Table of contents

Stoneham (see ibid., vol.3, L131-3, 1970) attempted to evaluate numerically the second order perturbation theory correction, delta ', to the ground state of a bound polaron. The author points out that Stoneham's numerical evaluation stars from a formula which itself is not exact, contrary to his implication.

A tunable infrared laser has been achieved using spin-flip magneto-Raman scattering in InSb. Dielectric coatings on the sides of the laser cavity gave the unexpected result of enhancing the collinear output up to a value of 10 W-a conversion efficiency approximately=1%.

The authors present a method for calculating the relaxation about lattice defects which avoids the very many computations of the energy which are usually required in such calculations. The energy of the crystal is minimized using a modified Newton-Raphson method in which the matrix of the second derivatives of the energy with respect to the relaxation coordinates is corrected after each iteration so that very rapid convergence is obtained.

Measurements of the static permittivity, epsilon _s, refractive index at the sodium D line, n_D, and permittivity and loss, epsilon ' and epsilon ", at wavelengths of 3.332, 0.848 and 0.435 cm have been made for chlorobenzene, bromobenzene, iodobenzene, nitrobenzene, quinoline, 2-chloro-2-methyl propane and chloroform at temperatures from 50 degrees C down to the freezing points. Measurements of epsilon ' and epsilon " at 0.848 and 0.435 cm have also been made for methanol and ethanol. The permittivity and loss measurements were made by the method suggested by Fatuzzo and Mason, using bridge arrangements at 0.848 and 0.435 cm and a standing wave method at 3.332 cm. Uncertainties in epsilon ' and epsilon " are about ¹/₂% and 1% respectively at 3.332 and 0.848 cm and about 1% and 2% respectively at 0.435 cm. It is demonstrated that the values for each liquid show deviations from a simple Debye type behaviour. The measurements for chlorobenzene have been reduced to 20 degrees C and plotted as a function of lg ( lambda _c/ lambda ), where lambda _c is the critical wavelength and lambda is the measuring wavelength, together with some infrared values.

The perturbation approach to the structure of a dense classical insulating liquid based on the random-phase approximation, although giving a good quantitative description of the low angle behaviour of the structure factor, fails at larger angles. A correction to the direct correlation function C(r) originally suggested by Woodhead-Galloway et al. is given which removes this shortcoming without affecting the low angle result. The theory is tested against the results of Verlet's molecular dynamics calculation on a Lennard-Jones fluid, and the agreement is rather good.

A restricted walk of order r is defined as a random walk in which polygons with r vertices or less are excluded. The sequence of restricted walks approaches a selfavoiding walk in the limit r to infinity . Although exact enumerations and Monte Carlo runs provide better data for numerical analysis, a study of restricted walks for increasing r provides an understanding of how the transition in properties is effected from random to selfavoiding walks. The eigenvalues of the transition matrix governing a restricted walk have been calculated up to r=7 for the triangular lattice and r=5 for the fcc lattice. It is found that the dominant contribution to the total number of walks comes from the largest eigenvalue lambda _1r which satisfies approximately the relation lambda _1r approximately= mu (1+g/r). Here mu is the selfavoiding walk limit and g=1/3 for the triangular and 1/6 for the fcc lattice.

The coupled Ising chain model for rare-earth systems with metal sublattice space group P6₃/mmc is extended to include larger clusters of chains. The specific heat is determined numerically as a function of temperature in the eight chain case by the transfer matrix method. Approximate analytical expressions are also derived using the high temperature series method. Good agreement with the experimental results for NdCl₃ is obtained.

The formalism developed by Fletcher (1967) to take account of the presence of short range order in the calculation of the electronic energy spectrum of amorphous covalent semiconductors is examined critically and found to have fundamental difficulties.

Previous experimental and theoretical work on thermal conduction in dirty type II superconductors is discussed with particular reference to possible effects of irreversibility on the theoretical models. Thermal conductivity and magnetization measurements have been made on a series of superconducting lead alloys. Mixed-state conductivity results cannot be explained in terms of existing models particularly for decreasing magnetic fields. It is shown that magnetic induction may be used as a parameter in describing the mixed-state conductivity for both increasing and decreasing fields even when specimens exhibit strong irreversibility. A model based on this observation is proposed. The theoretical results obtained are in good agreement with experiment for a wide range of alloy compositions, including those where there is a conductivity minimum, and for differing degrees of irreversibility.

The Baym-Kadanoff method for generating conserving approximations is generalized so that it may be applied to the drone-fermion representation of the spin ¹/₂ Heisenberg model. It is shown that the generalized procedure gives approximations in which the correlation functions preserve (i) commutation rules between spin operator components, (ii) conservation laws for the total spin, (iii) the relation between long wavelength longitudinal susceptibility and the field derivative of the magnetization, and (iv) the isotropy of the system in the paramagnetic phase in zero field. Moreover the approximate free energy is stationary with respect to variations of the Green function, and its derivatives with respect to external parameters are correctly related to the correlation functions.

A finite temperature perturbation expansion is employed to obtain an approximate description of the thermodynamic behaviour of a Heisenberg antiferromagnet for spin half. The calculations are carried out using the drone-fermion representation, and contributions are classified with respect to a high density parameter 1/z, where z is the number of spins interacting with any given spin. This leads to the results of molecular field theory in lowest order (1/z)⁰. The spin fluctuation effects, which are absent in molecular field theory, are introduced in higher orders. Calculations of the sublattice magnetization, free energy, and internal energy are carried out up to and including (1/z)¹. The results are valid provided the fluctuation effects are sufficiently small, which is the case for all temperatures below the Neel temperature T_N and also for higher temperatures if there is a suitable applied magnetic field or anisotropy field acting on the system. In a low temperature approximation the results are found to be consistent with linear spin wave theory, including zero point effects.

The correlation functions of a Heisenberg antiferromagnet are investigated. The method employs a drone-fermion representation for spin-half and a classification of terms with respect to a high density parameter 1/z. One- and two-particle correlation functions are evaluated up to order (1/z)¹ and their connection with the physical properties of an antiferromagnet discussed. This enables results with a determined range of validity to be obtained for the spin wave energy and damping, assumed small, as functions of momentum and temperature. The damping is found to increase with temperature, but is small for any temperature below T_N for sufficiently long wavelengths. This is similar to the result obtained for the ferromagnet by Vaks et al. The spin wave energy and damping can be deduced from neutron scattering experiments, and the theoretical predictions are found to be in good qualitative agreement with measurements obtained for CoF₂ and NiF₂.

The high density expansions derived for the thermodynamic quantities and correlation functions of the spin half Heisenberg antiferromagnet are extended to higher order, for the low temperature case. The (1/z)² terms in the sublattice magnetization, free energy and internal energy are evaluated and contact made with the interacting spin wave theory of Oguchi. The selfconsistency of the method in this order is demonstrated, and the criteria for the validity of the results determined. The spin wave damping in order (1/z)² is also investigated. This includes spin wave scattering contributions and gives the dominant contribution at low temperatures.

Study of the dependences of the intensities of the 0.89 mu m, 2.3 mu m and 2.47 mu m luminescence emission bands in cadmium telluride on the temperature of the sample and the intensity of the exciting radiation suggests an energy transfer process between luminescence centres and permits the positioning of the ground states of the emission bands relative to one another. The location of the ground states of these luminescence centres in the forbidden energy gap near the valence band has been confirmed by the determination of the thermal ionization energies associated with the energy transfer process.

Thirty samples of n- and p-type 6H and n-type 3C silicon carbide single crystals were irradiated at room temperature with either 0.8 or 1.0 MeV electrons or reactor neutrons. Seven different radiation- induced e.s.r. spectra were found. Some of these have been described before, but further investigations of production rates and annealing behaviour have necessitated changes in the previously proposed models. The e.s.r. parameters of these centres are given. Three of the spectra are tentatively ascribed to (1) the uncharged carbon vacancy, (2) the negatively charged carbon divacancy, and (3) the uncharged silicon vacancy trapped at a boron site. Tentative models for three other centres are discussed.

For pt.I see abstr. A15098 of 1970. Electron spin resonance studies have been made of trapped hole centres in CaF₂ that have a F₂^- molecular ion structure with nearly axial symmetry along (110) directions, and unequal hyperfine interaction with the two ¹⁹F nuclei involved in each centre. The centres are formed in samples containing trivalent Y and Lu substitutional impurity ions by X-irradiation at low temperatures and subsequent warming, or by irradiation at room temperature. A model is proposed in which the hole is trapped at a pair of nearest neighbour interstitial F^- ions which themselves form an aggregate defect complex with the trivalent cation impurities.

A discussion is given of the coupled nuclear-electronic spin wave modes which arise when one has strong hyperfine coupling in a system with an unperturbed electronic spin wave branch starting from zero frequency, such as is the case in spiral, conical, or fan spin structures of wave vector incommensurate with the lattice. Such systems with strong hyperfine interactions are found in certain rare-earth metals (for example). The coupled bands differ markedly from the unperturbed bands at small momenta and exhibit forbidden energy gaps. In the absence of quadrupolar terms the k=0 mode of the upper band is proportional to the hyperfine constant, is temperature-dependent through the average nuclear magnetization, and is excited with an amplitude determined by the Bohr, rather than the nuclear, magneton. This leads to the possibility of measuring the hyperfine constant by observing the temperature dependence of a ferromagnetic resonance experiment.