Table of contents

The kinetic and potential parts of the nuclear surface energy are calculated on the basis of the statistical model of the nucleus taken to first order and using a gaussian interaction between particles. The resulting surface energy is found to be of the right order of magnitude, the calculated figure being in fact 55% of the empirical value.

A previous paper examined the directional correlation I(θ) between two conversion electrons in cascade, each electron being ejected, with energy much less than mc², from an initial s-state, under the action of a pure electric multipole γ-transition, and I(θ) was shown to be completely determined by symmetry arguments alone in this case. In the present paper we consider the same problem for pure magnetic, and for mixed transitions. Here I(θ) usually appears as a weighted mixture of constituents I₁(θ), I₂(θ), etc., each of which is completely determined by symmetry arguments alone The weight factors, however, must be determined from standard internal-conversion theory.

A complete molecular orbital calculation has been made for the linear system of four protons with four associated electrons. Results indicate the validity of the assumptions usually made in approximate calculations of this type. All the three- and four-centred integrals usually neglected in such work have been evaluated and found to be of great importance in determining the energy levels of the system.

Part I. A short discussion is given of the magnetic properties of large aromatic hydrocarbons and of the applicability of various wave-mechanical methods of calculating the diamagnetic susceptibility. The ultimate particles of most cokes and carbon blacks are not sufficiently large to be regarded as crystalline and must be treated as large molecules: calculations on certain simple types of molecule are to be carried out with a view to elucidating the effect of particle size and shape on the magnetic properties of such carbons. For systems of these dimensions the molecular orbital method should be valid and, in fact, appears to constitute the only feasible approach to the problem.

Part II. The method of molecular orbitals is applied in a discussion of the diamagnetic anisotropy of the p-polyphenyls, which may be regarded as the simplest type of aromatic chain molecule. An almost perfectly linear relationship is predicted between diamagnetic anisotropy and chain length: in this case the molecular orbital method should be valid for chains of up to at least 2,000 rings. The results are discussed and the desirability of further accurate experimental work on these molecules is pointed out: this would make possible a stringent test of the whole theory.

A simplified quantum-mechanical model for the LiF crystal is described. The lattice parameter, cohesive energy and compressibility are calculated using three different choices of wave function for the fluorine ion in the crystal; these are (i) the Hartree wave functions for the free ion F^-, (ii) wave functions orthogonalized to the 1s-orbitals of the six nearest neighbour lithium ions, (iii) functions similar to (ii) but based on wave functions for the free ion which have been contracted to give agreement with the diamagnetism of F^-.

The results obtained in (i) are in fair agreement with the empirical values Large discrepancies are observed when the more complete wave functions (ii) are employed. This is taken as indicating that the Hartree wave functions for the free ion are too diffuse and the results of the third calculation, which agree well with experiment, substantiate this interpretation.

It has long been known that silver can grow epitaxially on a rock-salt cleavage face. It has now been found by electron diffraction that silver also grows in parallel orientation on (110) and (111) faces of rock-salt and that the silver crystals are twinned repeatedly on their {111} faces. A new example of rotational slip has been noted in which silver crystals were found to have slipped rotationally on their {110} planes.

Approximate formulae are obtained for the interaction (free) energy of the electric double layers of two parallel plates immersed in an electrolyte of the binary, symmetrical valency type. The three separate simplified expressions which are derived are good approximations at (i) large separations between the plates, (ii) small separations between the plates, and (iii) moderate potentials. The first form is an extension of a result proposed by Verwey and Overbeek in their recent book on the theory of the stability of lyophobic colloids. The third form is a power series in the surface potential, the first term of which is identical with the expression obtained when the linear Debye-Huckel equation in the theory of electrolytes is used. These results are more suitable for numerical computations than the exact formula for the free energy, which is expressed in terms of elliptic integrals.

The paper contains a discussion of the necessity for using a coordinate condition in the calculations for the derivation of the equations of motion from the field equations. It is found that no coordinate condition is necessary in the first approximation; i.e. one gets the Newtonian equations of motion if one merely assumes that the gravitational field is weak and quasi-static. In the higher approximations a coordinate condition is indispensable in order to eliminate all apparent accelerations from the equations of motion