Table of contents

A unified theory of gravitation and electromagnetism is derived from a variational principle. The characteristic action function is an invariant density formed from the Ricci tensor of a semi-symmetric connection. The field equations have the same general character as those of the Born-Infeld electrodynamics and its generalization by Hoffmann and Infeld. The theory presupposes the existence of a fundamental length of the order of magnitude of the electron radius. The Einstein-Maxwell equations are obtained from a special choice of the action function.

The correlations between the displacements and momenta of atoms in a crystal near a point defect are calculated using the method of double-time thermal Green's functions. As a simple example, the mean square displacement and momentum of an atom of different mass in a cubic crystal are found to confirm earlier derivations by different techniques. The scattering of lattice waves by impurities is also calculated by the same technique in a simple case. Resonant scattering is found under certain conditions, and this may have a marked effect on the thermal conductivity of insulating crystals. A comparison is made with experimental results on KCl containing iodine impurities. The effect of Sn impurities on the thermal conductivity of Si is predicted.

X-ray diffraction studies on the crystal structure of copper ammonium chloride dihydrate, carried out by Hendricks and Dickinson and Chrobak, suggested different probable structures instead of a single unique one. With a view to find out the correct structure, the principal g factors are theoretically calculated for each of these structures on the basis of a point charge point dipole model. Comparison of the calculated values with values obtained experimentally clearly indicate that only one of the proposed structures, the one which is closely similar to the established structure of the isomorphous potassium salt, gives values agreeing with experimental observations, while a wide disagreement is evident in the case of the other structures.

When resonance fluorescence is excited in atoms whose excited states have Zeeman or hyperfine structure, it is to be expected that the character of the fluorescent light will be affected if the intensity of the exiciting light is modulated or pulsed. An earlier theory of resonance fluorescence is developed to take account of such variations of the intensity of the exciting light. Resonance effects are predicted if the light is modulated at a frequency which coincides with a characteristic frequency of the atoms. A particular case, which has been studied experimentally, is worked out in detail. If the exciting light is pulsed, the prediction is that the fluorescent light will be modulated, in addition to being damped at the ordinary rate for spontaneous emission.

A type of double resonance experiment is reported in which resonance fluorescence from an atomic vapour is excited by modulated light. The amplitude of modulation of the fluorescent light undergoes changes which indicate an atomic resonance when the frequency of modulation is equal to the Larmor frequency of the atoms in an applied magnetic field, or equal to twice that frequency. The effects have been studied in the intercombination line, λ 3261 Å, of cadmium. They are in good agreement with theoretical predictions.

The method could be applied to the spectroscopy of excited atoms.

Infra-red Faraday rotation has been measured in n-type AlSb giving a value of the electron effective mass m* = 0.39±0.03 m₀. Experimental curves showing the rotation due to the subsidiary absorption bands at 4.3 and 3.0 μm in n-type AlSb and GaP, respectively, are given. These provide evidence for rejecting the postulate that a deep donor level causes this excess absorption.

Measurements of interband Faraday rotation in GaP for wavelengths between 0.5 and 5.0 μm are compared with theoretical results. They show that the contribution of the fundamental indirect edge predominates, and give an effective g factor of +15 for this transition.

Cross sections for the formation of a positronium atom in the ground state by positrons in atomic hydrogen are calculated in the Born and impulse approximations in the energy range 10 ev to 500 ev. Although the total cross sections predicted by these approximations are similar at high energies it is found that their angular distributions differ considerably.

A study has been made of the production of evaporation neutrons in the interactions of cosmic ray protons with lead nuclei. For the thick target used the mean number of neutrons produced (the mean `multiplicity') increases from 10 to 100 over the range of energy 0.2 to 200 GeV.

At low energies, not greater than about 0.5 GeV, there is good agreement with the mean multiplicities computed by Metropolis et al. in 1958, but, as the energy increases, the observed multiplicities fall increasingly below expectation. At the highest energies, not less than about 10 GeV, there is evidence for a flattening of the multiplicity variation and the results are not inconsistent with a variation of the form expected from the Heisenberg model of the nucleon-nucleon collision.

A study has been made of the production of evaporation neutrons in the interactions of fast negative muons from the cosmic radiation in lead. The detected neutrons arise from the direct electromagnetic interaction of the muons with lead nuclei and the interaction of photons from cascades initiated by knock-on electrons. The measured value of the product of the cross section per atom and mean neutron multiplicity divided by A, σv/A, is found to increase from 10 to 200, ×10^-29 cm² per nucleon, over the range of muon momentum, 1-100 GeV/c.

The measured values of σv/A are close to those expected on the basis of the Williams-Weizsacker treatment as given by Heitler but the results cannot be regarded as inconsistent with other recent evaluations in view of the uncertainties in the measurements.

The conclusion is drawn that there is no evidence for any marked anomaly in the behaviour of the muon in interactions in which neutrons are produced.

Ionization currents between parallel plates are subject to statistical fluctuations owing to the current development being a statistical process. The theoretical study of these effects presents a number of statistical problems, and some of these problems have been treated by Legler. The present paper treats some of the remaining problems: namely, the statistical scatter of the current, at any time, due to an initial flash illumination (which liberates a statistically distributed number of electrons); the statistical scatter of the current, at times less than the electron transit time, using maintained illumination; the rapidity of the fluctuations, at large times, using maintained illumination and a potential less than the sparking potential; the probable time for the occurrence of a spark, due to statistical fluctuations, using maintained illumination and a potential less than the sparking potential.

A discussion is presented of the so-called precursor effects which occur in intense electrical discharges in gases. These phenomena embody the observation of the growth of electron populations in regions remote from the main discharge. The name `precursor' stems from the observation of electron growth ahead of intense electrically driven shock waves. This paper presents two possible theories of the phenomenon, one which discusses the photoionization effects induced by the discharge acting as a radiation source and the other which discusses the electric field effects remote from a typical azimuthal type discharge. The relative merits of the two approaches are discussed and a comparison is made with recent experimental work.

Processes involved in electrical breakdown at residual gas pressures of the order of 10^-5 mmHg (so-called vacuum breakdown) are discussed, and an experimental investigation using uniform fields is described. The initiatory electron emission from heat-treated electrodes of gold and of nickel in the presence of nitrogen (p similar 600 mmHg) was measured using a time-lag technique, and the total gap current between the same electrodes in vacuo (p similar 10^-5 mmHg) was measured by means of an electrometer. The observed initiatory currents were found to be in the range 10² to 10⁵ electrons/sec, and were field dependent over the range 4 × 10⁴ to 9 × 10⁴ v cm^-1 investigated, but the dependence was not in accordance with the Fowler-Nordheim or Schottky-Richardson relationships. The cathode emission currents are considered to be important in initiating the process of vacuum breakdown. The role played by gas layers adsorbed on the electrodes in causing breakdown of the gap is then discussed. It is concluded that the amount of gas evolved from the electrode surface under bombardment by pre-breakdown currents in many cases can permit gas-amplified ionization eventually to produce breakdown.

The variation of the electronic transition moment with internuclear separation for the NO β(B²II-X²II) and NO γ(A²Σ⁺-X²II) systems inferred from available intensity measurements is used to evaluate band strengths and band absorption oscillator strengths. It is doubtful whether the concept of an electronic oscillator strength for the whole system is meaningful for these transitions.

The response of a ⁶LiI(Eu) scintillation spectrometer as a function of temperature has been investigated down to 77 °K. As previously observed the resolution to fast neutrons improves at lower temperatures. The pulse height from neutrons increases with fall in crystal temperature and reaches a maximum at about 120 °K. Murray and Meyer's model proposed in 1961 of the luminescent process in ionic crystals has been extended to explain this behaviour in terms of electron traps. This explanation is further supported by an observed increase in efficiency of the phosphor to α particles relative to tritons, and neutrons relative to gamma radiation, and also by the response of the crystal as a function of neutron energy at room temperature and liquid nitrogen point.

The critical magnetic field of a Pippard superconductor is derived from the microscopic theory in a manner more satisfactory than the usual one. The free energy of the normal state only in magnetic fields above the supercooling one is used. At the same time the supercooling field is calculated from a consideration of the stability of the normal state. The result agrees with that obtained earlier by Gor'kov from a calculation based on a microscopic derivation of the Ginsburg-Landau theory.

The concentration dependence of the lifetime of minority carriers in copper-diffused germanium is explained quantitatively. The fit yields an Auger effect mass-action constant which is shown to be in order-of-magnitude agreement with theory.

This letter establishes the non-existence of any physically acceptable solution of the Einstein-Maxwell equations which can be identified as that of a charged infinite cylinder with a radial electrostatic field.

Rotational analyses have been made of three bands of a system of S₂ observed in emission between 2600 Å and 2900 Å. The transition appears to be ¹Δ_u-x¹Δ_g, where the lower state x is the ¹Δ_g state arising from the lowest electron configuration, and is tentatively identified with the state x previously observed in systems in the Schumann region.

An optical radio-frequency double resonance experiment on the level 5³P₁ of cadmium is described. Atoms in a static magnetic field and a field oscillating at about 2 Mc/s are excited by light modulated at 462 kc/s. Resonance effects in the fluorescent light are found when the modulation frequency is near the nutational frequency γ[(H - H₀)² + H₁²]^1/2.