Table of contents

The differential cross sections for the elastic scattering of electrons by helium atoms and by hydrogen molecules have been calculated over a wide range of electron impact energies with allowance made for the contribution to the scattering from the static fields of the target systems, for the effect of electron exchange and, in the case of helium, for the polarization of the target atom by the Coulomb field of the incident electron. The approximate methods which have been used include the Born approximation, the first-order exchange approximation and, in the case of helium, the numerical solution of the differential equations derived by making a partial wave analysis and employing the static field approximation together with a polarization potential term, which behaves as - α/r⁴ for large radial distances r and vanishes as r approaches zero. In addition, use has been made of the zero- and first-order phase shifts calculated by Morse and Allis from the exact numerical solutions of the appropriate exchange approximation integro-differential equations for the helium case.

It is found that the agreement between theory and experiment is quite satisfactory provided the experimental data for the angular distribution of elastically scattered electrons are normalized separately from the calculated differential cross section curves for each energy of impact, though there remains a tendency for the very small and the large scattering angle data to lie somewhat above that predicted by the theory. However, if the normalization of the experimental data is carried out at just a single high energy of impact, the calculated curves are found to lie well above the experimental points at low electron energies over most of the range of scattering angles.

The satisfactory accord obtained for molecular hydrogen between the experimental data and the differential cross sections calculated with polarization neglected suggests that in this case the effect of polarization may be small even though the polarizability of molecular hydrogen is considerably greater than that of helium for which its role is found to be important.

The prior and post Born matrix elements are used to calculate the cross sections for H^-(1s²) production in hydrogen atom collisions. In contrast to the original version of this work done by Mapleton in 1960, the plane wave approximation to the Coulomb function is partially corrected. The same H^- wave functions are used, and the post cross sections are substantially unaltered. Cross sections calculated with the improved H^- wave function as compared with the other H^- wave functions are from twenty to thirty-five per cent larger for the prior case and twenty to thirty per cent larger for the post case. The post-prior discrepancy, expressed as a ratio, varies between 0.001 and 0.33.

The rate coefficient for radiative charge transfer from He atoms to He²⁺ ions is calculated for temperatures up to 16 000 °K. It is found to be a slowly increasing function of the temperature with a mean value of 4 × 10^-15 cm³ sec^-1.

Measurements have been made of the ratios of electron-nuclear scattering cross sections for scattering angles of 20°, 30° and 45° to a scattering angle of 65° over the energy range 100-400 kev. The results favour the corresponding screened theoretical cross section ratios rather than the unscreened ones.

The Monte Carlo method described by Green in 1963 has been used to investigate the scattering of 29 kev electrons in a copper target. The results are compared with experimental data and are used to suggest how theoretical expressions obtained for an infinite solid may be modified to apply to the practical case of a semi-infinite target.

With the aid of the method of summing infinite series of non-relativistic graphs accurate integral equations are obtained for the deuteron-nuclear elastic and inelastic amplitudes at low energies. The method based on field theory using the second quantization formalism was applied earlier by Komarov and Popova for the solving of the three- and four-nucleon problem.

Formulae are obtained for the dependence of the muon decay electron spectrum on the mass of the muon's neutrino, with both radiative and intermediate boson corrections included by convenient and accurate approximation methods. The restrictions which the usual V-A prescription places on the form of the decay interaction are relaxed in the calculations to the extent that either the electron or the muon is assumed to be coupled by an arbitrary mixture of vector and axial vector terms. The range of neutrino mass values consistent with available measurements of the electron end-point energy is ressessed, the shape of the spectrum near the end-point being taken into consideration.

A study has been made of electron impact ionization of argon and xenon. It has been found that singly and doubly charged metastable ions are produced near the threshold energies for double and treble ionization respectively. These excited ions were found to decay by autoionization. Measurements were made of the excitation functions of these ions and in some instances the lifetime and production cross section. Argon was studied in most detail, but similar processes were found to occur in Ne and Kr although the results are not reported in this paper.

An apparatus for the measurement of steady-state pre-breakdown ionization currents in helium at high pressures is described, and the sampling procedure necessary to obtain with it reproducible results discussed. The primary and secondary ionization coefficients determined from these measurements are given for 3 3 < E/p₀ < 5.0 v cm^-1 mmHg^-1 and for 150 < p₀ < 560 mmHg. The values of α are discussed in relation to previous theoretically computed values and the experimental values obtained at lower gas pressures but with similar values of E/p₀. The values of the generalized secondary ionization coefficient are found to be relatively high (similar 0.1) and to increase as E/p₀ decreases.

The problem of computing the phonon distribution and thermal conductivity in the presence of N processes is examined in the framework of the Boltzmann-Peierls equation. A heat flow may be associated with drift and diffusive distributions respectively; this intuitive concept is given specific mathematical basis as a natural method to solve the Boltzmann equation. A general operator form of this equation is used and the solution is expressed as the sum of an eigenstate of the N-process collision operator having zero eigenvalue plus a second term; the former is a drift term and the latter is diffusive. The amount of drift is determined by making the drift term orthogonal to the diffusive term; this is equivalent to a phonon momentum balance condition. As a special case, the general method may be approximated by relaxation time representation of the collision operators. The Callaway equation follows directly.

The absorption produced by direct inter-valence band transitions provides a sensitive test for the calculated valence band shapes. A calculation by Kane of the valence band shapes of p-type germanium near k = 0 using second-order degenerate k. p perturbation theory and of the resulting absorption spectrum indicated that the mass of the split-off valence band had not been determined accurately. This inadequacy was shown up even more when the Kane model was used to predict the change in absorption produced by a small change in lattice temperature and a comparison made with recent experimental results. The availability of these accurate absorption data has stimulated a more accurate calculation of the valence band structure. Here the interactions between the valence bands and the two neighbouring conduction bands are calculated exactly rather than by perturbation theory. The next nearest conduction band is included as a perturbation. It is then found that the mass of the split-off band is substantially heavier than calculated by Kane, a requirement that better agreement with the observed spectrum be obtained. An expression for the conduction band energy is also presented. The coefficients of k² and k⁴ in this expression are calculated and compared with the results of magneto-absorption experiments. Agreement within experimental error is achieved.

The momentum distribution of electrons in semiconductors in the presence of electric fields is in the hot electron theory frequently assumed to be a displaced Maxwell distribution, corresponding to a temperature T larger than the temperature T₀ in the absence of the field. We demonstrate in the present paper that conditions exist in which T < T₀, although the mean energy of an electron is larger than 3/2kT₀. Detailed consideration of various types of electron scattering leads to the suggestion of a number of materials in which the effect T < T₀ should be observable.

The effects of superzone boundaries on the electrical resistivity of dysprosium have been studied by measuring the magnetoresistance of two crystals of dysprosium with the field applied in the basal plane. The maximum effect occurs parallel to the c axis and amounts to some 15%. The results are in agreement with the conclusions of Elliott and Wedgwood that the predominant effect is produced by superzone boundaries whose planes are perpendicular to the c axis. Some evidence for the presence of superzone boundaries whose planes are at an angle to the c axis is provided by a small magnetoresistance in the basal plane, attributable to the destruction of the superzone boundaries.

The magnetic susceptibility and electrical resistivity of yttrium metal have been measured below 300 °K. The susceptibility of yttrium increases from 186 ± 5 × 10^-6 e.m.u. (g atom)^-1 at 293 °K to 195 ± 5 × 10^-6 e.m.u. (g atom)^-1 at 10 °K. The susceptibility results disagree completely with the recent measurements of Chechernikov et al. In addition, no anomaly in either the susceptibility values or the resistivity values is evident at about 170 °K.

Measurements have been made of the magnetic properties of a single crystal of NiF₂, both above and below its Néel temperature. Below T_N the magnetic moment along the appropriate crystal axis contains two contributions. One of these is associated with χ_⊥ of an antiferromagnet and is linear with field and independent of temperature. The other contribution approaches a saturation moment which is temperature dependent and is ferromagnetic in nature. Immediately above T_N the paramagnetic susceptibility along the same axis becomes very large as T_N is approached, which is unusual in a substance undergoing a transition to the antiferromagnetic state but can be understood in the light of the weak ferromagnetic properties of NiF₂ below T_N. These and previous results show that in the ordered state the spins are almost antiparallel in a plane perpendicular to the tetragonal axis, but are tilted away from the antiparallel position in such a way that the crystal acquires a ferromagnetic moment in the same plane perpendicular to the axis of antiferromagnetic ordering.

In the positive column of a low-pressure mercury arc measurements of the transmission of electroacoustic waves are made in small and zero axial magnetic fields. Externally excited and self-excited waves are shown to propagate similarly: a low frequency cut-off in transmission appears for both at about 20 kc/s.

Over the lower part of the frequency range a simple theory using the measured steady-state parameters of the discharge fits the observations, usually within the combined experimental errors (±20%). Above 40 kc/s the slope of the experimental dispersion curve falls sharply: this is the upper limit at which an external exciter coil is effective in a magnetic field, and at this frequency the exciter is least effective in zero field. The change in wave character is not understood.

The wave damping is less than that expected from the rate at which ions strike the wall. The boundary conditions are not clear.

Balmer lines emitted from a Penning discharge in hydrogen gas show a Doppler shift indicating rotation around the axis of the discharge column. This effect is explained as a result of the charge exchange collisions of the drifting plasma ions with the neutral atoms, and the fast neutral particle thus produced being excited by the plasma electrons. Accordingly we identify this rotation with the drift motion of the plasma. The velocity of rotation v_rot is obtained as a function of radius from the measured Doppler shifts for two values of the confining magnetic field strength B_z The results show that for plasma layers with radial distances r smaller than or equal to the radius of the hollow anode cylinder, that means inside a tube which contains radial currents I_r, the rotational speed v_rot can be expressed by the following very simple formula: v_rot = (I_rB_z / n_im_in₀ σ_coll2πrL)^1/2. A derivation of this expression is given.

The optical constants of copper and gold have been determined over a range of wavelengths from 4600 Å to 460 Å by measuring the reflection coefficient for unpolarized light at four angles of incidence. The results are expressed by means of graphs of ₁ and ₂, the real and imaginary parts of a complex dielectric constant, against photon energy, from 1 to 26 eV. They agree with recent determinations by Roberts and by Otto in the visible, but disagree somewhat with the work of Ehrenreich and Philipp and of Canfield, Hass and Hunter in the ultra-violet. Precautions were taken to avoid surface distortion and contamination and to correct for stray light, and it is claimed that on this account the present data, where they depart from the old, are to be preferred. The Kronig-Kramers relations are used to show that the data are internally consistent and also to suggest how they may be extrapolated to higher and lower energies.

Surface structures of some two hundred rhombohedral faces of cultured quartz are studied, using optical techniques. Simple triangular and interlaced spirals observed on some (011) and (101) faces are reported. With the aid of multiple-beam interferometry it is shown that these spirals differ from the usual growth spirals since the profile of the surfaces between their successive turns is convex, with no abrupt steps. The mechanism of the formation of such a profile is discussed, and it is suggested that it is a result of bunching of growth fronts followed by their etching.

Raman spectrum of rubidium iodide has been recorded for the first time using the resonance radiation of mercury (λ 2537 Å) as the exciter. The frequencies of the 24p limiting modes (p = 2, the number of non-equivalent atoms in the unit cell), postulated by Raman in 1943, which correspond to the frequencies from the critical points Γ, L and X, have been worked out using the shell model of Cochran, taking into account the nearest and the next-nearest neighbour short-range interactions and the polarization of both the ions. The observed Raman lines have been assigned to the overtones and the combinations of the phonon branches from Γ, L and X.

The lattice-vibration Raman spectrum of calcium tungstate has been measured, using excitation by a He-Ne laser. Eleven of the thirteen long-wave-length phonon modes which are Raman active in first order have been detected. Polarization studies have revealed the group-theoretical symmetries of ten of the phonons. The linewidths and relative intensities of the Raman peaks have also been measured. These results complement the information obtained from the infra-red reflection spectrum of calcium tungstate. The frequencies of the infrared and Raman active phonons are discussed in terms of the normal modes of the lattice.

The equations of motion of a spinning particle in a conformally flat space-time are derived and applied to Nordström's theory, in which the strong principle of equivalence is found not to hold.

A short discussion of the author's work on liquid junction potentials is given in the light of recent comments by Fröhlich and Guggenheim.

A recent proposal for an experiment to test special relativity theory is criticized.

The rotational analysis of three bands of a system of BiO(ν_e similar 14183 cm^-1) has been carried out. The system was observed in absorption and the analysis shows it to be ²II_1/2-²II_1/2 or case c, Ω = ½ - Ω = ½, where the lower state is the Ω = ½ component of the ground state. The internuclear distance r₀" is 1.894 Å. The rotational lines are broad, with a width of about 0.4 cm^-1, and the width varies little with J, at least in the range 30 ⩽ J ⩽ 80. It appears that the lines represent unresolved patterns of hyperfine structure components.