Table of contents

This paper discusses the gravitational instability of a non-uniformly rotating, infinite, axisymmetric cylinder of a homogeneous, heat conducting medium. It is found that the Bel and Schatzman criterion of gravitational instability remains unaffected, even when the medium is heat conducting.

Rotational analyses have been carried out for the 1-0, 2-0, 3-0 and 1-1 bands, of the far ultraviolet system of AsO⁺. The analysis confirms that the system arises from a ¹Σ-¹Σ transition. The following rotational constants were determined for the upper and lower states:

B_e' = 0.421₈ cm^-1 αe' = 0.0050 cm^-1r_e' = 1.741 Å

B_e" = 0.421₈ cm^-1 αe" = 0.0055 cm^-1r_e" = 1.611 Å

The electronic transition energy T_e = 42601.1 cm^-1.

When the pressure of a molecular gas surrounding a carbon arc is reduced below a certain value a sudden contraction of the cathode spot is observed. This is interpreted as a change from the thermionic to the vapour cathode arc.

A transition mechanism is suggested: on decreasing the molecular concentration of the ambient gas optical quenching is reduced and thus a decreasing number of molecules remove potential energy from excited vapour atoms. Hence an increasing number of excited atoms are available which transfer their potential energy to the electrons in the cathode substance, thereby releasing electrons from the cathode so that a vapour cathode spot is formed.

A numerical estimate of the required quenching cross section (order 10^-15 cm²) shows that it is in accord with the values found in optical quenching experiments. The implications of this approach in regard to tungsten, mercury and copper cathodes are discussed.

The semi-classical impact parameter method gives transition probabilities P_ji(R) which, for impact parameters R large compared with the atomic radius, are proportional to the oscillator strengths f_ji. When modified in such a way that reciprocity conditions are satisfied, the results obtained are in good agreement with quantal calculations even for near-threshold energies.

Cross sections are calculated in two ways. When the coupling is weak

Q(i→j) = ∫^∞_R0P_ji(R)2πRdR

where R₀ ≃ r_<, the smaller of the mean radii r_i, r_j, and when the coupling is strong

Q(i→j) = ½πR12 + ∫^∞_R1P_ji(R)2πRdR

where P_ji(R₁) = ½. We adopt the smaller of the two cross sections obtained.

The method gives good agreement with experiment for H 1s rightarrow 2p, He 1s rightarrow 3p and Na 3s rightarrow 3p. It is superior to the Born approximation, which overestimates the low-energy contribution from small impact parameters.

Cross sections are calculated for transitions between excited states of hydrogen.

Measurements are reported of the total charge transfer cross sections for Ne, A, Kr, Xe doubly charged ions in their own gas. They are for the processes 20σ02 + ½20σ11. Comparisons are made with experiments and with the quantum theory calculations of Fetisov and Firsov.

The value of the high temperature correction to the lattice specific heat arising from the anharmonic terms in the crystal potential energy is estimated for two cases on the basis of the elastic continuum approximation. The anharmonic constants are estimated from the measured thermal expansion and dependence of the elastic constants on both temperature and pressure. In the evaluation of the temperature dependence of the elastic constants the Born approximation ω² → ω² is not made since it neglects the effect of strain on the phonon frequencies arising from the perturbation of the polarization vectors. The results are compared with those of the anharmonic oscillator and linear chain models, and with a lattice model with nearest-neighbour interatomic forces. The anharmonic specific heat correction (at constant pressure) of a metal such as iron is estimated to be of the order of 15-20% at 1000 °K on the basis of present experimental data, but this result is sensitive to the measured values of the temperature coefficients of the elastic constants, which are not known too well for iron. The continuum model predicts the correct order of magnitude of the effect for germanium.

The infra-red absorption spectrum of two natural Type IIb semi-conducting diamonds has been measured by high resolution grating spectroscopy in the range 0.1 to 0.7 eV and at temperatures from 70° to 293 °K. The various absorption features (observed in much greater detail at low temperature than hitherto) were as follows: (i) a series of three lines due to excited states of bound holes at 0.305, 0.347 and 0.363 eV together with many smaller peaks, (ii) secondary peaks at 0.462, 0.508, 0.625 and 0.670 eV in the continuum and (iii) a low-level absorption near 0.16 eV. The observed widths of the excited states are inconsistent with the broadening theory of Lax and Burstein. However Kane's recent theory of lifetime broadening predicts the observed width of the 0.305 eV line to the correct order of magnitude. Hardy has shown that both (a) optical-phonon-assisted transitions and (b) impurity-induced single-phonon absorption are likely to occur in diamond. These conclusions are confirmed by (a) the observation of peaks in the continuum at energies separated from the excited states by 0.159 eV, the TO phonon energy and (b) the presence of absorption just below the Raman energy at 0.165 eV. The cross section for this single-phonon absorption is much higher than for the Type I (nitrogen) or irradiation-induced lattice absorption.

The interaction between optical lattice vibrations and carriers bound in shallow impurity levels in diamond structure crystals is investigated. It is shown that, while electronic transitions assisted by the emission of optical mode phonons are likely to produce easily observable infra-red absorption peaks in diamond, the corresponding peaks are not likely to be observable in the absorption spectra of doped silicon and germanium. An attempt is made to show that these optical phonon-assisted transitions will also be difficult to observe for deep-lying levels in silicon and germanium.

An account is given of conductivity measurements made on barium titanate single crystals. Previously reported results are extended and it is shown that the current per unit area through a crystal at fixed temperature is accurately given by

i = a(V/L) + b(V/L)²

where V is the applied potential, L the thickness, a is characteristic of the bulk material and b characteristic of the cathode material. Radio tracer experiments designed to elucidate electrochemical interactions at the anode are also reported.

The effective range theory due to Bethe for the elastic scattering of electrons by a potential behaving asymptotically like a Coulomb field is employed to derive an exact relation between the phase shift and the quantum defect. For zero energy electrons this relation reduces to the formula obtained by Seaton.

Extensive air showers in the size range N = 3 × 10⁵ to 4 × 10⁶ have been studied with an array of four water tanks, in which the shower particles are detected by the Cerenkov light they produce when passing through the water. It is found that the differential size spectrum of the showers has a rapid change of slope in the neighbourhood of N = 6 × 10⁵, the exponent changing from 2.3 ± 0.1 to 3.0 ± 0.15 with increasing N.

The cascade multiplication or attenuation of the number of particles as they pass through the depth of water in the tanks is reflected in the amount of Cerenkov light produced, and from this effect an estimate has been made of the effective exponent s of the shower particle integral energy spectrum E^-s. The values found for s range from s = 0.58 ± 0.06 for distances less than 3 metres from the shower axis to s = 1.7 ± 0.3 for distances greater than 30 metres.

In this paper an account is given of the investigations on the decay asymmetry of cosmic-ray muons carried out in two different energy bands with the help of a multiplate cloud chamber. Although similar investigations have been made in different laboratories with scintillation counters, employing the delayed coincidence technique for the detection of the decay electrons, the cloud chamber has been chosen for some special advantages which are discussed in the paper. The most important among these are (i) the decay electrons are detected from zero delay up to a delay of about 50 milliseconds, which is never possible in the delayed coincidence method, (ii) the change of direction of the decay electrons in the absorbing material due to scattering is avoided by dividing the whole absorber into thin plates separated by gaps in which the electrons are observed. Even if these electrons are subsequently scattered their original direction of emission is clearly observed, as shown in figure 1 (a) and (b).

After careful scanning of about 36 000 photographs taken by means of a fourfold coincidence and anticoincidence system about 1500 unambiguous μ-e decay events were selected. Of these, 1021 events correspond to a muon momentum interval 0.30-0.40 GeV/c and 482 events to a momentum interval 1.3-1.4 GeV/c at the experimental station, which was situated at a height 2.2 km. The up-down ratios of electrons emitted in the two momentum intervals are 1.17 ± 0.05 and 1.18 ± 0.08 respectively, which yield partial longitudinal polarizations of 0.34 ± 0.09 and 0.36 ± 0.11 after correcting for the depolarization effect of the atmosphere and moderator. Our results, therefore, show no evidence for the increase in the degree of polarization with increase of momentum of the muons which some workers have observed. The absolute magnitude of the polarization observed is consistent with a K/π ratio of about 5% in the pion spectral region 0.2 to 5.6 GeV.

The relative numbers of negative and positive pions produced from calcium by bremsstrahlung beams (280 and 320 MeV maximum energy) have been measured. Pions of 15, 28 and 48 MeV mean energy (emitted at 152° to the photon beam) were magnetically selected and counted in a coincidence arrangement. The π^-/π⁺ ratio drops from about unity to 0.28 with increasing pion and decreasing photon energy. The results agree qualitatively with the surface-production model proposed by S. T. Butler in 1952.

The normal modes of vibration of a molecule chemisorbed on a metal are modified because the metal atoms to which the molecule is bonded themselves form part of a giant molecule (the crystal lattice) with a quasi-continuous band of normal mode frequencies. This problem has the structure of a system of particles (the molecular modes) interacting with a field (the lattice modes), and the effect of the interaction is to raise the molecular frequencies. If a molecular frequency already lies above the top of the lattice band, it still remains as a discrete frequency when the interaction is included. On the other hand, a molecular frequency which falls within the lattice band can only persist as a discrete frequency if it is forced clear of the band by the interaction. If this does not happen, the molecular frequency disappears, and an extra frequency is added to the lattice band. The chemisorbed atom and the chemisorbed diatomic molecule are treated in detail. Two molecules chemisorbed on the same crystal are in interaction with each other via the normal modes of the lattice. This interaction, which is formally analogous to the retarded van der Waals interaction between neutral molecules, is small. The important interaction between chemisorbed molecules is connected with changes in the electronic structure as the two molecules approach each other.

This paper deals with the lattice thermal conductivity λ_g of three polycrystalline rods of silver alloys (containing respectively 0.55, 0.32 and 0.14 atom per cent of manganese in random solid solution), as obtained by applying the method of Grüneisen and de Haas to our thermal and electrical conductivity data on these alloys at helium temperatures, in magnetic fields ranging from 0 to 25.5 kilogauss. Contrary to the normal behaviour, it is found that the heat conductivity by the phonons is not limited by scattering by the conduction electrons. It has a T³ temperature dependence, but the magnitude is much too small to be attributed to the scattering at grain boundaries. Since these alloys are known to turn antiferro/ferromagnetic at these temperatures, it is possible that the phonons are scattered at domain boundary walls. It is also, suggested that heat transport through the medium of magnons is not significant in these alloys.

Low density polyethylene was cold-drawn by simple tensile loading to produce transversely isotropic material. The elastic behaviour of such materials can, according to classical elasticity theory, be defined by five independent elastic constants. Three of these can be derived from Young's modulus measurements in various directions and the remaining two from shear moduli. The Young's modulus determinations have been previously reported, and the present paper concerns the determination of the shear moduli by means of torsional experiments (carried out at room temperature) on rectangular prisms of polyethylene. The draw ratios ranged from undrawn (isotropic) to draw ratio 4.6. The shear modulus governing torsion about the symmetry direction fell from 4.6 × 10⁸ dyn cm^-2 for the isotropic material to about one-third of this value for the highest draw ratio. The shear modulus for the other two principal directions increased over this range of draw ratios to about 3 times the isotropic value.

All the experimentally determined shear moduli fell within the range calculated from the Young's moduli and the assumption that all deformations occurred at constant volume. Thus, although polyethylene is a viscoelastic material, for the small, elastic (completely recoverable with time) deformations here considered the well-established treatments of classical elasticity theory can be usefully employed.

The five elastic compliances were calculated and, for the highly drawn polyethylene, showed a wider numerical range of values than most crystals and polymers previously reported.

No molecular interpretation of these results can at present be suggested.

A proposition of Hanbury-Brown and Twiss is shown to imply that interference of light cannot occur unless either the transverse or the longitudinal component of photon momentum is so restricted that the position of the photon becomes so uncertain that the various geometrical paths through the apparatus cannot be distinguished.

Domain walls in ferromagnetic films may be imaged by out-of-focus electron microscopy. The wall images are light or dark depending on the relative sense of the magnetization either side of the wall, the incident electron beam being diverged or converged about the wall position. A relationship is obtained between the image widths of light and dark walls, for all distances out of focus and the true domain wall width. Values obtained for evaporated polycrystalline films are (to ±30%) permalloy, 1800 Å; iron, 1000 Å; nickel, 550 Å.

Domains in a thin evaporated film of a low anisotropy nickel-iron alloy with an induced uniaxial anisotropy were observed by the longitudinal Kerr effect. The magnetization reversal process of the film was observed in different transverse fields; the resulting variation of the domain wall coercivity is compared with theory.

A thorough investigation into the nature of magnetite colloids suitable for the Bitter technique has been undertaken. From the results of the investigation, changes in the method of manufacture are proposed to improve performance. These include the application of a strong magnetic field to the colloid during its preparation, and the careful control of conditions prior to the dispersal of the colloid.

Two grades of colloid are described - one to reveal the fine structure of domain walls under electron microscope examination, and the other to follow domain wall movements and trace domain growth under optical microscope examination whilst the fields are still applied.

Photographs of the results obtained with these colloids are included.

The determination of the permeability of ferromagnetic strips from measurements of their resistance and inductance is seriously complicated by concentration of the current at the edges of the strip. But in a stack of strips, carrying current in alternate directions, such as can be produced by folding a long strip, the current distribution across the width of a strip is more uniform; the behaviour of such a stack is analysed mathematically.

Detailed measurements on the variation of magnetization with applied field and temperature in the region of the Curie point are reported for nickel ferrite, cobalt ferrite, several cobalt-zinc and nickel-zinc ferrites, for manganese ferrite and for a magnesium-zinc ferrite. New observations on the magnetocaloric effect in magnesium zinc ferrite have also been made. Anomalies observed in the form of the curves of constant magnetization of ferrites with mixed structure but not with the fully inverse structure are tentatively ascribed to the presence in the specimens of two kinds of region with different Curie points. X-ray examination of some of the ferrites showed that it is unlikely that major variations of composition are responsible for the anomalies.

The form of the magnetic isothermals of a bulk specimen of the ferrite CoO_0.18ZnO_0.75Fe₂O₃ between 77° K and room temperature indicates the presence of strongly magnetic particles of maximum diameter about 40 Å in a superparamagnetic state dispersed in a non-magnetic matrix. Cooling in an applied field down to 4.2° K produces a displaced hysteresis loop characteristic of unidirectional exchange anisotropy. The coercivity at 4.2° K after cooling in zero field is about 5000 Oe.

The electrical conductivity of electrons moving in a one-dimensional disordered potential is discussed on the basis of the exact expression for the conductivity obtained from the density matrix, and the conductivity evaluated in the limits of weak and of strong scattering potentials. The method depends on a property of electron wave functions in such a potential, noticed by Mott.

It is shown that when a single crystal of an ionic solid is subjected to pure bending, the sign of the charge carried by edge dislocation lines can be determined. An experiment is described in which a specimen is deformed by four-point loading, and the potentials developed between the crystal faces and an electrode lying on the elastic neutral axis are measured. In sodium chloride under these conditions the surfaces are positively charged, indicating that a positive charge is carried by jogged edge dislocation lines.