Table of contents

An examination is made of the spin-lattice relaxation in the solid state of nuclei whose energy level spacings in a magnetic field are rendered unequal by quadrupole interactions with the crystalline electric field. Attention is directed to two special cases: (1) when the main magnetic field is suddenly increased from zero, and (2) after saturation of the central line of the resonance spectrum; in the case of imperfect cubic crystals this is the only observed line. In general, 2I relaxation times characterize the relaxation behaviour, though in the two special cases the effective number is reduced. Detailed calculations of the relaxation behaviour have been made for spin number fraction three-twos and fraction five-twos for a quadrupolar relaxation mechanism. The behaviour in the two special cases differs and to a degree which depends on the relative strength of quadrupolar relaxation by transitions involving Δm = 1 and 2. The relevance of the results to the experiments of Day and Squire on potassium iodide is discussed. Magnetic relaxation is also treated and an expression is found for the 2I relaxation times.

An account is given of microscopic and interferometric studies on slightly raised disk formations which appear on the dodecahedral faces of several diamonds. One small diamond exhibits more than a thousand such disks on its faces. Interferometry shows that the disks are slight elevations. It is conjectured that they owe their origin to a protective action of small bubbles. Evidence is given that the crystals showing the disks have been subjected to a solution or etch mechanism in the final stages of the crystal formation. The suggested micro-bubbles adhering to the surface would locally prevent dissolution, leaving ultimately slightly raised disks on the surface. By postulating the possibility of slight movement or oscillation of the conjectured bubbles, most of the observed complex topographical features of the disks can be accounted for.

Torque curves have been measured at 82°K on gallium- and aluminium-substituted single crystals of magnetite. The paper consists of two parts, one dealing with the values of the constants required to describe the intrinsic anisotropy of Fe₃O₄ below the crystallographic transition and the other concerned with the irreversible nature of the torque curves observed on some of the gallium-substituted crystals. A model based on the ordering of Fe²⁺ and Fe³⁺ ions is proposed to explain this rotational hysteresis which occurs in higher fields than would be necessary for magnetic saturation.

Single-crystal thin films of nickel, in the thickness range 50-500 Å have been prepared, by epitaxial growth on rock-salt, and their magnetic anisotropy measured.

All films show a uniaxial anisotropy superposed on the normal cubic anisotropy. In the discontinuous films, annealing in vacuum reduces the uniaxial component whilst in continuous films annealing increases it. Films grown in a vacuum of 10^-7mm are found to have few imperfections visible in the electron microscope and give more consistent results. The uniaxial component of anisotropy is shown to be a function of thickness, and is affected by the degree of vacuum achieved during deposition. It is suggested that the mechanism of directional ordering of oxygen atoms in the metal lattice, as proposed by Heidenreich, Nesbit and Burbank in 1959 would account for the results.

Thin films of nickel and some face-centred cubic nickel-iron alloys have been grown epitaxially from the vapour phase on to the principal planes of rock-salt and copper, and their structure and orientation investigated by transmission electron microscopy. Conditions have been determined for the production of continuous films of thickness down to 100 Å. The mass and composition were determined microchemically; thicknesses given are on the assumption of bulk density.

An experiment is described in which a longitudinal wave of ultrasonic frequency travelling in a crystal of LiF (anisotropic medium) is incident on a crystal-air boundary and is reflected as a transverse wave. Such a mode conversion, or complete change in the state of polarization, of an elastic wave had previously been observed only in isotropic media. The corresponding calculations are also given; they agree with the experimental results.

In the sea the repeated horizontal deflection of a sound ray due to reflection at a sloping bottom produces a curvature of the horizontal path. The reflection angles in three dimensions are calculated for a sloping bottom or sound velocity interface. Even if the stratification varies in both horizontal directions there is for slow variations a simple relation between the changes in vertical and horizontal ray angle. It is then shown that the horizontal curvature may be predicted by associating a refractive index or phase velocity with each horizontal position. A formula for intensity and some illustrative problems are presented. For example it is shown that on reflection from a coastline the vertical ray angle at closest approach is equal to half the total horizontal angle through which the ray is turned.

Numerical integration in elliptical coordinates is proposed as a convenient method for the computation of most types of two-electron molecular integrals including some types of three- and four-centre integrals, and in some cases, of one-electron two- and three-centre integrals. This method removes a great deal of the burden of analysis and in addition lifts many of the restrictions on the form of the orbitals which are imposed by existing methods.

For Slater-type orbitals general formulae are given to facilitate the calculation of two-centre Coulomb integrals, hybrid repulsion integrals and certain three-centre integrals. Explicit expressions are listed for integrals involving orbitals of the first, second and third quantum shell.

A redetermination of the g_J value of the 6³P₁ level in mercury using the `double-resonance' technique is described. The value is in agreement with recent measurements using the `level-crossing' technique but not with the value obtained in earlier experiments. A weighted mean of all determinations suggests the value g_J=1.486 31±0.000 08.

The first part of this work is a study of the changes of intensity of the resonance fluorescence from mercury vapour as a small magnetic field H is applied either parallel or anti-parallel to the direction of the incident light. The changes follow either a Lorentzian or a dispersion-type function of the Zeeman splitting of the excited state, according to the orientations of polarizer and analyser in the beams of light.

In an experiment with an additional oscillatory field at a frequency ω₀, similar curves are observed in the region H = H₀/2. (H₀ is the field for which ω₀ is the Larmor frequency.)

The observations are relevant to a recently developed technique in which intensity changes of this sort are used to make precision measurements in spectroscopy. The Lorentzian line shape is usually observed. The possibility of obtaining line profiles of other shapes was pointed out by Franken.

Some relationships involving line-width and second moment of broadened resonance lines are investigated.

It is of particular interest to determine how the properties such as line-shape of a multiply-broadened line depend on the properties of the individual lines. In certain cases the shape of the broadened line is the same as that of the individual lines, and particular attention is paid to this class of `self-folding' functions.

The reactions ¹⁰B(³He, d)¹¹C and ¹¹B(³He, d)¹²C have been studied, using magnetic analysis, at a bombarding energy of 9.84 MeV. A new level in ¹¹C at 6.345 ± 0.010 MeV excitation was observed. Deuteron angular distributions leading to the ground and first five excited states of ¹¹C were measured, and an attempt has been made to fit these with stripping curves. Absolute proton reduced widths for the ¹¹C levels have been extracted.

Using the ¹¹B(³He, d) reaction, the energy levels of ¹²C between 9 and 15 MeV have been studied. Natural widths of levels at 10.84, 11.82 and 13.38 MeV were measured to be 320, 300 and 700 kev respectively. Stripping analyses of the deuteron angular distributions yielded l-values of 2, 0, 0 and 1 respectively for the states of ¹²C at 9.63, 10.84, 11.82 and 12.70 MeV. Absolute proton reduced widths and also α-particle reduced widths, from the measured total widths, have been extracted for some levels of ¹²C.

Detailed studies of pre-breakdown ionization in hydrogen gas at low pressures have been made in the presence of uniform electric fields and appropriate analytical methods and experimental procedures suitable for similar studies in crossed electric and magnetic fields have been established. The factors influencing determinations of the first Townsend ionization coefficient α/p₀ from pre-breakdown ionization measurements are discussed and an observed pressure dependence of α/p₀ at E/p₀ = 350 is shown to be due to the presence of vapour impurities which can give rise to the large values of α/p₀ recently reported. Values of α/p₀ have been measured for the range of values of E/p₀ from 50 to 450 v cm^-1 (mm Hg)^-1.

The density spectrum of cosmic-ray air showers has been measured using Wilson cloud chambers in two different density regions. From 50 to 500 particles per square metre the differential spectrum can be approximated by a power law of exponent - 2.5, in good agreement with many previous results. Above 1100 particles per square metre the measured exponent is - 3.9±0.5. The result is compared with recent experiments using emulsion chambers and an explanation in terms of the characteristics of high energy nuclear interactions is outlined.

The unrestricted Hartree-Fock method is a convenient method of calculating neutron form factors and hyperfine interactions, but because the method gives wave functions which are not eigenfunctions of S², the validity of it must be questioned. It is shown that the unrestricted Hartree-Fock method gives spin densities which are approximately correct to first order provided certain exchange energies are small relative to `promotion' energies. Furthermore, it is shown that the wave functions obtained must be used directly and that it is a poor approximation to project out the unwanted parts after the energy minimization procedure has been performed.

The theory of the Faraday effect, due to free charge carriers, is developed for non-degenerate semiconductors with spherical energy surfaces. General expressions for the Faraday rotation θ and the ellipticity δ are given, which are valid for all frequencies from the microwave region to the infra-red, and for all magnetic field strengths within the limitations of the Boltzmann equation.

The cases of lattice scattering and impurity scattering are considered separately and the numerical calculations are based on experimental data for n-type germanium. The rotation θ changes sign at the cyclotron resonance frequency in strong fields and at a lower frequency (determined by the relaxation time) in weak fields. The ellipticity δ passes through zero at a frequency corresponding to maximum θ, and reaches a maximum when θ is zero. In the limit of high frequencies and weak fields θ (but not δ) is independent of the relaxation mechanism. Both θ and δ vary linearly with field strength in weak fields but subsequently pass through a maximum.

The temperature dependence of θ and δ is examined in the range 100-300°K for lattice scattering and 15-100°K for impurity scattering. As the temperature is lowered, in general θ and δ both increase in the case of lattice scattering, and both decrease in the case of impurity scattering.

Experiments are described in which Berthelot tubes containing water are used in an attempt to estimate the maximum tension that can be sustained by a water-glass system under static conditions. The Berthelot tube is sealed at both ends and is almost completely filled with the liquid under investigation. On heating the tube the liquid expands until it completely fills the tube, but when it is subsequently allowed to cool the adhesion of the liquid to the walls of the tube prevents the liquid from contracting at a greater rate than the internal volume of the tube. Consequently a progressively increasing tension is set up in the liquid until it eventually ruptures. The tension in the liquid immediately prior to the instant of rupture is measured by estimating the sudden increase in the external volume of the Berthelot tube at this instant.

The results show that the critical tension occurring in any one tube varies considerably in successive experiments; this variation is liable to be as great as thirty atmospheres. Furthermore, the magnitude of this tension varies from tube to tube; some tubes can sustain sixty atmospheres while others are incapable of sustaining even five atmospheres.

Experiments with tubes constructed from steel gave substantially similar results. So also did glass tubes containing suspensions of ultramarine powder in water and carbontetrachloride with water.

Furthermore, pre-compression of the liquid has no detectable effect on the critical tension. Neither has rate of build-up of the applied tension, nor mechanical shock.

An incidental result has been the verification of the equality of the extensibility and compressibility of water.

Correction to Proc. Phys. Soc.77, 1193