Table of contents

The allowed and forbidden paramagnetic resonance transitions of Mn²⁺ ions in single crystals of cubic ZnSe have been investigated. The parameters describing the spectrum observed at 77 °K have the values g = 2.0069 ± 0.0002, A = -61.8 ± 0.1 × 10^-4 cm^-1 and a = 19.3 ± 0.1 × 10^-4 cm^-1 and the quadrupole constant P is zero within the experimental error of +0.03 × 10^-4 cm^-1. These parameters were found from a third-order calculation of the eigenvalues and they are discussed with reference to the nature of the bonding. The forbidden transition absorption line positions were found experimentally to be independent of the crystal orientation and this is explained by considering only the nuclear spin-electronic spin interaction term AS. I. However, in order to explain the experimentally observed intensity variation with crystal orientation for the forbidden transitions an interaction between the cubic crystal-line electric field and the term AS. I must be considered. An expression is obtained for the intensity of the forbidden transitions of an ion with electron spin S and nuclear spin I in a cubic field.

The solution of the equation of transfer of radiation for Doppler broadened resonance lines emitted by a two-level atom in a uniform plane parallel plasma has been calculated allowing for the variation of the source function in frequency and angle. This solution is compared with that obtained by assuming the source function is constant in frequency and angle, that is assuming complete redistribution. The line profiles and total line intensities calculated from the constant source function solution agree to within 10% with the profiles and intensities obtained from the exact solution. Thus the constant source function solution may be used with confidence.

The width of the spin resonance of conduction electrons in n-type silicon, which is related to the spin-lattice relaxation time, has been measured at microwave frequencies, between helium and room temperature.

There are two temperature regions of interest: (i) above about 50 °K scattering by lattice vibrations is the dominant relaxation mechanism, and the results are compared with existing theories due to Elliott and Yafet, and (ii) at lower temperatures the results are considered in the light of existing theories of scattering from ionized donor impurities.

The energy loss of fast electrons in heavily doped n-type silicon is calculated using optical constants which are deduced from the conductivity and carrier scattering time using classical dispersion theory.

These results are compared with the theory of the collective longitudinal motion of electrons in solids, the so-called plasmon effect.

The band constants deduced from the results of cyclotron resonance measurements at 4.2 and 1.2 °K carried out by Rauch have been used to calculate the hole concentrations at temperatures for which kT > Δ, the spin-orbit splitting (= 0.006 eV). The calculated hole concentrations may be expressed in terms of a density of states mass m*, and the value of m* found is between 3.6 and 4.8 electron mass units (e^-.m.u.).

From their experiments on the variation of Hall constant with temperature Wedepohl and Kemmey deduced a value of m* = 0.4 ± 0.2 e^-.m.u. Reasons for this discrepancy are discussed and it is shown that the experimentally observed value of m* can be obtained from the band structure if it is assumed that the relaxation times for carriers in one of the bands are much greater than in the other two bands. The value of mass is discussed in relation to the spin statistics of the acceptor state.

It has recently been shown that gases may be broken down by the intense electromagnetic radiation of focused laser beams. This paper describes the theory of this type of breakdown. The mechanism analysed is that in which an electron acquires energy from the radiation field by inverse bremsstrahlung absorption. When it has gained sufficient energy the electron collides inelastically with a gas atom. In some cases this will cause ionization, but in most cases the atom will be excited to a higher level. Photoionization by the absorption of a number of photons from the light pulse rapidly ensues. In this way the electron population multiplies exponentially. There is reasonable agreement between this theory and previously published experimental results.

The box variational method developed by Risberg and Percival is extended to include exchange in the one-state approximation. The computational labour involved in the calculations is greater than in the non-exchange case owing to the use of a non-orthogonal function basis which leads to a more general type of eigenvalue problem. Phase shifts are obtained for s-wave and p-wave scattering and these compare well with those resulting from direct solution of the integro-differential equation for the problem. Agreement is particularly good in the case of the s-wave results.

The energies of long-wavelength spin waves in iron-nickel alloys have been measured as a function of composition, using a neutron small-angle scattering technique. The behaviour of the composition dependence can be explained in terms of a simple model invoking long-range interaction functions J(r) between the three different types of atom pair, Fe-Fe, Fe-Ni, and Ni-Ni. There is evidence that on the body-centred cubic lattice the iron-nickel interaction J(r) changes sign from positive to negative as a function of distance. Between Fe-Fe pairs on a face-centred cubic lattice, the `exchange integral' as normally defined is found to be -9 ± 2.6 mev, which is consistent with other indications that face-centred cubic iron is antiferromagnetic.

The wave vector q of the magnetic order observed in the heavy rare earth metals is calculated on a model using an exchange interaction between the localized moments and the conduction electrons, assumed free. For a finite amount of order, energy gaps appear in the conduction bands at new Brillouin `superzone' boundaries associated with q. The Fermi surface is distorted by these boundaries. The total energy of the system is computed for finite order and minimized with respect to q. For small order this leads to the usual Ruderman-Kittel result, but as the order increases the value of q at the minimum decreases. The agreement with experiment is good for the simple model of Tm, Er and Ho, but less satisfactory in Dy and Tb where spin-disorder scattering is important. A modification of this model also accounts for the behaviour of the electrical resistivity. It indicates that the real Fermi surface lies just inside the plane hexagonal faces of the Brillouin zone, and that a large area of it is destroyed by the magnetic ordering.

The conflicting theories of the thickness of the moving helium II film given by Kontorovich and Franchetti are examined. The former is found to be consistent with the basic postulates of the two-fluid model, while Franchetti's derivation is shown to require correction. By arguments based on the thermodynamics of a system in which relative motion occurs, the two approaches are reconciled, confirming Kontorovich's result that the moving film is thinner than the static film.

The basic equation of the coupled heirarchy for the energy-dependent thermodynamic Green's function of two operators is shown to be equivalent to an obvious identity. This clear notion of the meaning of the equation permits a discussion of the connection between poles and excitation energies. It is shown that difficulties which arise from the use of the grand-canonical distribution may be avoided by using a simple ground-state average.

The boundary conditions in the impact parameter treatment of ion-atom collisions are examined. It is shown that the Coulomb interaction between the bound electron and the incident ion gives rise to a phase term which is not included in previous treatments of this problem. A new approximation, which takes account of this phase, is presented and applied to the resonant capture process H⁺ + H(1s) -> H(1s) + H⁺. First and second order cross sections are shown to have the asymptotic energy dependence of the impulse and second Born approximations, respectively.

The accidentally resonant single charge transfer cross section for the collision I⁺Hg (ΔE_[infinity] = 0.019 ev) has been measured in the impact energy range E_p = 5 - 1200 ev. Narrow (similar 0.02E_p) energy distribution of the incident ions is ensured by momentum analysis without subsequent retardation. Separation of the considerable elastic scattering component is achieved by slow charge collection at a single electrode in parallel electric and magnetic fields, and the energy distributions of the scattered ions are calculated. Despite large angle inelastic scattering, no enhancement of the cross section attributable to inward spiralling is found.

Using trial wave functions previously proposed by Flowers and Irvine, approximations are derived which allow the parameters and energies of seniority 1 and 2 states to be calculated from a single variational calculation of the seniority 0 ground state. The wave functions so obtained are used in conjunction with the Inglis formula for the moment of inertia. As in the Belyaev approach the effect of pairing is found to reduce the moment of inertia to about half the rigid-body value, but some of the ambiguities of that approach are removed. The effect of two-pair excitations has been re-examined and the results applied to the nickel isotopes.

We have analysed elastic electron scattering differential cross section data and interpreted them in terms of nuclear form factors. We conclude that the surface thickness of the proton distribution is smaller than had previously been thought and that there is some evidence that the proton density is depressed at the centre of the nucleus for nuclides in the region A [similar, equals] 58. The evidence from scattering by neighbouring nuclei also indicates that there is little difference, if any, between the proton and neutron distributions, and that the nuclear compressibility is the same in the region A [similar, equals] 58 and in the region of heavy nuclei.

An X-band (3 cm) microwave cavity method has been used to measure the electron loss rate in the afterglow of a pulsed discharge in helium. Further purification of spectroscopically pure gas samples was undertaken to give more reliable results and afterglow periods up to 60 msec were investigated. The positive ion reduced mobility μ₀ (as deduced from a measurement of the ambipolar diffusion coefficient) was found to be constant at 16.7 ± 0.5 cm² v^-1 sec^-1 in the pressure range 4-83 mmHg and this is attributed to the molecular ion He₂⁺. Measurements at pressures below 4 mmHg indicated the presence of both atomic and molecular ions and an extrapolation to zero pressure yielded a figure of 10.6 cm² v^-1 sec^-1 for the mobility of the atomic species He⁺. The frequency of conversion of atomic into molecular ions by three-body collisions was found to be 115p² sec^-1 in good agreement with theory.

The association of the origin of cosmic rays with the extragalactic radio sources yields an average intergalactic energy density not greatly different from the value measured for cosmic rays in the vicinity of the Earth, i.e. it may be as high as about 10^-12 erg cm^-3. Both the radio sources and the cosmic rays probably arise from violent events in the nuclei of galaxies.

Although it is possible that the energy spectrum of cosmic rays may arise directly in the violent events themselves, the characteristic spectrum dE/E^-r (r = 2.5 to 3) can also be due to the operation of a Fermi process on an extragalactic scale. It is shown that, provided the rate of energy gain for the whole cosmic ray distribution is greater than the rate at which energy is injected, and provided the process reaches a steady state, the spectral index must lie between 2 and 3.

An upper limit to the particle energies is to be expected when Larmor radii become comparable with the dimensions of the accelerating elements. This condition, applied to a particle energy of the order of 10²⁰ eV, leads to a dimension of about 10 megaparsec, if the acceleration process is extragalactic in origin.

Hall effect and resistivity measurements have been made on single crystal n-type samples of GaAs irradiated by electrons of energy 0.4 to 1.0 MeV at liquid nitrogen temperature. Results have been compared with predictions from the theory for displacement of lattice atoms based on a `sharp threshold' model. Acceptable agreement is obtained for both the energy dependence and the order of magnitude of the removal rate of conduction electrons, assuming a displacement energy of 17-18 eV. This result is compared with the minimum energy for displacements of about 9 eV found by von Bäuerlein. Calculations are included for secondary displacements using the assumptions of Harrison and Seitz, but it seems unlikely on this model that all our effects are caused by secondary events. Some observations are made concerning the nature of the displacement process.

Effects produced by nuclear resonant (Mössbauer) diffraction are usually masked by accompanying changes in electronic scattering. This complication can be removed by scattering from a compound at a diffraction spectrum for which the structure factor for electronic scattering is very small. Measurements on such a spectrum from a crystal of potassium ferrocyanide clearly show a diffraction peak in the ⁵⁷Fe nuclear resonance scattering.

Measurements of the drift velocity W and the diffusion coefficient D for selected species of neon ions in neon were made over the range 3 < E/p₀ < 45 v cm^-1 torr^-1. Two species of ion, having zero field mobilities of 4 and 7.5 cm² sec^-1 v^-1, were observed. The diffusion coefficient for the slower species increased from an approximately constant value at low values of E/p₀ and tended to the form D [is proportional to] (E/p₀)^1/2 at high values of E/p₀. Above a value of E/p₀ about 3 v cm^-1 torr^-1 the energy of these ions was shown to increase with increasing E/p₀.

The electronic Landé g factors for four energy levels in Ge I and Sn I have been recalculated by an empirical method without assuming the Slater ratio of the term intervals in the p² configuration. Improved agreement with observation is obtained.

A theoretical prediction that, under certain conditions, a single pulse of optical excitation can result in a modulated fluorescent intensity from the atoms in a vapour, has been tested by experiment. Measurements obtained after the pulsed excitation of mercury vapour, with Zeeman splitting in a magnetic field, have provided evidence that the predicted modulation does occur.

A faulty discussion by Bopp in 1959 leading to an alleged lower bound for the energy of an N-electron system suggests a very simple approximate formula for the ground state energy. Calculations for the series of ions Be⁺, C^{2 +},... A^{8 +} yield results with an accuracy to about 2%.