Table of contents

Contrary to the argument of Dancz, Edwards and March (see abstr. A30388 of 1973), the distribution of logarithmic derivatives of the wavefunction in an infinite noncyclic free electron network is shown to be indeterminate.

By assuming that the electron gas near a metal surface can be treated by retaining only the lowest-order term in a gradient expansion, it is demonstrated that a relation exists between bulk compressibility, surface energy and the 'thickness' of the electron density distribution at the metal surface. Such a relation is confirmed empirically.

The selfconsistent tight-binding theory of the electron-phonon interaction is applied to the problem of the phonon softening in K₂Pt(CN)₄Br_0.3.3H₂O. Of all phonon modes with the component of the wavevector along the chain equal to twice the one-dimensional Fermi wavevector k_F, the softest (critical) one appears to be that with the shortest wavelength.

A ferromagnetic lattice of localized electronic spins coupled by a Heisenberg exchange interaction is considered. The electronic spins interact via a hyperfine interaction with the nuclear spins, and a model is chosen in which only a fraction c of sites is occupied by nuclear spins. The coupled mode spectrum is calculated for c<<1 and is shown to be identical with the results yielded by molecular field theory. An analysis of the terms in the self-energy of the electronic spin propagator shows that because the hyperfine coupling is very much less than the exchange coupling, these molecular field theory results must hold for arbitrary c.

Measurements of the infrared absorption by acoustoelectric domains in ZnO at a wavelength of 10.6 mu m are reported. The results give good agreement with a theory recently published by the authors.

The application is discussed of the expression for the compressibility, in terms of the long wavelength limit of the structure factor, to a liquid metal. Taking density-dependent pair potentials obtained by perturbation of the electron gas by a model potential, it is shown that in order to obtain agreement with the result obtained by direct differentiation of the pressure with respect to volume when phi _q, the Fourier transform of the pair potential, is calculated to second order in the model potential for a general q, the contributions of second order in the model potential must be included in the mean value phi ₀. These terms arise as the q to 0 limits of the terms which for a general q are of third and fourth order in the model potential. The author also shows by direct calculation, using the Ashcroft model potential, that the resulting contribution to the compressibilities of the simple liquid metals is considerable.

A general theory of critical phenomena in constrained systems is presented. An ideal second-order phase transition is assumed to occur in the unconstrained system. It is shown that this transition can either remain as it was, or be renormalized, or be changed into a first order transition when the system is constrained. Systems with an arbitrary number of constraints are discussed. Such systems have the advantage that the physical realizability of constraints which lead to a first order transition can be made more obvious. A soluble model is described which exemplifies all the different types of behaviour that are possible.

Selection rules for indirect transitions are derived starting from a geometrical interpretation of the Brillouin zone. The effect of time reversal symmetry is included in the procedure. The final results, valid both for single group and double group representations, are presented in a way very convenient for operational applications. The case of diamond lattice is given as a specific example. The comparison between this treatment and previous ones is discussed.

The influence of spin-phonon coupling on the Schottky specific heat of a system is studied via an exactly soluble model of a single two-level system interacting with one phonon mode. An alternative method of diagonalization is given in which the diagonalized hamiltonian is expressed in operator form. The specific heat behaviour is discussed for arbitrary spin-phonon coupling parameters, and strong coupling is found to change the qualitative features of the specific heat significantly.

The singularities that emerge when approaching the critical point from below in a three-dimensional itinerant ferromagnet are studied by using the theory of Bhagavan and Blomberg. The following scaling laws are obtained from the theory: m approximately (T_c-T)^1.3, chi approximately (T_c-T)^-4/3 and C_Hmag=0 approximately log(T_c-T).

A broad, structured, emission band extending from 0.4-2.65 eV has been observed when Schottky diodes on n-type ZnSe without deliberately added impurities are driven in reverse bias. Evidence is given that the emission results from transitions of electrons within the conduction bands. In contrast with previous interpretations, it is suggested that the predominant transitions occur between valleys at different points in the Brillouin zone. Structure in the emission is correlated with conduction band structure. A comparison of calculated and observed emission intensities supports the proposed interpretation. Measurements of this type of electroluminescence provide a new means of studying band structure which should be applicable to a wide range of semiconductors.

A decoupling scheme for the three-current correlation function describing the external photocurrent within the quadratic response formalism is introduced. Terms attributed to 'simple scattering processes', which do not contain the three-particle interaction vertex, are analysed explicitly applying many-body Green function techniques. It is possible to separate from these terms one part, which describes the excitation of the dressed electron by the external field through renormalized current vertices and the transport of this electron to the detector in terms of a Bethe-Salpeter equation for a particle-hole function. The latter equation is solved by the scattering-time approximation. The resultant expression is compared with commonly used formulae for photoemitted primary electrons.