Table of contents

A potential function is computed for the lithium ion core, and is used to calculate the cohesive energy of metallic lithium, which is found to be in good agreement with experiment. Eigenvalues for conduction electrons in metallic lithium are calculated for points of high symmetry in the Brillouin zone, using the improved cellular method of Howarth and Jones, in which boundary conditions are applied at a large number of points on the surface of the atomic polyhedron; the merits of this type of boundary condition are discussed. The energy gap at the centre of a face of the zone is found to be 2.57 eV, the lowest state at that point having a p-like symmetry, and the interpretation of the soft x-ray emission spectrum of lithium is discussed in the light of this result.

Experimental results giving the shape of the Compton profile in X-ray scattering show that the momentum distribution of the electrons in metallic Li and Be differs markedly from that given by wave-mechanical calculations for isolated atoms.

As the starting point of a detailed theoretical investigation the present paper is concerned with examining the momentum distribution of electrons in metals on the basis of the Thomas-Fermi theory. Quantitative results are presented for Li, Be, Na, K and Rb, and a considerable broadening of the Compton line due to the interaction of atoms in a lattice is unmistakably shown. Agreement with experiment is, however, poor for Li, and it is concluded that the momentum distribution of the valence electrons in metallic Li differs considerably from a free electron distribution. For Be there is surprisingly good agreement with experiment, but unfortunately no experimental results exist as yet for the other metals.

The effect of introducing exchange is examined in detail for Na and some additional broadening of the Compton line is found. Finally the concept of free electrons in the Thomas-Fermi theory is discussed.

Using a modified definition of Riesz potential it is shown that the divergences arising in quantum electrodynamics from (i) the point nature of charge, (ii) the electron self energy and (iii) the vertex part of a Feynman graph, can be eliminated in a consistent way, without having to introduce any cut-off factors or auxiliary fields.

The Ritz variational method in conjunction with an extrapolation procedure has been employed to calculate the electron affinities of atomic fluorine, oxygen and lithium, the values obtained being 3.05, 1.12 and 0.74 eV respectively. In the case of fluorine the accord with the value 3.57 eV found by using the Born-Haber cycle is reasonable. The electron affinity of oxygen obtained from collision experiments is 2.2±0.2 eV, which is considerably larger than the value calculated in this paper. No comparison data are available for lithium.

A self-consistent improvement of Bloch's spin-wave treatment of the ferromagnetic exchange problem at low temperatures is developed. This leads to appreciable corrections to the spontaneous magnetization.

The isotopic-spin purity of some low-lying excited states in light nuclei is calculated in first order perturbation theory. Special attention is given to the odd parity states in even nuclei. The isotopic spin impurity caused by coulomb forces is shown to be sufficient to account for the electric dipole transition in ¹⁶O between the 7.12 MeV excited state and the ground state.

The absorption spectrum produced when bismuth is heated in a furnace up to 1500°C has been analysed. It extends from 2450 Å to 3800 Å. Evidence is given to attribute it to the diatomic molecule BiO. The bands are grouped into four systems and there is evidence of the existence of a fifth.

The vibrational constants proposed for these systems are:

νe	ωe	xeωe
40930	770
38551.8	769.3	6.2
30500	-
30220	487
28739.5	487.0	6.5
0	695.9	4.9

The ground state is considered to be the lower component of a case a²Π with probable ω-ω coupling and the doublet splitting is estimated to be between the limits 8000 and 13 500 cm^-1. The relation of the adsorption spectrum to the emission spectrum is considered and an attempt is made to account for the energy levels in terms of electron configurations.

The method of Wigner and Seitz for calculating the cohesive energy of metallic sodium is compared with a recent method of Löwdin, and reasons are given for preferring the former. A simple calculation shows that Löwdin's use of the LCAO method in constructing his one-electron functions must give rise to an error in the energy greater than the correlation energy as estimated by Wigner, so that Löwdin's results should not be used in assessing the accuracy of Wigner's formula.

Previous work on the mesonic Auger effect is extended to meson capture in non-circular orbits, and to Auger emission of L shell electrons. Corrections to the theoretical results are discussed and calculations made of the probable Auger emission from heavy elements for capture in photographic emulsions. The results are compared with observations and reasons suggested for a deviation.

A many-lined spectrum in the region 2200 to 2600 Å has been obtained in hollow-cathode discharges in hydrogen in the presence of potassium fluoride. A rotational analysis has shown this to be a ν' = constant progression of a Σ-Σ transition, probably singlet. The emitter has not been identified.

A quantum-mechanical method is described for calculating the effect on the optical absorption of metals and semiconductors of any of the factors responsible for electrical resistance. In this method the electrons which are scattered by imperfections in the crystal lattice are considered to absorb light by a photoelectric process. The calculation is carried out for the case where the conduction electrons are scattered by dissolved impurities. A first order approximation method is used. The results obtained are compared with those of the semi-classical theory used in existing textbooks, in which the current set up by the light is assumed to be damped by the impurities. It is found that the two methods give very similar results for metals. For semiconductors, on the other hand, the approximate method used here gives considerably less absorption than the semi-classical method. The use of exact wave functions for the very slow electrons in semiconductors would give greatly increased absorption coefficients because the intensity of these wave functions is high near the scattering centres. It is suggested that in this way the high absorption of infra-red radiation in semiconductors can be explained.

The wave functions and energy eigenvalues of a ferromagnetic crystal at low temperature are obtained assuming a model of two electrons localized on each atom. The results are applied to the problem of inelastic scattering of neutrons following Moorhouse. The effect of assuming two electrons per atom is quite unimportant. However, a more realistic estimate of the exchange integral leads to narrower peaks than predicted by Moorhouse and therefore tends to make the effect easier to observe.