Table of contents

The exact static exterior and interior solution of Einstein's equations for a plane thick disk is obtained. It has been shown that the corresponding energy-momentum tensor fulfils the generalized O'Brien-Synge junction conditions. The correspondence of this tensor to the surface energy-momentum tensor of a thin plane plate is demonstrated. The disk being neither very thick nor very dense, a connection with the Newtonian theory has been obtained.

The dynamics of a neutral particle is examined from the viewpoint of the theory of gravito-inertial fields. In particular, the concept of mass and the equivalence of the inertial and gravitational mass of a body are analysed here in more detail, suggesting a special mass structure for a fundamental particle. In close parallel with the treatment by Rohrlich (1960) of the Abraham-Lorentz theory of the electron, it is shown that the field equations lead to the correct relativistically invariant energy and momentum relationships.

A method is developed for the derivation of general relativistic Lagrangian functions of 'Bose' fields. The method consists of the solution of some functional equations which are based only on the requirements of general covariance. The most general exact solutions of the 'strong' equations are derived.

Hegerfeldt and Kraus's criticisms (see abstr. A42300 of 1968) of Aharonov and Susskind's discussion (see abstr. A27919 of 1967) of the above question are investigated. It is shown that the rotation operator applied to a wave function can be equivalent to solving Schrodinger's equation if gravitational fields are present. The specific example of quantum mechanics on a cone is considered in detail.

It is shown that Dirac's equation for a particle of spin one-half in de Sitter space can be derived by the use of a simple group-theoretic argument. The significance of this is discussed.

A generalized Prufer transformation is used to derive comparison and oscillation theorems for the matrix Sturm-Liouville eigenvalue problem. It is shown in particular that if the eigenvectors are required to vanish at one (at least) of the end points, then the eigenvalues are uniquely characterized by the number of points (termed focal points) at which a certain determinant (of linearly independent solutions each satisfying the other boundary condition) vanishes. Simple but effective computational procedures based on this analysis are suggested, and their use is illustrated by a single-centre calculation on the 3s sigma state of the hydrogen molecular ion.

The Schwinger variational principle, together with arbitrary trial functions, is used to derive exact expressions for the scattering amplitudes arising in multichannel scattering by separable non-local interactions.

Complementary variational principles are developed for ground-state wave function corrections which are induced by frequency-dependent perturbations. These principles lead to upper and lower bounds for dynamic polarizabilities which are either measured at real frequencies less in magnitude than the first excitation energy, or measured at any imaginary frequencies. In the latter case there is a choice of upper bounds, different forms being suited to small and large frequencies. Illustrative results are presented for the hydrogen atom, and reasonable accuracy is obtained with simple one-parameter trial functions.

Canonical formalism, including Hamilton's equations, transformation theory and Poisson brackets for classical field theory with higher time and/or spatial derivatives, is established.

The field near a line focus is developed in cylindrical coordinates, and the result is expressed in a series expansion readily applicable to scattering by an infinite cylinder. The properties of a line focus are found to be similar to those of a point focus. Scattering by metal cylinders is discussed, and it is shown that scattering of focused waves can be obtained by a simple modification of the existing theory for plane-wave scattering.

Thermodynamic Green function techniques are applied to the Compton scatter of photons by electrons in a hot plasma. An expression is obtained for the scattering rate, including relativistic effects but neglecting coupling to ions or other electrons; this restricts the formula to high-energy photons and non-zero scattering angles. The method of calculating explicit cross sections is illustrated by deducing the known result for Doppler-broadened scattering from free electrons in the non-relativistic case.

The plasma perturbation in the presence of a high-frequency electromagnetic field is represented by a Maxwellian distribution function. The electron energy gained in the plasma in the presence of the applied electromagnetic field is calculated from the Boltzmann transport equation. The variation of electron energy with the duration of the field is calculated. It is shown that the electromagnetic field interaction with an extended plasma results in a steady-state electron temperature. The time for the electron temperature to reach the steady state is found to depend on the electron collision frequency.

Using a new device for extensive air shower core localization consisting of four sets of Conversi neon detectors of total area 9 m² (comprising 36000 neon tubes), cores have been located with high accuracy and the lateral muon distribution and density have been measured for a threshold energy of 0.6 GeV. The interpretation of the shape of this distribution is discussed and compared with theoretical calculations. As the muon lateral distribution is mainly determined by the angles of emission of parent pions, some features of the distribution of transverse momenta p_t of pions produced in air can be analysed. For low p_t values a discrepancy is found with the Cocconi empirical p_t distribution which comes from accelerator data. A flattening of the muons' lateral distribution near the shower axis is interpreted as being due to a lack of small p_t values.

Three-dimensional Monte Carlo calculations have been performed on the development of the hadronic component of extensive air showers using a semi-empirical model of high-energy nuclear interactions. Results include integral energy spectra and lateral distribution of nuclear active particles as well as total hadronic energy flux. The probability of multi-core showers is discussed. The contribution of pionization tends to mask the dependence of this probability on primary atomic number. Fluctuations of total and central hadronic energy flux are investigated. Maps of hadronic energy flux in the core region of individual showers are presented.

For Pt. II see abstr. A15896 of 1968. A theoretical analysis has been made of the muon component of extensive air showers incident at large angles to the vertical. Using the model described previously, calculations have been made of the expected numbers of muons reaching ground level as a function of threshold energy and zenith angle for primary particles of various energies. The data have been combined with alternative primary spectra of cosmic rays, with and without an enhanced contribution from heavy nuclei, to give the expected muon density spectra. It is found that the density spectrum is sensitive to the distribution of transverse momentum among the parents of the muons and to a lesser extent to the mass composition of the primaries. There is thus the possibility of deriving information about the mean transverse momentum, and perhaps setting limits on the mass composition, from a comparison with experiment.

A large vertical array of muon detectors has been used to measure the frequency of multiple muons from extensive air showers as a function of zenith angle over the range 30 degrees -85 degrees . The experimental data have been compared with the predictions of the theory developed by de Beer et al. (see preceding abstract); accepting the values of the parameters used in this theory it is concluded that there is no evidence for a large increase in the relative flux of heavy nuclei in the energy range 10¹⁵l10¹⁷ eV. If all the other parameters but the mean transverse momentum (p_T) are assumed to be known, the data suggest a mean value of (p_T) increasing from 0.37 GeV/c to 0.44 GeV/c as the interaction energy increases from 200 to 3000 GeV.

Data gathered with the University of Utah neutrino detector during late spring and summer of 1967 were used to study penetrating muon showers. These downward-going events contained two or more nearly parallel muons incident in a range of zenith angles between 30 degrees and 75 having penetrated from 1500 to 6000 hg cm^-2 of rock overburden. Studies were made to determine the radial extent of the showers, the frequency of occurrences of showers of each multiplicity, and the degree of isotropy of the arrival directions of shower events was plotted in celestial coordinates, with the result that these shower events could be characterized by a radius of 6 to 10 m, a multiplicity spectrum which is a power law in multiplicity having an exponent between -3.4 and -4.0 and no observable anisotropy. These shower data, together with measurements of events containing a single penetrating muon, were used to derive an empirical shower density function that accounts for the energy and angular dependence of the events of multiplicity 1, 2 and 3, as well as the absolute numbers of these events observed.

The 0.87 keV K electron capture peak of ²²Na has been observed using an internal source, scintillation counter technique. Direct measurement of the K/ beta ⁺ ratio was therefore possible: the result obtained was K/ beta ⁺=0.105+or-0.009. A review is given of recent precise results of the total capture to positron ratio (e/ beta ⁺) in ²²Na and the interpretation of these experiments is discussed. In conclusion, it is shown that the correction for electron exchange and overlap effects to the K/ beta ⁺ ratio has a smaller effect than has been supposed for low atomic numbers and that it is impossible to deduce an estimate for the Fierz interference term b from K/ beta ⁺ or e/ beta ⁺ measurements on light isotopes.

The absorption and refractive index increments due to continuous distributions of resonances have been calculated for both Debye-type distributions and for distributions Gaussian in logarithmic frequency. Comparison of the results with the available experimental data shows that it is not possible to discriminate between the two types of distribution, but suggests that the damping constant of the individual resonances must be of the order of unity.

There the theory of the excluded volume effect for a polymer chain is given. The mutual interaction of the monomer units is approximated by the repulsive potential of hard spheres. In a single-contact approximation formulae were obtained, for small volume effects, which were identical with the Fixman perturbation theory of the first order. The theory can be extended, in principle, to models of a chain with a larger number of contacts.

The analogue of a theorem of Van Vleck on the spectrum of clipped noise is formulated for use in optical spectroscopy.

This latter presents spectral decompositions (in the Dirac formalism) of certain functionals which are useful in finding approximate estimates, through the calculation of rigorous lower and upper bounds to the true value, of some quantum-mechanical sums.

Conditions behind the incident and reflected shock wave in a shock tube are calculated from the initial conditions of pressure, density and temperature, together with the known speed of the incident shock wave. In this method the enthalpy of the gas is regarded as consisting of two parts: (i) the enthalpy evaluated for a gas consisting of molecules having no internal excitation and (ii) a correction term to be added to (i) to take account of internal excitation. An iterative solution to the flow equations for incident and reflected shock waves based on this correction term is obtained. Results for carbon monoxide are given in graphical form.