Table of contents

The total energy and momentum of a mechanical-electromagnetic system are regarded as key concepts. The usual theory for a continuous system may not be applied without some alteration to a system of point charges because the orthodox electromagnetic energy-momentum tensor for the field leads to infinite self energies. In the present paper the method adopted is to assume that Maxwell's equations hold for point charge sources but to regard the equations of motion of the charges as dependent on the energy-momentum tensor chosen. A class of modified energy-momentum tensors are constructed in such a way that the field singularities do not lead to difficulty and the corresponding equations of motion are derived. Thus a class of theories is obtained each of which is capable of describing the history of a point charge system in terms of energy and momentum flow. One member of the class gives the Lorentz-Dirac equation of motion with radiation reaction term and the energy-momentum flow picture provides an interpretation of the runaway solutions and of pre-acceleration. One other member of the class is of particular interest because it does not lead to such results. In this theory, named the interaction theory, the equations of motion do not contain radiation reaction terms and whereas a group of charges may radiate on account of their mutual interactions an isolated point charge cannot, whatever its motion. By considering a slowly moving periodic system it is shown in detail how in the interaction theory the forces maintaining the motion supply the energy for the radiation. When certain reasonable conditions are satisfied it is shown that the interaction theory leads to the same results as the orthodox theory for the dipole radiation involved in a wide range of processes including Thomson and Coulomb scattering. The differences are only significant when the number of point charges is small. There is a possibility that the interaction theory may lead to a clearer understanding of the methods of renormalization used in quantum electrodynamics.

An approximate equation of state, previously derived on the basis of information theory, is applied to a classical system of non-interacting hard spheres, and the results are compared with those from the cell and tunnel models. By a slight modification of the original statistical argument, it is shown that the cell and tunnel model equations of state are obtained as particular cases. With either approach, at low densities PV/NT is obtained as a power series in V^-1/3 instead of the correct form in powers of V^-1, indicating in this region a break-down in the statistical approximations.

The first-order terms in a separation-type calculation applied to a nuclear spectrum are investigated in detail. The assumption that the separation distance is independent of state is not satisfied well in the particular case considered (¹⁸O, using the Kallio-Kolltveit singlet S potential); allowance for its variation makes an appreciable change in the predicted spectrum.

Cross sections for the excitation of the B ²Σ state of N₂⁺ by electron impact on N₂ have been measured using a crossed beam technique. Maximum cross sections for the ν = 0 and ν = 1 levels are 20.5 × 10^-18 cm² and 1.7 × 10^-18 cm² respectively. The ratio of effective cross sections of the (0, 0), (0, 1) and (0, 2) bands of the B ²Σ-X ²Σ system is 1:0.32:0.075. Comparisons are made with theoretical predictions and the results of other workers.

At large impact energies E, the cross sections Q, for the electron or proton ionization of the inert gas atoms, are written in the form QE = A log E + B. A is calculated using theoretical and experimental values of the photoionization cross sections. The calculated A's are in good agreement with the proton ionization of Hooper et al. but disagree with the electron ionization data of Schram et al. It is found that the electron ionization data of Golden and Rapp and of Smith are not sufficiently accurate to give reliable values for A. However, when the calculated values of A are normalized to these electron ionization data at impact energies between 20 and 30 atomic units we can obtain estimates for the B's which are in good agreement with the proton ionization data. These B's differ greatly from those of Schram et al.

An iteration-variation method applicable to elastic and inelastic atomic collision problems is described. The method uses trial functions formed from a sequence of Born iterations and, making use of recursion relations, is able to save much computer storage space, particularly in inelastic problems. Convergence is speeded in cases where the iterations themselves converge, and is obtained also from diverging sequences of iterations.

Examples are presented from electron-helium collisions (elastic), positron-hydrogen collisions (elastic) and electron-hydrogen collisions (elastic and inelastic).

The photoionization cross section of the hydrogen molecule is calculated for wavelengths between the threshold (804 Å if the initial state is rotationless) and 430 Å. The Weinbaum approximation is used for the initial electronic state, and in the final state the system is taken to consist of an H₂+ ion in the 1sσ_g ground electronic state and a free electron moving in a field which includes the contribution from the quadrupole moment of the ion. Simplifying approximations are made in the treatment of the rotational and, in some of the calculations, also of the vibrational states. It is believed, however, that the most important source of error is the uncertainty in the phase shift of the continuum pσ orbitals, and because of this the cross sections may be in error by up to 12%. The results agree fairly well with the experimental results by Wainfan, Walker and Weissler, and by Cook and Metzger.

Using a variational principle, a narrow ²S resonance of the He^- system just below the first excited state of helium has been calculated. The position of this resonance is E_n = 19.5^+0.1_-0.2 eV and the width Γ_n lies in the range 0.8 × 10^-2 eV to 3 × 10^-2 eV, or possibly a little higher.

The dependence of the width on the structure of the resonant state has been analysed for two alternative expressions.

We have analysed elastic electron scattering data by means of charge distributions derived from single-particle proton wave functions in a central potential of the Saxon-Woods type, and have found that it is possible to fit both the electron scattering and the proton binding energies as far as these are known from (p, 2p) scattering experiments. In this paper we report results for ⁴⁰Ca and ³²S, and, in the case of ⁴⁰Ca, compare the electron scattering results with those obtained using phenomenological charge distributions.

A simple method proposed by the author for evaluating the van der Waals constant has been extended to give the non-additive third-order perturbation energy for three interacting atoms separated by large distances. For three hydrogen atoms in their ground states, separated by distances R₁, R₂ and R₃, the leading term has been calculated as ₀⁽³⁾ = (43.2854±0.0020)ΩR₁^-3R₂^-3R₃^-3a₀⁹ ryd where Ω is an angular factor. This result compares favourably with the previous most accurate estimate ₀⁽³⁾ = 42.8ΩR₁^-3R₂^-3R₃^-3a₀⁹ ryd obtained by Midzuno and Kihara.

This paper extends the work reported by Grant in 1961 on matrix elements of two-electron interactions by providing sum rules for the elements of the magnetic part of the Breit interaction over closed groups.

Coefficients of direct and exchange integrals occurring in relativistic self-consistent field theory are tabulated for the electrostatic interaction involving electrons of f or g type; reference is made to a recent tabulation of the corresponding coefficients for the magnetic interaction involving electrons up to f type. With these coefficients it is now practicable to calculate relativistic Hartree-Fock self-consistent field wave functions for the ground states of all the naturally occurring elements.

The spatial distribution of magnetic moment disturbance around fifteen different transition metal impurities in iron (Ti, V, Cr, Mn, Co, Ni, Mo, Ru, Rh, Pd, W, Re, Os, Ir and Pt) and around four such impurities in nickel (V, Cr, Mn and Fe) has been investigated. A neutron scattering technique was employed that gives information on the spherically averaged moment distribution out to large distances from the impurity atom (similar 10 Å). V, Cr, Co, Ni, Mo, Ru, Rh, Pd, W, Re, Os, Ir and Pt produce a small net increase in moment on iron atoms around an impurity site. Those elements that lie to the right of iron in the periodic table, Co, N1, etc., seem to produce a uniformly positive disturbance in the iron matrix while the remaining elements give a positive disturbance which is apparently confined to a region of a radial extent of approximately 5 Å. All the solutes produce a loss of moment relative to pure iron at the impurity atom sites. The impurity atom moments are generally consistent with those measurements that are available for the more concentrated alloys. Around iron impurities in nickel the moment disturbance is effectively confined to the solute atom site. On the other hand vanadium or chromium impurities reduce the magnetic moment on neighbouring nickel atoms very markedly. The latter system is studied over a range of solute concentrations.

Proton spin-lattice relaxation times T₁ for anhydrous solutions of hydrogen chloride and deuterium chloride have been measured at 20.8 Mc/s by a 90°-τ-90° pulse method. The measurements have been made, for most solutions, from the supercooled liquid (-116 °c) up to the liquid-vapour critical temperature (51.4 °c) and a little above. These T₁ results for the HCl-DCl liquid solutions have provided direct evidence of the significant part played by the spinrotation interaction mechanism of relaxation in liquid HCl and have allowed a detailed analysis. The correlation times for the dipole-dipole intramolecular interaction τ_d and the spin-rotation interaction τ_sr have been determined independently and shown to vary in the opposite way with temperature. The product τ_dτ_sr was found to be almost independent of temperature and approximately six times greater than a theoretical value for spherical molecules given by Hubbard. It is suggested that τ_d and τ_sr are approximately equal at the critical temperature. The use of viscosity data is remarkably successful in the interpretation of molecular motion in this liquid for which the mean rotational quantum number is quite low. Two new contributions to relaxation, inter spin-rotation interactions, are evaluated approximately but they are probably negligible in liquid HCl.

It is shown that covalent bonding affects the absolute intensities and form factors for neutron diffraction from antiferromagnetic and ferromagnetic salts. The general effect is to reduce the absolute intensity below the theoretical value for a purely ionic salt and to make the form-factor curve somewhat flatter (except in directions very close to the forward direction).

In the case of Ni²⁺ and Cr³⁺ salts the reductions in absolute intensities observed by Nathans, Alperin and others are roughly consistent with the degree of covalency indicated by the nuclear magnetic resonance measurements of Shulman and Knox. Furthermore, Alperin's observed form-factor curve for NiO can be largely explained by allowing for the same degree of covalency. On the other hand, we have not been able to explain the observed absolute intensities or the form factors for Mn²⁺ salts in these terms.

It is also shown that Bragg scattering experiments on crystals with large unit cells or measurements of diffuse elastic scattering should reveal a sharp forward peak in the form factor.

2: 1 harmonic cross-relaxation processes in ruby have been investigated experimentally by a continuous saturation method at a fundamental frequency of about 9.6 Gc/s. The linewidths and maximum rates relative to spin-lattice relaxation have been measured as functions of Cr concentration in the range 0.024%-0.13% at 4.2 °K and for a concentration of 0.13% at 20.3 °K. The linewidths were approximately independent of concentration and temperature. Existing theories due to Hirono and Grant are only partially satisfactory in explaining the results.

The width and the shape of the electron spin resonance absorption line have been measured as a function of the spin concentration in irradiated frozen peroxide solutions. Good agreement is found with a modified version of the Kittel and Abrahams formula. It is shown that line-width measurements can be used to obtain the local concentrations of radicals when these are produced by irradiation in clusters.

Temperature dependence of chlorine pure quadrupole resonance frequency in 2,5 dichloroaniline and 3,4 dichloronitrobenzene is experimentally studied and the experimental data are compared with the corresponding theoretical calculations based upon Bayer's theory. An attempt is made to calculate the temperature dependence of torsional frequencies in these molecules. Effect of NO₂ and NH₂ substitutions on the resonance frequency is pointed out.

Possible mechanisms for the enhancing action of a magnetic field on the relative intensity of spectrum lines from higher ionization stages are suggested for the interrupted vacuum arc and for the open arc. The susceptibility to this phenomenon exhibited by rare earth elements is interpreted in terms of the presence of low-lying energy levels.

Results of measurements through the near infra-red of the optical and magneto-optical properties of iron, nickel and cobalt are reported and it is shown how they can be used to obtain spectroscopic information about the unpaired (ferromagnetic) electrons.

Sharp zero-phonon absorption lines in lithium fluoride have been studied under uniaxial stresses of up to 16 kg mm^-2 applied along crystalline symmetry directions to investigate the electronic properties of the colour centres involved. The centres have been produced by electron irradiation at dose rates of 10⁶ rad min^-1 for one hour and, in some cases, subsequent optical bleaching procedures. High resolution optical absorption measurements have been made at 4 °K on eight of the most prominent lines produced, which have air wavelengths of 3599, 3909, 3932, 4747, 4874, 5234, 5612 and 6009 Å. All the lines show splittings into several components on the application of the stress, the maximum observed splitting being about 40 cm^-1. The spectra have been investigated using polarized light and the results are interpreted in terms of electronic and/or orientational degeneracy of the centres.

Many zero-phonon lines are known in the absorption spectra of diamonds at 77 °K. Some lines are only produced in irradiated diamonds and others by a further thermal annealing. All these lines split under an applied uniaxial stress and polarization spectra have been obtained for stress applied along the three principal directions [100], [110] and [111]. A parallel theoretical investigation has been made of possible stress spectra for cubic crystals and these have been grouped into seventeen types dependent on the orientational and electronic degeneracy present. The application to the diamond spectra supports the [111] orientation of the centre responsible for the 4152 Å line (N3a) found in many natural diamonds.

Conditions for the growth and propagation of infinitesimal space-charge waves in the presence of a differential negative resistance are derived. It is assumed that:

1. The charge carriers are electrons.

2. The differential negative resistance is due to field-induced transfer of electrons to zero-mobility states.

3. The rate of escape from these states is independent of electric field.

4. Effects due to momentum and energy relaxation can be neglected.

A rough extension of the linear theory to the problem of the steady state mobile domain is made and it is inferred that the velocity of the domain in n-type golddoped Ge at 20 °K is equal to the phase velocity of the wave associated with conditions pertaining near the drift-current peak. Order of magnititude agreement with experiment is obtained. Applying the same criteria to n-type GaAs and comparing with the observed domain velocity yields a rough estimate for the time constant of scattering to low-mobility states, namely of the order of or less than 10^-12 sec. However, this is short enough to suggest that momentum and energy relaxation effects ought to be included in a description of negative resistance effects in this material.

From resistance measurements on dilute alloys of manganese in titanium it has been concluded that the resistance minimum observed in these alloys is associated both with localized moments on manganese atoms in the α phase and also with a proposed transformation of any β filaments which are present.

Measurements of the volume coefficient of thermal expansion and of the self-diffusion coefficient of 99.999% pure tin in the solid phase at temperatures up to 0.05 °C below the melting point, and of the expansion coefficient of liquid tin supercooled through the melting point, show no evidence of the pre- and post-melting anomalies predicted by the Frenkel-Bartenev theory of melting and invoked by Khomyakov et al. and Boyle et al. to explain their experimental data. It is shown theoretically that impurities which do not form a solid solution should produce pre-melting effects with the same temperature dependence as that predicted by the Frenkel-Bartenev theory.

Attention is drawn to an error in the paper of Champeney and Moon. The simplest interpretation of this experiment and that of Moon et al. is that time dilatation is a consequence of acceleration and not of relative velocity.

A four-body operator is constructed which allows a physically significant and complete classification of states of all irreducible representations of the rotation group R(5) appropriate to jj coupling in the nuclear shell model with charge-independent pairing interactions. The corresponding operator for R(8) allows complete classification of some important irreducible representations required in LS coupling.

A method is described for the measurement of small energy losses of relativistic particles by balancing the signals from two gas Cerenkov detectors.

An 8 × 8 array of Franck-Condon factors and r centroids is reported for the A ¹II-x ¹Σ⁺ system of CS. q_ν'ν" and r_ν'ν" are obtained by numerical integration of the Morse wave functions.

It is shown that the calculations previously made for H_c2 and H_c3 in the Ginzburg-Landau temperature region can be extended to all temperatures using the methods given by de Gennes and by Maki.

A fine structure in the excimer emission band of naphthalene in toluene in the presence of quenching agents is reported, and an explanation given in terms of a proposed quenching mechanism.

Corrections to 1965 Proc. Phys. Soc.85 1048.