centres in germanium at 20 °K have been measured as a function of electric field in specimens containing N_Sb antimony and N_Au gold atoms per cubic centimetre where N_Au < N_Sb < 2N_Au. Capture by Au^2- centres dominated at high fields. The capture rate per Au^2- centre at high fields was a factor 2 × 10³ higher than the zero-field value, which confirmed previous results. A direct measurement of the capture rate per Au^- centre at high fields was not possible and the value had to be estimated from current density measurements. This estimate gave an increase of capture rate per Au^- centre over the zero-field value by a factor of about 20. The zero-field value of the capture rate per Au^- centre at 20 °K was found to be 3 × 10^-12 cm³ sec^-1.

The hot electron results for both Au^- and Au^2- centres were conveniently summarized by assuming an energy dependence of the capture rate α(E) of the form α(E) = AS(E)E^p+½, where A was temperature dependent and S(E) was the coulombic tunnelling factor for the transverse effective mass. For Au^2- centres p = -0.8 ± 0 1. For Au^- centres p = -1.0 ± 0.1 from the 77 °K results, and this was adequate to explain the 20 °K results. For low electron energies the approximate formula of Bonch-Bruevitch for the zero-field capture rate, α = A exp{-(T₀/T)^1/3}, was applicable, with T₀ = 1.34 × 10⁴ °K for Au^- centres and T₀ = 5.35 × 10⁴ °K for Au^2- centres.

The results of an experimental study of helicon wave propagation in a partially ionized cylindrical plasma are reported. Conditions were chosen so that the phase velocity of the wave was independent of both the electron and ion mass.

The phase velocity, the attenuation and the structure of the plasma magnetic fields are compared with the theoretical treatment of Klozenberg, McNamara and Thonemann in 1964. The agreement is satisfactory. In particular, evidence is presented which supports the anomalously high attenuation due to surface currents which the above theory predicts.

Measurements have been made of the phase velocity and the attenuation of helicon waves propagated parallel to the axis of a long cylinder of indium metal at 4.2 °K. A constant magnetic field was applied parallel to the axis of the cylinder. Both the axisymmetric (m = 0) and dipole (m = ±1) modes were studied.

The experimental results are compared with the predictions of theory for two different assumptions concerning the boundary conditions. It is shown that the theoretical predictions which include non-zero vacuum fields give the best agreement with the experiment.

The Hall coefficient derived from these measurements is consistent with that calculated on the assumption of one hole per atom within the experimental error (similar 1.5%).

It is first shown that Thouless' method for finding the critical temperature of a pure superconductor can be extended to include non-magnetic impurities in the superconductor. Then explicit expressions for the critical temperature, anisotropy and jump in specific heat of a superconductor doped with small quantities of non-magnetic impurities are given. The method is extended so as to include paramagnetic impurities in the superconductor and the results for the critical temperature are compared with experimental work on aluminium doped with iron-group impurities.

The magnetic, electrical and thermal properties of the body-centred cubic FeCr system suggest that ferromagnetism and antiferromagnetism may coexist in the alloy containing 20% Fe and this behaviour may extend from about 16% Fe to 50% Fe in Cr.

The ferromagnetism is due to localized moments associated with the Fe atoms, while the antiferromagnetism is due to spin density waves as in pure chromium.

The magnetic susceptibility χ has been measured for alloys containing 90.2%, 80 6%, 69.4%, 57.2%, 47.6%, 34.6%, 20.2%, 15% and 8.3% gadolinium in lutetium. These measurements have enabled the Curie temperature and magnetic moment p_eff of the alloys to be determined. Only the 20.2% Gd alloy shows any departure from the Curie-Weiss behaviour and this is attributed to the onset of antiferromagnetic ordering.

Values of the photoelectric secondary coefficient δ'/α due to the incidence of delayed non-resonance photons, having energies of approximately 20 eV on a silver cathode in a low pressure (10 < P₀ < 39 mmHg) discharge in helium in the range 9 < E/P₀ < 22 v cm^-1 mmHg^-1 of electric field E to gas pressure P₀, have been obtained from measurements of the ionization growth times. Estimates of absolute photoelectric yield have been deduced from the values of δ'/α and are found to lie between 0.2 and 0.3 electrons per quantum.

Experiments were carried out with a Bradbury electron filter apparatus to determine electron attachment coefficients in carbon dioxide, carbon monoxide, air and helium-oxygen mixtures. The data obtained, where comparable, are in reasonable agreement with earlier work. Certain features of the electron filter method are described and discussed, for example the various effects of particle collection at the grids, and electron detachment.

Absolute cross sections for the emission of some of the more intense lines induced in various rare gas ion-atom impacts have been determined in the spectral range 3900-6000 Å by the analysis of radiation (assumed isotropic) emitted under single-collision conditions. In most cases it is found that the principal emision lines are associated with the singly ionized states of the incident and target particles. Probable excitation mechanisms are discussed with reference to relevant charge-rearrangement collision cross sections.

Electron diffraction studies have been carried out on thin films of the solidified gases argon, krypton, neon, xenon, oxygen and nitrogen, using a liquid helium cooled specimen stage. In transmission all the inert gases studied were found to crystallize in their normal close-packed cubic structures. When deposited on a (111) single-crystal silver face and studied in reflection, solid argon, neon and xenon were observed again to crystallize with close-packed cubic structures. Solid krypton, however, was found to give a pattern consisting of sharp and diffuse arcs which are found to be consistent with the formation, during deposition, of stacking faults in (111) krypton planes. The probability of plane faulting α was deduced to lie in the range 2√3 - 3 < α < ½, indicating that for krypton under the conditions of the experiment the close-packed hexagonal structure is almost as likely as the close-packed cubic structure.

Electron diffraction studies on solid α nitrogen confirmed the recent results of Hörl and Marton. The diffraction patterns obtained from solid β oxygen were in agreement with the R m space group proposed by Hörl. The 10.4 ring, not observed by Hörl but allowed by his proposed structure, was present in all the diffraction patterns obtained.

The intermolecular potential parameters of solid Ne and Xe for a Lennard-Jones m-6 potential are calculated using the recent experimental lattice spacing determinations of Bolz and Mauer and Sears and Klug. Values of , σ and the de Boer parameter A are tabulated for values of m = 10, 11, 12, 13 and 14 and for 1N, 2N and AN interactions. We have also included recalculated (quasi-harmonic) values of Θ₀, Θ_∞ and γ₀ to replace the values given by Horton and Leech. The effect of the strain dependence of the zero-point energy is calculated according to the method of Barron and Klein, and is found to be small.

Corrected values for several matrix elements of standard crystal field operators are given.