Table of contents

The equations of the two-body problem of general relativity are derived by a Hamiltonian method based on an expansion of the general covariant Lagrangian in powers of the gravitational constant and by employing the techniques and the viewpoint of quantum field theory. It is found that, within the approximation in which they have so far been calculated, the equations could have been obtained identically from a linear theory of gravitation.

An attempt has been made to check the validity of Mott's theory of single scattering of electrons by heavy nuclei such as silver, platinum and uranium at various angles of scattering and thus to investigate whether there is any marked deviation from theory at large angles of scattering as observed by some previous workers in this field. An electron beam from the 4.5 MeV microtron at University College, London, was used for the experiment and the scattered electrons were detected in Ilford G5-50 micron emulsions. It has been found from these measurements that the scattering of 4.33 MeV electrons by the above mentioned nuclei agrees with Mott's theory within the experimental accuracy of a few per cent for angles of scattering from 45° to 90°. Measurements made at angles of scattering of 120° and 135° were found to have been affected by the presence of spurious scattering from the walls of the apparatus so that no definite conclusions can be drawn regarding the scattering at these angles.

A simple independent-particle model is used to treat the elastic and inelastic scattering of electrons by light nuclei at high energies, using the relativistic first Born approximation. The matrix elements are calculated for a harmonic oscillator nucleus and a spherical box nucleus. Comparison is made with experiment for the scattering of 190 MeV electrons by ⁹Be.

A helium 3 neutron spectrometer has been used to study the spectrum of neutrons inside a spherical uranium shell, 3 cm thick, when the latter is bombarded with monoenergetic neutrons of various energies between 500 keV and 1.0 MeV. The spectra of neutrons scattered inelastically and also the cross sections for this process have been derived, and the results compared with those predicted by current nuclear theory. Evidence for the existence of the low-lying rotational levels of uranium 238 is presented, and at least one new level at 700 keV (and possibly more at higher energies) has been found. Qualitative confirmation has been obtained by measuring the spectrum of neutrons from a uranium shell, 11.5 cm thick, with a neutron source in the centre.

A magnetic spectrograph with photographic detection has been used to analyse the spectra of charged particles emitted from the bombardment of a thin teflon target by 8.9 MeV deuterons. Angular distribution measurements are also reported for several proton and deuteron groups produced in this bombardment.

Two inelastically scattered deuteron groups corresponding to excited states in ¹⁹F at 1.60 ± 0.02 MeV and 2.83 ± 0.02 MeV have been observed. The angular distribution of the former group is compared with a theory proposed by Huby and Newns. A number of proton groups have been assigned to the ¹⁹F(d, p)²⁰F reaction. Eight new excited states in ²⁰F are observed at 5.04, 5.19, 5.27, 5.72, 5.87, 5.95, 6.25 and 6.52 MeV, with errors of ± 0.02 MeV. The deuteron stripping theories have been applied to determine the l_n-values as well as the reduced widths of 21 excited states in ²⁰F. The general behaviour of the energy levels of this nucleus is discussed.

The angular distribution of a proton group associated with the transition to the 6.091 MeV level in ¹⁴C is found to have l_n = 0. A possible configuration for this state is (1p_1/2)¹ (2s_{1 2})¹.

A reformulation of Saxon and Hutner's scattering matrix method for lattices is introduced, and a connection shown between the characteristic matrix for going across a cell in the lattice and proper Lorentz transformations. This provides a convenient geometrical model for analysing mixed lattices of A and B atoms. Luttinger's proof of a theorem on the persistence of forbiddenness, in the mixed lattice, of energies forbidden in the pure component lattices is generalized. It is shown also that there are energy levels in mixed lattices whose forbidden or allowed character is invariant to any re-arrangement of lattice atoms, and that there are physically distinguishable lattices having identical band structures. The major problem of finding the probability that a given energy is allowed or forbidden in a random mixed lattice is taken up. A method for finding the moments of the relevant random variable is provided, and the complete analysis for the Poisson limit of a few B atoms sprinkled in a long A lattice is given, with quantitative conclusions as to the persistence of allowedness in mixed lattices, the effect of strong forbiddenness in the pure B lattice on the band structure of the mixed lattice, and the like.

The molecular orbital method is used to calculate the intensities of the symmetry-forbidden bands of benzene. Both the bands at 2650 Å and 2000 Å derive intensity by interaction with the upper state of the 1800 Å band. The states of symmetry B_1u and B_2u are made accessible by e_2g vibrations of the benzene framework at 606 cm^-1 and 1595 cm^-1. The 606 cm^-1 vibration is most important in making the transition to the B_2u state (at 2650 Å) allowed, whereas that at 1595 cm^-1 is most important for the A_1g → B_1u transition. The alternative assignments B_1u and E_2g are considered for the 2000 Å band, but the calculated total intensities cannot differentiate between them.

The r-centroid r_ν'ν'' of a molecular band is defined by ∫ Ψ_ν'rΨ_ν''dr/∫ Ψ_ν'Ψ_ν''dr and is an average internuclear separation which may be associated with the ν' → ν'' transition. Ψ_ν' and Ψ_ν'' are vibrational wave functions. The physical meaning of r-centroids is discussed and it is shown that the average internuclear separation r_ν' in the level ν' may be represented by the weighted mean of r-centroids with respect to Franck-Condon factors q_ν'ν''; i.e. r_ν' = Σ_ν''q_ν'ν''r_ν'ν''. Methods for evaluating arrays of r-centroids are developed and values are reported for ten band systems. The smooth relationship between r-centroid and wavelength is described and illustrated. A knowledge of r-centroids has been found very useful in the discussion of variation with internuclear separation of the electronic transition moment and it may reasonably be expected to have value in the study of other molecular properties.

A thin gas target was used for measurements of the cross sections and angular distributions of the ³He and ³H disintegration products at bombarding energies of 52 and 87 keV, two symmetrically placed proportional counters being used as detectors. The angular range covered was from 18° to 150° in the laboratory coordinate frame. In addition, the ratio of the differential cross sections of the reactions was measured for a laboratory angle of 48° at bombarding energies of 39 and 65 keV.

The results obtained are consistent with earlier measurements using the same technique, and show that the neutron-producing reaction has the greater anisotropy, and that the ratio of the total cross sections is energy dependent.

A calculation has been made of the cross section for destruction of He(2¹ S) metastable atoms by collision-induced radiation in two-body collisions with neutral helium atoms. The four-electron wave functions used for the system were built up from unperturbed atomic orbitals. Assuming the form of interaction between normal and metastable atoms calculated by Buckingham and Dalgarno which exhibits a repulsive barrier of a height of 0.26 eV at separations greater than 2.1 × 10^-8 cm, the calculated cross section was 9 × 10^-26 cm² at a temperature of 300° K. However, even if no barrier was assumed the cross section increased only to 5 × 10^-22 cm², still much too small to account for the value of 3 × 10^-20 cm² measured by Phelps for the destruction cross section.