Table of contents

The theory developed by Andrews and Swift-Hook for a spherical probe in a flowing plasma can be applied to a cylindrical probe. As with a sphere, a stagnation point forms downstream and there is a small change in floating potential and in ion saturation current. These changes are smaller than for a sphere and opposite in sign; it might just be possible to obtain some indication of the flow velocity from them. Apart from this, existing low pressure, subsonic probe theories are substantially correct numerically.

Results are given of an investigation into an electron avalanche produced by microwaves at the electron cyclotron resonance frequency in the presence of crossed electric and magnetic fields.

A comparison of the ion acoustic instability with the E*B electron drift instability leads to predictions concerning observations of enhanced fluctuations in perpendicular collisionless shock waves.

The magnitude of the electric charge of sea level cosmic ray particles producing energy transfers greater than or approximately equal to 25 GeV in a 22.9 cm thick steel target have been measured. The charge distribution shows a peak at the electron charge and an apparent high charge tail. Spurious effects contributing to the high charge tail are knock-on electrons, and nuclear interactions in the proportional counter walls, which are used to measure the charge. The limit obtained on the flux of 4e/3, 5e/3 and 7e/3 quarks is less than 8.2*10^-10 cm^-2s^-1sr^-1.

It is suggested that coherent production of pions in pion-air nucleus interactions is responsible for the bundles of muons observed in extensive air showers.

Under the assumption that cosmic rays are of extragalactic origin above 10¹⁸ eV it is shown that the presence of the 2.7K black body radiation may lead to a detectable flux of very energetic gamma rays.

The analytic representation of quantum field theory suggested in a previous paper by Valatin and the author (see abstr. A 22494 of 1969) is further investigated, by working out its details for quantum electrodynamics. The coupled equations for Green's functions are discussed and the lowest order contributions to Compton and Moller scatterings are calculated. Through the Fourier transforms, the expressions show close agreement with the results of the conventional approach. A nonlocal modification of the interaction kernel is studied. This leads to finite self-energy, vacuum polarisation and vertex operator expressions, and in the limit, to a simple regularization of quantum electrodynamics.

Approximate iterative solutions to the Born-Infeld nonlinear electromagnetic equations are developed in flat space-time. Incoming radiation terms, or wave tails, are shown to arise from the iterative correction of initially purely outgoing approximate solutions.

The tensor identity alpha . curl alpha . curl F= mod alpha mod (grad div alpha ^-1. F-div alpha ^-1. grad F) where alpha is a constant and nonsingular matrix and F is a properly regular vector field, is derived and used to discuss the analogies between second order equations for fields in an anisotropic medium and the Helmholtz equation. The scalar equation for fields in uniform media is also considered; it is shown that this equation is of fourth order for plane waves in an unbounded medium it is reduced to the generalized Fresnel equation.

It is shown that no non-flat empty space-time can be embedded locally and isometrically in a five-dimensional space of nonzero constant curvature.

Conditions for the existence of a neutrino field are expressed in terms of spin coefficients. It is shown that a neutrino-gravitational field with positive energy density necessarily defines a null geodesic congruence. The structure of the Ricci tensor is examined and shown to be closely related to the twist and shear of the congruence.

The scattering of two charged particles by a separable nonlocal potential and a repulsive Coulomb potential has been studied. Exact expressions have been derived for the scattering amplitude and an equivalent local potential.

The problem of the alpha-particle S and D state binding energies is formulated in coordinate space and is followed by a variational calculation of the trial function (of the form (¹S₀+⁵D₀)) contribution to the binding energy of the alpha particle (BE(⁴He)) using a radial wavefunction. The calculation is based on the nuclear forces given by Omojola taking into account the effect of a 'hard core' on BE(⁴He). It is shown that by fixing the value of the variation parameter of ¹S₀ to the well-established value from the high energy e-⁴He scattering and by using a repulsive core of suitable radius given by Hamada and Johnston, the excessive binding obtained with two-body central potentials may be reduced to reasonable values. The results obtained are compared with those of other authors.

Recently derived formulae for the integrated intensity distribution, the photon-counting distribution and its factorial moments in the statistics of the superposition of coherent and chaotic multimode fields are proposed as approximate formulae for light of arbitrary spectrum. It is shown by explicit calculations of the third factorial moment for the superposition of a one-mode coherent field with a Gaussian-Lorentzian field that the proposed formulae hold with good accuracy over a wide range of conditions. An application to the determination of spectral parameters of light is given.

The threshold condition for the onset of amplified spontaneous emission is derived and experimentally verified in the 3.39 mu m He-Ne and the 0.614 mu m Ne systems. A short discussion is given concerning the confusion between this type of radiation and superradiance.

The authors present results of a Regge quark model fit to 2 body charge exchange and elastic O^-1/₂⁺ to O^-1/₂⁺ scattering. Both constant and exponential t-dependent residues are used; the latter giving the better description of the data.

A sample of 176723 single cosmic ray muon events, 2802 two-muon events, and 225 three-muon events have been collected and analysed to obtain muon rates adjusted for an equivalent detector having a constant normal area of 20 m². The measurements span the range of zenith angles between 40 and 70 degrees and slant depths of standard rock between 2*10⁵g cm^-2 and 6.5*10⁵ g cm^-2, corresponding to minimum muon energies at ground level of between 750 and 8000 GeV. A comparison of these measurements with those predicted by a conservative model based upon extrapolation from results at lower energies is given in the paper by Adcock et al. (see ibid. vol. 4, 276, 1971).

For Pt IV see abstr. A. 3283 of 1970. Previous calculations by the present group (Adcock et al. in 1969) have been extended to yield predictions of the frequencies of multiple muons in the comprehensive experiment of Cannon and Stenerson (see ibid., vol 4, 266, 1971). It is shown how comparison with experiment can give information about the magnitude of the mean transverse momentum (p_t) of the parent pions, the form of the multiplicity law and the magnitude of the primary cosmic ray intensity, all in the region of 2*10⁵ GeV primary energy. Comparison is also made with the previous experiments and the areas of agreement and disagreement are explored.

The authors attempt to prove the equivalence theorem for S-matrix elements. The dynamical aspect-which ensures that the dynamics is coordinate independent, and requires care in preservation of the order of non-commuting operators-and the kinematical aspect, which ensures that asymptotic fields are unchanged are distinguished. It is the latter condition which causes difficulty; whilst trivial for the free field the authors give non-trivial examples which violate it.

Upper and lower bounds on generalized scattering lengths for static potentials are presented. Their derivation is based on complementary variational principles for a certain class of linear operator equations. Generalized forms of the well-known bounds of Schwinger and of Spruch and Rosenberg are obtained from this approach together with related complementary bounds which are new. The results are illustrated with calculations for screened Coulomb potentials.

It is shown that there exist Einstein-neutrino fields which are not defined uniquely by the metric of space-time. These fields form a subclass of the neutrino pure radiation fields and are analogous to Peres' exceptional case for Einstein-Maxwell null fields.