Table of contents

Methods introduced by Edwards (1965) and de Gennes (1969) for the study of polymer configurations with excluded volume are applied to the case of a uniformly charged polyelectrolyte immersed in a 1:1 strong electrolyte of density n₀. The electrolyte is treated using the Debye-Huckel approximation and the following expression is obtained for the asymptotic mean square radius: R²=((5/3)( alpha / kappa ^2/3)(2 beta q²/3 alpha ))⁶5/N⁵ where N is the number of links in the polyelectrolyte.

A prescription is given for obtaining mixed multiple soliton and bisoliton bound state solutions of the sine-Gordon equation and of related equations in nonlinear optics. Some applications in nonlinear optics and other branches of physics are sketched.

The first excited state of ²⁶Mg was studied by inelastic electron scattering in the momentum transfer range 0.4 to 1.05 fm^-1. The reduced transition probability and transition radius were measured to be 275+or-20e² fm⁴ and 4.13+or-0.06 fm respectively. The reduced transition probability was found to be more accurate and of slightly smaller magnitude than existing experimental results. A Nilsson model form factor calculation was found to provide reasonable agreement with the experimental data.

Computer simulations of the optical Cerenkov emission from large cosmic ray showers indicate that the form of the lateral distribution of photons is sensitive to the longitudinal development of the electron cascade and so to the nature of the primary particle. The breadth of the computed distribution of photons, confirmed by measurements made at the Haverah Park air shower array, suggest the possibility of detection of the largest air showers widely separated, simple detectors.

The unitary irreducible representations of the group SL(2C) are studied by taking the coupled states of two angular momenta J₁ and J₂ as basis functions. The unitarity of the representations leads to unphysical values of j₁ and j₂ such that one of the quantities sigma =j₁+j₂+1 and j₁₂=j₁-j₂ is integral or half-integral and the other is purely imaginary or real. The formulae derived in this paper exhibit a beautiful symmetry with respect to the interchange of these two quantities. The basis functions are expressible in terms of terminating hypergeometric series and, by using the properties of the latter, the matrices of the generators and of finite transformations are easily determined. The matrix element of the 'boost operator' corresponding to a pure Lorentz transformation in the x₃-x₄ plane is found to take the form of a finite linear combination of ₃F₂ functions.

Only the well known relations between SU(n) and the n dimensional isotropic harmonic oscillator is examined and extended to show exactly which representations of SU(n) can occur on the degeneracy spaces. The method is further extended to show which representations of SU(n,1) can be generated by the oscillator problem.

A connection between the reality type of a group representation, and the symmetrized and antisymmetrized squares of that representation is noted. The correspondence leads to a simple reality test for space group representations. A detailed analysis reproduces the Herring test.

A development of R^lY^m_l( theta _R, phi _R) has been established in a series of products r^f₁Y^p_f( theta ₁, phi ₁)r^1-f₂Y^m-p_l-f( theta ₂, phi ₂) where (r₁, theta ₁, phi ₁), (r₂, theta ₂, phi ₂) and (R, theta _R, phi _R) are the spherical polar coordinates of the vectors r₁,r₂ and R=r-r₂. The expansion of 1/ mod r₁-r₂ mod as a series of spherical harmonics in ( theta ₁, phi ₁) and ( theta ₂, phi ₂) has been generalized for the case 1/ mod r₁-r₂ mod ^t, where t is an integer.

The theory of averaged lagrangians is extended to the case of lagrangians containing higher derivatives. The frequency equation and averaged stored energy of oscillatory systems are expressed in terms of the averaged lagrangian. The relation between averaged energy and the averaged hamiltonian is discussed and finally the analysis is applied to two well known mechanical examples and compared with the conventional approach.

A general theory is developed to study the effect of boundaries on the dispersion interaction between molecules in a bounded region. By way of illustration the method is applied to the study of the interaction between two oscillators located between two conducting plates. When the oscillators are separated by a distance larger than the plate separation the force law becomes considerably different from London and Casimir-Polder results.

The allowed electromagnetic modes in the presence of a symmetric array of macroscopic bodies are investigated. They are systematically classified by their behaviour with respect to the different symmetry operations. In the presence of two bodies the modes are required to be even or odd, in the presence of lattices Floquet's theorem is applied, The van der Waals (vdW) energy of the array under consideration is calculated from the average quantum energy of the electromagnetic modes. Since finite boundary conditions are used, no difficulties regarding branch points and different Riemann surfaces are encountered. Closed expressions for the vdW energy in periodic lattices of spheres or cylinders are obtained which can be explicitly evaluated at a reasonable rate of effort.

The motion of a macromolecule in a polymer melt is considerably restricted by interchain entanglements. This paper considers the topological constraints on the motion of a chain using the Wiener integral model. Two methods are considered: (i) a pipe constraint, (ii) the exact topological invariants. A Smoluchowsky-like equation is obtained by both methods and it is found that a point r(s,t) on the chain has a correlation function ((r(s,t)-r(s,t))²) varies as mod t-t' mod ^1/4 as opposed to the mod t-t mod ^1/2 dependence of a free Rouse-like chain. The type of diffusion considered is called cooperative diffusion and is contrasted to the reptative diffusion of de Gennes.

This paper continues the work of the authors on the effect of entanglements on polymer melt properties. The gaussian chain model is used, together with the pipe constraint previously discussed, to calculate the viscosity of the melt. This is done by employing a time correlation function which is derived from the Fokker-Planck equation of motion. The model predicts viscosity proportional to M, the molecular weight, below the entanglement point M_c, and M³ above M_c. This compares reasonably with the (M,M^3.4) dependence observed experimentally. It is speculated that the remaining discrepancy may be related to a critical index phenomenon.

Two-fold photoelectron counting statistics are studied for quasimonochromatic light of arbitrary spectral profile. A numerical scheme is developed for the evaluation of the double generating function from which the joint probabilities, the photoelectron correlation function, and the clipped photoelectron correlation function can be evaluated. The time need not be short compared to the coherence time as in previous studies. Numerical results are presented for the photoelectron correlation function and for the clipped correlation function for the spectrum which would be observed in a Brillouin scattering experiment.

A massive spin one vector field is quantized in the presence of an external potential, with source linear in the vector field, to provide an illustration of the aspects of a quantum theory in an external potential, which are reflections of the causal nature of the corresponding classical theory. In the examples considered, the S operator of the quantum theory is found to be Lorentz invariant or not, according as the corresponding classical theory is causal or not. The normal dependence of the interaction hamiltonian, and the applicability of the generalized Matthews' rule are also discussed.

Starting from a canonical quantum field theory model and imposing invariance of the theory under a group, acting nonlinearly on the fields, a group-invariant energy-momentum tensor of the Sugawara form is constructed which is free of ambiguities due to factor ordering and has the required properties.

The real Weinberg state method devised to calculate a suitable form factor of the resonant final state in a stripping reaction is applied to elastic resonance scattering of neutrons by ¹²C. The purpose is to establish the methodological accuracy of the theory. Some important adjustments to the theory are incorporated. The phase shifts of the different total angular momentum and parity (J^pi =¹/₂⁺,³/₂⁺,⁵/₂⁺) channels are compared with the exact solution obtained from a coupled-channel method. The agreement is generally satisfactory. The parameters of the resonances yielded by the respective methods are also compared. The Weinberg method describes the levels as mixtures of discrete configurations which are either BSEC (bound states embedded in the continuum) or single-particle resonances treated as Weinberg states. The wavefunctions of the respective methods are used as form factors in ¹²C(d,p)¹³C stripping calculations, again with satisfactory agreement. The role of Weinberg method as a schematic way of solving a coupled-channel problem is briefly discussed.

The mean heights of production of muons of various momenta in large air showers have been determined from measurements made with the Haverah Park magnet spectrograph of the lateral and angular scatter of muons from the shower core and the geomagnetic distortion of the muon charge ratio at various points in the shower front. The heights of origin of muons of momentum pGeV/c recorded at distances of r km from the core are given by: H(p,r)=H₀+ alpha lgp+r/ beta where H₀=1.68+or-0.15 km, alpha =1.74+or-0.20 km, beta =0.263+or-0.033.

The study of horizontal air showers (HAS) has been continued at Kiel with improved resolution in zenith angle determination. The zenith angle distribution of HAS is consistent with the sec theta distribution of muons in the size region between 2.5*10³ and 3.1*10⁴. The integral size spectrum is I(>or=N, >or=70 degrees )=(1.3+or-0.4)*10^-13(N/10⁴)^-2.4+or-0.2 cm^-2 s^-1 sr^-1 and is in agreement with the spectrum produced by muon bremsstrahlung as calculated by Kiraly et al. up to the shower size of 5*10⁴ within the experimental uncertainties. These results can be explained with the conventional model of muon production through pion decay (and to some extent through kaon decay) up to a muon energy of about 5*10¹³ eV. The number of muons observed in HAS is one order of magnitude larger than would be expected from the above bremsstrahlung hypothesis. The possibility of these muons being produced in HAS is discussed and methods of discrimination of remnant muons produced in EAS are presented. The upper limit of the flux of an isotropic component of muons or of heavy mass particles is discussed.

It is suggested that infrared radiation from the galactic centre is due to magnetic bremsstrahlung in intense magnetic fields from the non-degenerate layers of some white dwarfs.