Table of contents

The angular distribution of elastic and inelastic scattering of 89 Mev protons in carbon is calculated on the distorted wave approximation, assuming direct interaction in inelastic collisions. Different forms of nuclear potential are tried, and it is found that a satisfactory fit with the experimental curves may be obtained, provided direct interaction is assumed to take place throughout the nuclear volume, and not just at the surface. The Born approximation gives diffraction minima which are much too low, at angles which are appreciably too large; and gives far too little scattering at small angles for electric quadrupole excitation.

The first-order perturbation, c', of an eigenvector c of a symmetric matrix H satisfies the inhomogeneous equation (H-yI)c' = -(H'-y'I)c where I is the unit matrix, y the eigenvalue belonging to c, and the prime denotes the appropriate derivative. The derivative c' can be determined from y, y', c, and a particular solution of the inhomogeneous equation; a convenient computational procedure is demonstrated. In contrast, the conventional perturbation theory requires knowledge of a complete set of eigenvectors of H. Another advantage of the present method is that arithmetic checks are easily applied in numerical work. The method lends itself to the calculation of polarizabilities in the simple molecular-orbital theory. In this connection a complication associated with partly occupied degenerate orbitals is pointed out, the present method is convenient for dealing with this complication.

A more rapid method of reducing a matrix by use of symmetry than that commonly used is presented. It is useful in the present perturbation problem but it should prove equally convenient in other problems.

The determination of c' in certain cases of degeneracy is described and an error in the literature pointed out.

The analysis throughout is general, and may be of interest outside molecular-orbital theory.

The process of direct interaction with photons (the emission of fast particles) is formulated in nuclear dispersion theory. The cross section can be evaluated for energies far from the single particle resonances; an order of magnitude estimate can be made for the region of the resonances. The results are in rough agreement with those from Wilkinson's modified shell model.

The dipole-quadrupole interference is estimated to give an appreciable forward asymmetry for photo protons.

A method of deriving the equation of state of crystals belonging to the hexagonal system from the experimental data on specific heat, thermal expansion and elastic constants has been developed. The method is a modification of the one given by Dayal for cubic crystals. The pressures along the hexagonal axis and those perpendicular to it are divided into two parts, of which the first is the static part due to a non-vibrating lattice and the second due to the thermal vibrations. Two average Grüneisen constants have been calculated from the experimental data and have been used in the calculation of the thermal pressures, along the two axes. The static pressure for a non-vibrating lattice is calculated as a function of the linear dimension from the condition that for the linear dimension measured at zero pressure, the sum of the thermal and static pressures must be zero. In this way the total pressure comes out to be the difference between the thermal pressure at a temperature T and length l and the one calculated for a temperature at which the crystal has the same length at P=0. Detailed calculations have been made for zinc, cadmium and magnesium. It is found that in all cases except in the case of cadmium perpendicular to the hexagonal axis, the calculated results are in good agreement with Bridgman's experimental measurements.

It has been shown that the equation of state derived from the assumption made by Gruneisen about two Debye characteristic temperatures, one perpendicular and the other parallel to the hexagonal axis, does not agree with the experimental observations made by Bridgman.

The electronic structure of an ionic crystal is investigated with the assumption that the solutions of Fock's equations for the valence electrons can be expressed as linear combinations of the outer orbitals on the negative ions and the first vacant orbitals on the metal ions. The inclusion of this latter group of orbitals allows for homopolar binding. Numerical calculations are made for LiF and the width of the F-2p band is found to be 5.4 ev of which about 5% is due to homopolar binding. The main homopolar effect is to provide a coupling between ions which are second nearest neighbours in the halide ion lattice.

Electron diffraction patterns taken on the prism face of a cobalt crystal showed a distortion due to the magnetic leakage field. The normal diffraction spots were replaced by a series of arcs. When the primary beam was moved parallel to the edge of the crystal, the distorted pattern changed with a period characteristic of the domain spacing. On heating the crystal, the magnitude of the distortion decreased, and became negligible at about 250°C.

A method of calculating the ground state thermal dissociation energy and the electronic part of the optical (1s-2p) absorption energy of a colour centre in an ionic crystal is outlined. The electrostatic energy of interaction of the trapped electron and the lattice is determined by the summation of individual terms due to lattice charges and to dipoles induced at the lattice points. Polarizabilities of these dipoles can be determined readily from the results of Mott and Littleton for NaCl. The calculated thermal dissociation energy for this material is within 10% of the experimental value. A direct comparison with experiment for the optical absorption energy is not possible because of the relatively large lattice oscillator term which is not determined by the present method. A comparison with the results of Huang and Rhys for KBr indicates, however, that the electronic component of the absorption energy for NaCl here calculated is approximately correct.

The proton-proton differential elastic scattering cross section at 380 MeV has been accurately measured over the angular range 30° to 90° (c.m.) Coincidences between scattered and recoil protons were counted, using targets of polyethylene and carbon, and the number of incident protons determined with a calibrated ionization chamber. At 90° the differential cross section is 3.70 ± 0.06 mbn sterad^-1 and increases at smaller angles to a value 9% greater at 30°.

Measurements on the proton-proton differential elastic scattering cross section at 380 MeV have been made within the angular range 4° to 30° (c.m.). A target of liquid hydrogen was used and a threshold Cerenkov counter was included in the detecting telescope to eliminate particles from inelastic processes. The total cross section for deuteron production was found to be 0.57 ± 0.08 mbn.

Powder patterns were obtained on the cleaved surface of a single crystal of manganese ferrite by using a modification of the normal powder pattern technique. Two types of patterns were observed, a large scale pattern having a `fern'-like structure, and an underlying structure of exceptional fineness and unusual configuration.

Tensile strength measurements on ice cylinders adhering to stainless steel have been made as a function of rate of loading, thickness and cross-sectional area of specimens, and temperature. A rapid increase of tensile strength occurs as the volume is decreased. The data for a temperature of -4.5° c can be represented over a thousandfold range of volumes by an equation as follows S = 2.74AV^{-0 84} + 9.4 kg cm^-2 where S is the tensile strength, A the cross-sectional area in cm² and V the volume in cm³. The experimental results are interpreted by means of a statistical treatment involving imperfections in the specimens. The statistics for a model consisting of a large number of parallel elements is elaborated. The final equation derived on statistical grounds approximates the equation found empirically, and reads as follows S_{r, n} = kA^1/βV^-1/β + C where S_{r, n} is the number average of the tensile strength, k, β and C are constants and r is the number of imperfections in each of n parallel elements. This result is quite general and not confined to ice.

The conclusion is reached that due to imperfections the tensile strength is a statistical function of the volume and cross-sectional area of the specimens. Superimposed on the statistical effect is a stress distribution effect, which becomes predominant for large volumes.

The Schrodinger equation is set up for the hydrogen atom using spheroidal coordinates with the nucleus at one focus, and it is solved as completely as possible. An expression is obtained for the wave function in a general excited state, and orthogonality properties are proved. Relations are investigated between spheroidal, spherical polar and parabolic wave functions.

The interactions of a point charge and of a point dipole with a hydrogen atom are investigated. Interaction energies, dipole and quadrupole moments are calculated using exact perturbation theory. Spheroidal coordinates are necessary to solve the differential equations which arise, and wave functions for the atom in these coordinates are seen to be the correct zero-order ones to use. The exact form of the perturbing potential is employed, giving results with both polynomial and exponentially decreasing terms. These are compared with the simpler but less accurate results obtained when the expanded form of the perturbation is used.