Table of contents

A shell model study of the even parity levels of ¹⁸O and ¹⁸F is made in the light of much recent data. Particular attention is paid to the sensitivity of the results to assumptions regarding the exchange mixture and the shell model potential. Overall agreement with experiment is reasonable. Even when allowance has been made for collective enhancement, however, difficulties remain in understanding certain E2 transition probabilities. A 3⁺ level is predicted in ¹⁸O at an excitation energy of around 5 MeV.

Estimates are made of the error involved in the usual deuteron stripping calculation, which proceeds by means of the `zero-range approximation'. The finite-range effect may be simulated by maintaining the form of the zero-range calculation, but by multiplying the wave function of the captured neutron by a simple factor involving the optical-model potentials of the proton and deuteron, the potential describing the neutron binding and the binding energy of the deuteron. Numerical calculations, referring to the reactons ²⁴Mg(d, p)²⁵Mg, and ⁵²Cr(d, p)⁵³Cr, show that the effect on the angular distribution is very small.

Two alternative procedures are used to calculate the three-nucleon stripping cross section. In the first approach harmonic oscillator wave functions are used to describe the bound states of the captured nucleons. In the second approach the overlap integral is expanded in terms of a complete set of harmonic oscillator wave functions. The final formulae are obtained both with and without the introduction of the surface assumption. The surface formulae are similar to those derived before. The non-surface formulae are compared with some experimental data and satisfactory agreement is observed.

The interaction energy of a hydrogen and a helium atom in the ground state has been calculated for internuclear distances in the range 0 to 1 A.U., using a two-configuration molecular orbital wave function. The coefficients E₂ and E₃ in the expansion E₀ + E₂R² + E₃R³ +..., for the electronic interaction energy at small R, where R is the internuclear distance, have been calculated for the ground states of H + He, He + He and H + H, using formulae given by Bingel. These formulae involve the electron charge density of the united atom, and for each system several different wave functions were used to derive E₂ and E₃, and the resulting ratios compared with another formula derived by Bingel. A recent analysis by Brown and Steiner suggests that Bingel's expression for E₃ should be doubled, and the fitting of the molecular orbital energies calculated in this paper tends to support this conclusion. For H + He and He + He a fitting of the energy has been made for the range of R from 0 to the zero of the interaction energy, using calculated energies at small R, the calculated value of E₂, the experimental energy of the united atom and results derived from the scattering experiments.

The present paper derives conditions on which the Boltzmann equations for electron-phonon systems (two coupled equations) can be derived without the use of the objectionable random phase approximation. The treatment uses von Neumann's density matrix based on the Hamiltonian introduced some time ago by one of us in connection with superconductivity. Formally exact expressions for the rate of change of coarse-grained one-particle distribution functions are derived. They become identical with the collision terms in the Boltzmann equations if (i) the influence of an external field on them is negligible, (iia) particle correlation is absent at an initial time, and (iib) the relevant series in terms of the interaction parameter converges and is at all times dominated by a certain term. (iib) excludes the possibility of extensive correlations as they occur in superconductivity.

It is shown how the usual theory of phonon interaction may be extended to cover the case of one phonon having a wavelength larger than the mean free path of those with which it interacts. The results are applied to a consideration of the absorption of sound in dielectrics at arbitrary temperature.

Measurements have been made of the line width, intensity and shift of the ⁵¹V magnetic resonance from vanadium metal over the range 25-330 °K. The absence of any detectable anomalies in these properties shows that the transition at around 250 °K cannot be associated with the occurrence of antiferromagnetism unless the fluctuation frequency of the internal magnetic fields exceeds 2 × 10¹² c/s. From consideration of nuclear electric quadrupole interactions, it is estimated that any deviation from cubic crystal symmetry at or below the transition point is less than 2 parts in 10³. The Knight shift increases from 0.571% at 25 °K to 0.580% at 330 °K with an accuracy to ±0.001%. From a comparison of the temperature dependence of Knight shift and magnetic susceptibility, the hyperfine field at a vanadium nucleus due to one d-electron spin was estimated to be -112 ± 17 kilogauss.

The dipole approximation given by Seaton in 1962 is used to calculate cross sections for n → n + 1 transitions in hydrogen produced by electron impact. Results are tabulated for 1 ⩽ n ⩽ 40. It is found that the results differ significantly from those obtained by Gryzinski in 1959 using classical theory. It is believed that the dipole approximation gives the more reliable results.

Sound absorption measurements have been made in oxygen-helium, oxygen-hydrogen and oxygen-deuterium mixtures to investigate the effect of light impurities on the collisional de-excitation of vibrationally excited oxygen molecules. The results are compared with the theory of Herzfeld and Litovitz and it is found that the calculations overestimate the efficiency of the impurity in all cases. Possible reasons for the discrepancies are discussed.

The distribution of the number of photoelectrons counted when partially polarized Gaussian light falls on a photosensitive surface is derived by the methods of Kac and Siegert. When the counting time is much longer than the coherence time of the light, the distribution is approximately the same as that of n bosons assigned to two sets of s states each, corresponding to beams of relative intensities ½(1 + P) and ½(1 - P), where P, 0 <or= P <or= 1, describes the state of polarization of the light, and s is the ratio of the counting time to the coherence time of the light.

An analysis is made of the interaction between cold streams of charged particles flowing along a uniform, steady, magnetic field. The special case is considered of plane waves propagating along the field, when the dispersion equation always separates into two transverse modes and a longitudinal mode. Resonance between transverse waves and the gyromotions of the streaming particles results when the particles observe the wave to have a frequency equal to their gyrofrequency. Under such conditions `cyclotron' instabilities may arise. It is shown that wave amplification from convective instabilities is possible if the stream velocity is in the same direction as the group velocity, but greater in magnitude than the phase velocity, of the transverse waves which propagate in the ambient medium. Results are applied to particle streams in the exosphere of the earth, and it is concluded that noise in the very low frequency range will be amplified by ion streams in the presence of ambient electrons, or by electron streams in the presence of ambient protons. For slow streams (V/c < 1/50) the amplified frequencies will have a narrow bandwidth centred close to the gyrofrequency of the ambient particles.

A scanning Fabry-Pérot interferometer has been used to record the profiles of hydrogen and helium lines emitted by the plasma produced in a critically damped Z pinch. Individual line profiles were recorded in less than one microsecond while many profiles of the same line were recorded in successive time intervals during the course of a single discharge.

Broadening of the lines was caused mainly by plasma microfields and so interpretation according to Stark broadening theory has led directly to the electron density. Results obtained with the Fabry-Pérot interferometer have been compared with those obtained with other diagnostic techniques over the range 10¹⁴ <or= ne <or= 10¹⁷ cm^-3.

The theory of equilibrium black body radiation has been applied to an anisotropic medium, together with a special application to a magnetoionic medium. Numerical results are presented in a curve showing the angular spectrum in the `whistler mode' where X = 4, Y = 9 in the usual notation of magnetoionic theory. The flux per unit solid angle and unit frequency interval varies inversely as the Gaussian curvature of the wave vector surface. A discussion is given of singularities where the curvature vanishes; the integrated flux is finite. Finally Liouville's theorem and the Poynting identity are compared and their extension to non-equilibrium theory (radiation transfer) indicated.

In this paper the spectrum of radio-frequency radiation from a fully ionized ion-electron plasma is calculated, starting from the dependence of the dipole moment on the particle-particle Coulomb fields. These Coulomb fields are shielded according to the usual dielectric constant theory. The acceleration of a particle by others of like species gives rise to quadrupole radiation only; thus the second derivative of the dipole moment depends on the sum of ion-electron forces. It is simplest to find the total force acting on each ion due to all the electrons, and then to sum over the ions. Ion-ion correlation may be allowed for readily.

The final result agrees with calculations made by Dawson and Oberman and others whose approach was via the absorption coefficient and Kirchhoff's law. The present approach is rather simpler.

The three-photon coincidence method has been used to study orthopositronium formation and quenching in argon, nitrogen, oxygen and mixtures of these gases. Quenching rates were found to be proportional to pressure for all gases and gas mixtures, except commercial grade argon. Oxygen-argon mixtures showed a 20% increase in positronium formation for oxygen concentration of the order of 10 parts per million. An increase of about 50% in the formation fraction was obtained for nitrogen-argon mixtures for nitrogen concentrations of about 10%.

A uniform quenching rate was found for oxygen-argon mixtures containing up to 0.1% oxygen, and for nitrogen-argon mixtures containing up to 10% nitrogen.

The positron lifetime method has been used to study orthopositronium formation and quenching in argon, nitrogen, oxygen and mixtures of these gases. Quenching rates were found to be proportional to pressure for all gases and gas mixtures, except commercial grade argon. Highly quenched orthopositronium lifetimes were observed in pure argon and the formation fraction of positronium was estimated as 0.40±0.04.

The quenching rate in oxygen was found to be (2.3 ± 0.3) × 10⁷ sec^-1 atm^-1. This rate holds for oxygen concentration greater than 2% in oxygen-argon mixtures. A constant quenching rate (2.51 ± 0.05) × 10⁵ sec^-1 atm^-1 was obtained for lower oxygen concentrations; this rate is not significantly different from the quenching rate (2.42 ± 0.07) × 10⁵ sec^-1 atm^-1 obtained for nitrogen-argon mixtures containing less than 10% nitrogen.

The Durham cosmic ray spectrograph has been used to measure the momentum spectrum of cosmic ray protons in the vertical direction. The protons were detected by two methods: absorption in lead and neutron production in an I.G.Y. neutron monitor.

The ratio of the proton intensity to the muon intensity is found to fall with increasing momentum from 6% at 0.7 GeV/c to about 0.4% at 80 GeV/c.

Recent measurements of the sea-level spectra of cosmic ray protons and muons have been used, together with a trial spectrum of primary nucleons, to derive values for the nucleon inelasticity K_t and the fraction of energy passed on to the pion component K_π in nucleon-air-nucleus collisions. It is shown that the values of K_t and K_π are not very sensitive to the model assumed for the collisions, and the effect of fluctuations in the values of K_t and K_π from one collision to the next is found to be small.

Assuming a value for the difference K_t-K_π based on the results of other experiments (approximately 0.12) it is possible to estimate the energy spectrum of primary nucleons in the range 10¹¹-10¹⁵ ev/nucleon. When recent geomagnetic measurements are added, the integral spectrum is found to be represented by the expression I(>E) = 0.87^+0.52_-0.30E^-1.58 cm^-2 sec^-1 sterad^-1 over the range 10¹⁰-3 × 10¹³ ev/nucleon, where E is expressed in GeV. At higher energies the exponent increases reaching a value of about 2.1 in the region of 10¹⁵ eV.

It K_t-K_π is less than 0.12 the primary intensity is reduced; in the limit, with K_t-K_π = 0 the intensity is reduced by a factor of approximately 1.5.

The momentum spectrum of negative pions in the vertical direction has been measured using the Durham cosmic ray spectrograph in conjunction with an I.G.Y. neutron monitor. Pions were detected by means of their interaction and subsequent neutron production in the monitor.

The ratio of the intensity of charged pions to charged muons is found to vary slowly with energy, being in the range 0.1-0.2% in the region of energy studied.

The pion spectrum has been taken with the energy spectra of protons and muons to give the attenuation length for pions in the atmosphere. This quantity falls from about 160 g cm^-2 at 1 GeV to 110 g cm^-2 at 100 GeV; the corresponding inelasticity of pion-air-nucleus collisions increases from 50% to 100% over the same energy range.

Emission spectra in the region 5200-4800 Å have been excited in a vacuum arc and a stabilized plasma jet. A vibrational analysis of the B ¹Σ-x ¹Σ system has been made and molecular constants for the isotopic molecules are given. The emitter is certainly MgO and the analyses of Mahanti and of Lagerqvist and Uhler are confirmed.

The results of electron diffraction studies on deuterium previously reported by Curzon and Pawlowicz are withdrawn.

The results of subsequent studies suggest that solid deuterium has a face-centred cubic structure with four molecules per unit cell and a lattice parameter a₀ = 5.07 ± 0.02 Å at about 7 °K.

A number of band systems attributed to ScF have been observed both in absorption and in thermal emission at high temperatures (similar 2000 °c). Rotational analyses have been made of bands of four singlet systems. These systems all appear in absorption, and the lower state × ¹Σ is probably the lowest singlet state of ScF. Bands of more complex appearance, perhaps arising from triplet transitions, are also observed in absorption, so that the nature of the ground state is not yet established. The value of the internuclear distance r₀ in × ¹Σ is 1.791 Å.

A correction factor to compensate for back-diffusion of electrons in cylindrically symmetrical systems is deduced, and its effect on the results obtained from an earlier calculation is discussed.

Corrections to 1964 Proc. Phys. Soc.83 71.