Table of contents

The first Born approximation with both the proton-proton and proton-electron interaction is used to calculate the high energy electron capture cross section for the resonant process H⁺+H(1s) → H(1s)+H⁺. It is shown that the high energy proton-nucleus amplitude has a dominant peak for backward scattering (centre-of-mass system). As a consequence of this peak, if the protons are treated as distinguishable particles, the cross section depends upon the impact energy E as E^-3 in contrast to the commonly accepted E^-6 dependence. When the protons are treated as indistinguishable particles, the electron capture cross section is not defined at sufficiently high energies. This same cross section is also calculated using the distorted wave approximation as developed by Bassel and Gerjuoy in 1960. It is shown that the proton-nucleus amplitude is only cancelled in the forward direction, and consequently the electron capture cross section is again not defined at high energies. These same approximations, together with the approximate helium wave function (Z³/π) exp {-Z(r₁ + r₂)}, (Z = 1.6875) are used to calculate the asymptotic form of the cross section for the process H⁺+He(1s²) → H(1s)+He ^-(1s). It is shown that the distorted wave cross section is effectively the OBK cross section although the proton-nucleus amplitude is only cancelled in the forward direction as in the case of capture from atomic hydrogen.

It is shown that the asymptotic form of the impulse approximation to the cross section for the exact resonance electron capture process H⁺ + H(1s) → H(1s) +H⁺ is identical with that of the first Born approximation. That is, it behaves as (1/12)(m/M)²E^-3πa₀² as E → ∞ (in units of 100 kev) for distinguishable protons and is undefined for indistinguishable protons.

Double mass-spectrometer measurements are reported of one- and two-electron capture cross sections for Ne²⁺ Ne, Ar²⁺ Ar, Kr²⁺ Kr, Xe²⁺ Xe, CO²⁺ N₂, Kr⁴⁺ Ne in the energy region 400-3600 eV. The symmetrical resonance two-electron processes are compared with the theory of Fetisov and Firsov. The single-electron transitions are believed to occur at pseudo-crossings of potential energy curves and the data are successfully interpreted in terms of transitions at single crossings. Inferences are made of the second ionization potentials of CO and N₂, and of the fourth ionization potential of Kr.

In a previous paper Black, Evans and O'Connor developed the theory of the interference between Rayleigh and nuclear resonant scattering and presented experimental results for polycrystalline scatterers which showed a general qualitative agreement with the theory. Measurements have now been made on the scattering within Bragg peaks of ⁵⁷Fe gamma rays from a single crystal of natural iron. These are presented and interpreted in terms of a more sophisticated theory due to O'Connor and Black. The results give a satisfactory quantitative confirmation of the theory.

The recoilless fraction for the elastic nuclear resonant scattering of gamma rays has been investigated by measuring the temperature dependence of the interference between the elastic scattering of 14.4 kev ⁵⁷Fe gamma rays by the resonant nuclei and by the electrons in a single crystal of natural iron set for the (110) Bragg reflection. The measurements confirm that the recoilless fraction for nuclear resonant scattering is given by the product of the separate recoilless fractions for absorption and emission and not by the corresponding factor for atomic Rayleigh scattering, usually known as the x-ray Debye-Waller factor.

Using a simple classical model the electronic and nuclear resonant scattering of gamma rays by a monatomic crystal has been calculated neglecting extinction effects. The scattering due to interference between the electronic and nuclear systems has an elastic and an inelastic component and the angular distribution of the latter differs from the distribution of the inelastic Rayleigh component.

The elastic part of the interference scattering is concentrated in Bragg diffraction peaks provided only that the crystal is ordered atomically. Disorder in the nuclear structure of the crystal, however, results in the purely resonant scattering being distributed between a coherent and an incoherent component. Types of disorder considered are those due to dilution of the crystal with non-resonant nuclei, random distribution of nuclear ground states in a magnetic crystal and random distribution of line shifts in a `naturally broadened' crystal.

The absorption spectra and spin-lattice relaxation times have been measured for the proton magnetic resonance in solid cyclobutane in the temperature interval 115 °K to the melting point 182.3 °K.

At temperatures below 130 °K it is found that the lattice is effectively rigid. Between 130 °K and the heat capacity transition point temperature of 146 °K a restricted form of motion of the molecules in the lattice affects the absorption spectrum. It is shown that the form of motion is probably reorientation of molecules possessing D_4h symmetry about their fourfold axes. The possibility that molecules spend an appreciable time in a non-planar configuration with D_2d symmetry is not excluded.

At the transition temperature a discontinuous change in the form of the molecular motion is found to occur. Between the transition point and the melting point isotropic reorientation of the molecules takes place, combined with self-diffusion through the lattice.

From the spin-lattice relaxation time measurements it is possible to estimate the activation energies for molecular reorientation in the low temperature solid phase and for self-diffusion in the high temperature solid phase. These activation energies are found to be 10.5 ± 1 0 kcal mole^-1 and 4.1 ± 0.6 kcal mole^-1, respectively. Reorientation rates are also estimated.

The theory of magnetic anisotropy and susceptibility of V³⁺ salts has been worked out on the basis of the molecular orbital method of Stevens and others, since the usual electrostatic field theory is not quite adequate to explain the magnetic behaviour. It is found that the anisotropic part of the crystal field changes with temperature possibly owing to the thermal expansion and relaxation of the crystal lattice. The spin-orbit coupling coefficient has to be decreased anisotropically by 35 to 40% from its free ion value which indicates asymmetric overlap between the 3d V³⁺ and s and p ligand charge clouds. The agreement of the theoretical values with the experimental is good.

Marked changes in the infra-red emission bands of cadmium sulphide phosphors have been observed after irradiation with ⁶⁰Co gamma rays. The computed number of displaced atoms by direct production of defects from the ordered lattice is much smaller than for electron bombardment experiments and suggests a Seitz mechanism for defect formation.

It is shown that the resonances observed in microwave scattering from a positive column depend on the existence of a radial electron density gradient. Deductions are made about the boundary conditions governing the space charge distribution associated with the resonant scattering.

A comparison with electrostatic probe measurements shows that subsidiary resonances exist, their position being a function of number density and probing frequency. The principal resonance, on the other hand, depends also on the external geometry. It is a feature of measurements made in this way that the principal resonance occurs at a frequency somewhat less than the mean plasma frequency.

Measurements are reported of the nuclear magnetic resonance parameters of methyl alcohol and methyl mercaptan (CH₃SH). The spin-lattice relaxation time T₁ and the chemical shift δ have been measured for both liquids, and for both types of proton for T₁ from the supercooled liquid up to the critical temperature. The variations of both T₁ and δ reflect the considerable difference in the importance of hydrogen bonding in the two liquids. At low temperatures the T₁ values are controlled by direct dipolar interaction. At higher temperatures the T₁ values depend on the spin-rotation interaction and approximate values of the operative spin-rotation interaction constants are deduced and shown to be reasonable in magnitude. Some preliminary measurements in the dense mercaptan gas near the critical temperature are also reported.

Results are also given for T₁ and δ for the rotator phase in methyl alcohol, where the rate and extent of molecular motion is sufficiently great to allow the observation of the proton chemical shift. This is usually only possible in liquids.

Line shape studies are also made at lower temperatures for both substances. Above a certain temperature a superposed narrow line is observed. For solid methyl alcohol this narrow line is a doublet with a splitting equal to the chemical shift and so is interpreted as being due to mobile molecules which may be on crystal surfaces or imperfections.

An extension of the classical theory of electrostatic forces was given previously by the author, taking into account the double layer at the boundary between two media. The results obtained do not affect predictions about the net force and torque on a body and therefore operate only if a body is deformable, and it was shown recently that in the case of a body of liquid with no applied field the effect of the double-layer field is a mechanical action which may be interpreted as surface tension. In this paper an investigation is made of the hydrostatic equilibrium of a body of liquid under the more general conditions where there is an applied field. The problem is essentially to determine the shape of the boundary; the shape will usually be different if there is no applied field, and it may therefore be said that the field deforms the boundary. Firstly, the results of the general theory are suitably adapted and the general hydrostatic problem is formulated. Then the formulation is applied to the approximate solution of two specific problems, two- and three-dimensional sessile-drop problems in which the drop is influenced by an electric field. The solutions obtained contain a new constant related to the double-layer structure and could possibly have experimental application to the investigation of double layers.

Mayer and Mayer suggested in 1940 that there might be two distinct temperatures that could be called critical, one defined as in the van der Waals theory, the other associated with a singularity in the virial series. The hypothesis is tested by applying the Percus-Yevick approximation proposed in 1958, which is now known to be fairly reliable at high densities, to a model of Gaussian type which allows crudely for the effects of both attractions and repulsions between molecules. The treatment shows that the hypothesis may be correct; the two temperatures are expected to be close together but need not be identical. In certain limiting cases one of them disappears.

The eigenvalues of a system comprising two one-dimensional coupled oscillators are derived treating cubic and quartic terms in the potential as perturbations added to the harmonic terms. These yield energy terms that include products of the quantum numbers of the two normal modes. For a Morse potential the spacings between levels are broadened in energy by about 20% up to quantum number 8 in the low frequency mode. As the system expands with increasing temperature the frequencies of the two normal modes decrease.

It is shown that at certain frequencies, which are infinite in number, the integrated vibrational spectrum can be found exactly for an infinite random two-component chain of elastically coupled masses.

It is pointed out that the perturbation expansions of unrestricted Hartree-Fock orbitals, based on zero-order uncorrelated orbitals, contain terms of order Z^-1/2 which do not appear in the similar expansions of Hartree-Fock orbitals. It is shown that these terms give about 90% of the total radial correlation in the second-order energy of the ¹S ground state of the two-electron systems.

Ab initio calculations of the fine structure separation of the 1s²np ²P, n = 2, 3 and 4, states of the three-electron systems are made using wave functions of the open-shell type. Satisfactory agreement with experiment is obtained only in the case of the highly ionized systems.

A method of calculating potential energy curves for diatomic molecules from experimental data is described which depends upon direct numerical integration of Klein's equations, and avoids the use of analytical representations of the energy levels. It is of particular use in cases where data are available for a large number of vibrational levels converging to the dissociation limit. The procedure is tested by a calculation of the potential energy curve for the state B ³Σ_u^- of O₂. In contrast with the results of other calculations, no anomalous curvature is found in the r (minimum) limb.

A study has been made of the energy loss of cosmic ray muons in an organic scintillation counter over the momentum range 0.4 to 100 GeV/c. The results were obtained by using a block of plastic phosphor 3.82 g cm^-2 thick in the beam of the Durham cosmic ray spectrograph. The results are compatible with the Sternheimer density correction to the ionization loss theory of Bethe-Bloch up to 10-15 GeV/c, but they suggest that at higher momenta the most probable energy loss may be about 3%±1% above the predicted rise. The energy loss of positive and negative muons is found to be the same within 1%. The work described is based on 5089 particles, 810 having momentum not less than 20 GeV/c.

Using the exact equations, presented here, the complex refractive indices have been determined for single crystals of cadmium and zinc over the range 0 6 to 5.0 ev, using a reflection method with polarized light. Comparisons are made between surfaces prepared in different ways.

Peaks are found in the absorption curves for cadmium at 1.05 and 1.90 ev (basal plane) and 1.23 and 1.90 ev (optic axis). For zinc there is a single main peak at 1.63 ev in both directions.

It is suggested that the observed absorption peaks arise by transitions from band 1 to bands 2 and 4, in the notation of Harrison's band models, the energy difference between bands 2 and 4 being greatest in cadmium. The anisotropy in energy is strongest in cadmium.

Two questions relating to this subject were raised by MacDonald and Pearson in 1961. The first concerns the need to take specific account of normal and Umklapp processes even at high temperatures in calculating the phonon drag thermoelectric power S_g. The other discusses why the phonon drag contribution to the thermopower is always negligible compared with the diffusion contribution at ordinary temperatures. The first question is considered by both Bailyn and Ziman. The answer to the second is that theoretical estimates based on an assumed Debye spectrum very grossly overestimate both normal S_g^N and Umklapp S_g^U contributions to S_g at ordinary temperatures although at low temperatures such estimates are probably reasonably good. It is concluded that the unexpectedly small values of S_g at room temperature are, therefore, not the result of some curiously general and nearly precise cancellation between S_g^N and S_g^U.

It is shown that static, spherically symmetric models of the electron in general relativity have the property that the mass of the electron may be calculated from an integral over the matter energy density alone if the matter tensor satisfies certain boundary conditions and the condition that energy density equals radial stress. The analysis is independent of the pseudo-tensor concept.