Table of contents

The approximate linear form of Einstein's gravitational field is quantized by using an indefinite metric. It is shown that only two types of gravitons can be observed, though many more can exist in virtual states in the presence of interaction. The observable gravitons are shown to be particles of spin 2. Using the interaction representation, the interaction of the gravitational field with the matter field is briefly discussed.

A new coordinate condition has been considered and the equations of motion of two bodies in their weak and quasistatic gravitational field have been derived to the second approximation A number of additional second order terms appear in the new equations which, however, have no influence on either the secular motion of the centre of mass or the rotation of periastron of the two-body system.

A partially polarized beam of particles is represented by a statistical operator in spin space. For nucleon-nucleon scattering a theorem stated by Wolfenstein in 1949 connecting the two simplest experiments involving polarized nucleons is shown to depend on the invariance of the interaction potential under time-reflection.

The polarizability of the hydrogen molecule is calculated theoretically The energy of the molecule, under an external electrostatic field, is calculated by the variation method, using 11+10 terms and 11+9 terms James-Coolidge type wave functions, for the polarizability parallel to and perpendicular to the molecular axis respectively. By expanding the energy in powers of the field strength, the polarizability is determined. By using a Morse function for the adiabatic potential of the molecule, the 0-0 and 0-1 matrix elements of the polarizability between vibrational states are calculated, with the result: α₀₀=7.89, γ₀₀=2.78, α₀₁=1.39, γ₀₁=0.90 for ordinary hydrogen H₂, and α₀₀=7.75, γ₀₀=2.68, α₀₁=1.13, γ₀₁=0.71 for heavy hydrogen D₂ (in units of 10^-25 cm³), where α is the mean polarizability and γ the anisotropy.

It is shown that on the basis of the Bloch-Peierls-Bardeen theory of conductivity, the use of θ_R ≃ θ_D in the Bloch-Gruneisen formula is a reasonable approximation in the temperature range T ≳ θ_D. At very low temperatures T << θ_D, however, θ_R = θ_L. This, it is shown, disagrees with experimental data much more than the ad hoc use of θ_R ≃ θ_D in the Bloch-Grüneisen formula.

A calculation is made of the energy density of electronic states for the 3d electrons in metallic nickel, using the approximation of tight binding. The early stages of the calculations and preliminary results have been previously summarized by Fletcher and Wohlfarth in 1951 The theoretical basis of the approximation is outlined and the validity of the underlying assumptions examined. The required overlap integrals are evaluated and the secular equation for the energy as a function of wave vector is solved exactly over the energy range of interest for nickel. The density of states curve is computed graphically Among results of physical interest obtained are: bandwidth 2.7₀ eV, degeneracy temperature 1.4₅×10³ deg K, low temperature electronic heat coefficient γ 1.6₉×10^-3 cal.mol^-1 deg^-2 (compared with the experimental value of 1.74×10^-3). The results are compared with those obtained by the cellular method of approximation used by Krutter in 1935, and Slater in 1936.

By comparison with a calibrated neutron source, the total rate of emission of primary neutrons in the Graphite Low Energy Experimental Pile has been found. The rate of emission of spontaneous fission neutrons from natural uranium is computed to be 59.5±3 3 neutrons/g/hr of uranium

An account is given of the methods used to determine the matrix elements of crystal field potentials with particular reference to rare earth ions. Emphasis is laid on the importance of Wigner coefficients in such problems and the idea of using equivalent angular momentum operators is developed. For convenience in applying the results tables of matrix elements are included.

The decay and nuclear interaction schemes of κ-mesons are discussed. A tentative interpretation is made of some anomalous interactions of penetrating particles observed recently below ground. Further possible experiments testing the hypotheses made are suggested.

Further experiments have been made on the production in the laboratory of the `forbidden' red and green auroral lines, and the ultra-violet transauroral line of OI. The mean concentration of oxygen atoms in the 1¹S₀ and 5⁵D states in the columns has been found from absolute intensity measurements. The decay of the green radiation produced by a Tesla discharge through a high-pressure source has been investigated with a photo-multiplier tube. It occurs at approximately the rate to be expected if the atoms in the ¹S state are undergoing spontaneous transitions to lower atomic levels, but complicating factors make it difficult to deduce transition probabilities from the experiment.