Table of contents

The field equations of Bonnor's unified field theory have been considered to obtain the external field of a general nonstatic spherically symmetric isolated system containing electric and magnetic charges associated with matter. It has been found that there exists only one nontrivial solution and it represents a static isolated magnetic monopole.

The most recent Lorentz-covariant theory of gravitation is considered. It is shown how one could easily deduce this theory from Einstein's general relativity, so that agreement with the three celebrated tests follows as a trivial consequence, without need for calculations.

The similarity of Coleman's theory (see abstr. A66860 of 1971) to a special case of a class of theories presented by Papapetrou (1954) is discussed.

It is shown in a short note, that the expression derived by Mathur, Gupta and Sinha (see abstr. A.36132 of 1971) in their article entitled: 'Theoretical derivation of Wada's and Rao's relations' has been known for a long time. A short review of literature enclosed, makes possible the orientation in some problems related to the derivation and application of Kuczera's equation.

The historical development of those fields of physics investigated using storage rings is traced. The paper is divided into three parts. The first is the use of storage rings to investigate the validity of quantum electrodynamics. Second is their use in investigating vector meson dominance and lastly new aspects and preliminary results at high energy is given.

The solution of the gravitational field equations of general relativity is obtained for the metric field of a rotating rod. A Schwarzschildian correction term is found that represents a steady diminution of mass of the rod on account of the gravitational waves emitted.

The stability of static spherically symmetrical fluid spheres consisting of a core and an envelope, is investigated on the basis of general relativity. It is assumed that the core consists of ideal gas and radiation, in which the ratio beta of the gas pressure to the total pressure is a small constant, and that the envelope consists of an adiabatic gas. Numerical analysis indicates that for a given sigma =p_c/ rho _gcc² (the ratio of the central pressure to the central rest-energy density) the stability of such a sphere depends strongly on the position of the interface separating the core from the envelope, the sphere being stable for a greater range of values of sigma the closer the interface is to the centre.

The classical and quantal theories of angular momentum and spin are related using the spherical top as a model. The quantum mechanical spectral operator kernel of the spherical top is evaluated and expressed exactly as a sum over classical paths of terms containing the classical action. A relation between corresponding values of the classical and quantal angular momentum is obtained which holds for all values of the angular momentum quantum number.

Second quantization is used to expand the product of two harmonic oscillator wavefunctions, of two different particles, centred on different sites, in terms of relative and centre of mass coordinate dependent functions.

In a recent paper 'On Phythian's perturbation theory (see abstr. A.1292 of 1970) for stationary homogeneous turbulence' Lee (see abstr. A.18293 of 1971) claims to show that this perturbation theory requires a priori knowledge of the statistical distribution of the fluid velocity, and the assumption that this is gaussian. He also claims that the introduction of statistical elements into the dynamics in this theory is nonrigorous and that the derivation of the direct-interaction approximation by the truncation of the series involves the quasinormal hypothesis. These claims are disproved here and are shown to arise from a confusion of the actual fluid velocity with the gaussian velocity field on which the perturbation procedure is based.

The authors derive and test a simple approximate method for studying damped oscillations. The damping force as a function of velocity can be determined from measurements of the amplitudes of successive oscillations.

The analytic continuation of ₂F₁(a,b;1;z) into the region mod z mod >1 is derived by using a complex single loop Euler transform instead of the usual Mellin-Barnes transform This facilitates a general application of Nordsieck's technique, for the evaluation of space integrals over a product of Coulomb wavefunctions, in which single- loop Euler transforms of the ₁F₁ functions lead to considerable topological simplification. Due attention is given to the necessary phase specifications. The method is also contrasted with the single-loop Euler-transform derivation of the asymptotic expansion of ₁F₁(b:1:z) for mod z mod >>1, which follows Mott and Massey.

The interaction between a radiation field and a system of electrons in cyclotron motion in a homogeneous magnetic field is described from a quantum mechanical viewpoint. With high magnetic fields the interaction can give a means of far infrared detection and high resolution spectral analysis. the sources of fluctuations that limit the ultimate detectivity are discussed. It is concluded that this limit is set by background room temperature radiation fluctuations at a level of approximately 1.4*10^-16WHz^-1/2 when the interaction time is 10^-7s. With longer interaction times the limit of sensitivity may be well below 10^-16WHz^-1/2.

Kirchhoff diffraction theory is set up for the echo received back at the source when a spherical outgoing pulse of radiation is reflected from a rough surface. The formulation derived here permits a clear separation between those features of the echo that depend only on the form of the incident pulse, and those involving only the properties of the surface. The surface function depends on the contours of constant distance from the source which can be drawn in the surface; these are the appropriate analogues of Fresnel zone boundaries. Geometrical optics gives the singularities and discontinuities of the surface function. The problem of determining the surface function from echo data which are incomplete in the sense that they do not contain all radiation frequencies is discussed. For the special case of one dimensional roughness, the problem of how far the surface function can be deconvoluted to obtain the shape of the surface is considered.

The energy dependence and angular distribution of the sea level muon intensity have been determined from measurements made inside the second pyramid at Giza, Cairo. It is concluded from these measurements that the sea level muon integral spectrum may be represented in the energy range 50-70 GeV by the power law I(E, theta )=KE^-2.09(cos theta )^-0.02 where E is expressed in GeV, theta is the angle to the vertical and K is a constant. The above values of energy and cosine exponents are found to be in agreement with those calculated using the CKP interaction model if pions are assumed to be the parents of the majority of muons reaching sea level with energies in the range considered. Calculations made for various energies using this model also show general accordance with the experimental results of other authors. This indicates further support for the application of the model to primary interactions at high energies.

The mean lifetimes of levels in ²³Na, ²⁶Mg and ²⁶Al have been determined by the Doppler shift attenuation method. The levels were populated by the reactions ²³Na(p,p')²³Na, ²³Na ( alpha ,p) ²⁶Mg and ²³Na ( alpha ,n)²⁶Al at proton bombarding energies between 3.6 and 7.0 MeV and alpha particle energies between 4.6 and 7.5 MeV. The gamma rays were detected using a Ge(Li)-NaI(Tl) anti-Compton and pair spectrometer. A discussion of the rotational band structure of the levels in ²³Na below 5 MeV is given. The results for ²⁶Mg and ²⁶Al are compared with other recent determinations.

An attempt is made to assess quantitatively the dielectrophoretic force in liquids under the action of a nonuniform electric field. Applying 3 kV dc to two partly immersed electrodes of 0.13 mm radius, 1.3 cm apart, acetone would be pulled up to a height of 7.2 cm at the electrodes, if this phenomenon could be ascribed to dielectrophoretic force only.