Table of contents

The polarization of the protons from the reaction ¹²C(d,p)¹³C at 6.9 MeV bombarding bombarding energy, and from the reactions ⁹Be(d,p)¹⁰Be, ¹⁰B(d,p)¹¹B and ⁴⁰Ca(d,p)⁴¹Ca at 8.9 MeV bombarding energy has been measured at certain angles of emission. The sign of the polarization was found to be positive when J_n=l_n+½ and negative when j_n=l_n-½ except for the reaction ⁴⁰Ca(d,p)⁴¹Ca. The results of the ¹²C(d,p)¹³C measurements suggest that the polarization does not vary rapidly with bombarding energy.

An experiment is described in which the capture rates of negative muons were measured for selected elements. A comparison between the experimental results and the theoretical predictions of Tolkoek and Luyten suggests that tensor and/or axial vector couplings are favoured in the interaction.

The paper contains a calculation of the higher cluster terms neglected in the variational calculation of the binding energy of the ¹⁶O nucleus given in an earlier paper. All the different contributions to the next term in the Ursell-Jastrow cluster development are calculated with help of an approximation based on the short range of the correlations. The wave function found in the earlier paper is used. The numerical results show that with the higher cluster terms both binding and density of the ¹⁶O nucleus are still reproduced by the two-body interaction with the repulsive core radius between 0.2 and 0.6 fermi. The higher cluster terms are found to be of importance in any attempt at quantitative results.

The radiative capture cross sections for 14.5 MeV neutrons have been measured for some 30 nuclides selected over a wide range of the periodic table. Chemical procedures were found essential to separate and identify the residual activities arising from capture reactions from the activities caused by the many other competing reactions possible at this neutron energy. Errors due to capture reactions caused by the small percentage of low energy neutrons, which were unavoidably present during the irradiations, were taken into account.

The cross sections found were of the order of 5 mbn for all except the lightest of the nuclides examined. A plot of these cross sections with respect to neutron number indicates relatively low values for the cross section near magic neutron numbers. These depressions are not so marked as those observed in experiments with fission neutrons. The general level of 5 mbn found for radiative capture cross sections for 14.5 MeV neutrons is much higher than the value predicted from some considerations of the theory of the compound nucleus. The consequences of this disagreement are discussed.

Cyclotron resonance at microwave frequencies is used to observe the changes in the band structure of germanium and silicon caused by a non-isotropic elastic strain. It is shown that an elongation of the crystal in a given direction raises the energy of those minima of the conduction band which lie on the corresponding direction in momentum space and, conversely, a contraction lowers the energy. A non-isotropic strain decreases the intensities of the hole resonances but this effect has not been studied in detail. The results are consistent with conclusions drawn from piezo-resistance measurements.

Using an interpolation procedure the Born approximation to the cross sections for the excitation of hydrogen atoms from the 2s state to the eighth and higher levels has been obtained from computed cross sections for transitions to the lower discrete levels and to the continuum. An incident energy range of from 5 ev to 120 ev is covered.

It is shown that previous applications of Onsager's theory to dielectric dispersion have contained an incorrect assumption about the behaviour of the reaction field when the applied field is varying. An equation for the complex dielectric constant is derived, using Onsager's model and taking proper account of the reaction field. An approximate method of solving the equation is developed and it is shown that the equation approximates closely to the simple Debye equation - _∞ = (₀ - _∞)/(1 + jωτ) the microscopic and macroscopic relaxation times being almost identical.

An analysis is given of the radio- and audio-frequency modulation method employed in microwave spectroscopy. The results of the theory are compared with measurements taken on a 8 mm microwave spectrometer and are found to be in close agreement. The calculations are extended to include the case where an absorbing gas is enclosed in a resonant cavity.

The shape of the absorption edge in the semiconductor Bi₂Te₃ has been determined from transmission measurements on cleavage sections. The edge is of the form expected for indirect transitions, but an interpretation in terms of phonons characterized by a single energy is not applicable. A brief study of anisotropy effects is included.

The energy gap at room temperature is close to 0.13 ev with a temperature coefficient of -0.95 × 10^-4 ev deg^-1. The refractive index, determined from interference fringes, is 9.2 in the region 8-14_μ.

In degenerate samples the absorption edge is displaced towards higher energies. A simple quantitative discussion of this effect is given.

A magnetic field splits up electron energy bands in a solid into a series of sub-bands. The absorption edge which arises from transitions between two such bands across an energy gap then shows a structure from transitions between the various sub-bands. The shape of this structure is considered for direct transitions between simple spherical bands, spheroidal bands and degenerate bands. This often takes the form of a series of peaks from which the effective masses of the bands can be determined, but there are cases in which the effect of the field is less dramatic and forms a series of steps. Absorption from indirect transitions involving phonons also forms a series of steps.

Employing Born's theory of crystal lattices, the elastic constants of fluorspar have been evaluated theoretically. Besides the coulomb forces, repulsive forces between nearest neighbour calcium and fluorine atoms and fluorine-fluorine atoms have been assumed and the constants of the repulsive energy were evaluated from the equilibrium condition, the experimentally determined compressibility and the principal Raman frequency of fluorspar. The experimental values of c₁₁, c₁₂ and c₄₄ are in fair agreement with the theoretically calculated values. Born's theory gives the sign of c₁₂-c₄₄ for fluorspar correctly but the theoretically calculated value of c₁₂-c₄₄ is only about half the experimentally observed value.

When a liquid is placed in a vessel held by a torsional suspension and the whole is set in rotation about a vertical axis, the viscosity of the liquid may be deduced from observations of the time period and decrement of the oscillations. This method of measuring viscosity has many practical advantages, but there are mathematical difficulties in making the calculations. The cases of spherical and cylindrical vessels are considered in detail and formulae are obtained for the calculation of the viscosity which are very accurate and easier to use than those previously proposed. The case of an axially symmetrical vessel which departs slightly from the spherical form is also considered, and formulae (valid only when the frequency of oscillation is high) are obtained for an axially symmetrical vessel of any shape. Corrections for the effect of external air resistance are also discussed.

The practical possibilities of the oscillating vessel method for accurate absolute measurements have been investigated. An improvement in Andrade and Chiong's apparatus was effected by using a capillary tube for the stem of the spherical bulb so that the liquid acted as its own thermometer. Abnormally large logarithmic decrements were found to occur with large amplitudes of rotation, and attention has been given to the best statistical method of calculating the decrement while avoiding this effect. A value of 1.0025 ± 0.0005 CP was obtained for the viscosity of water at 20°C, but an analysis of the sources of error indicates that the accuracy could be increased by further improvements well beyond that of the best capillary tube determination (1.0019 ± 0.0003 CP). These improvements would include the replacement of the spherical bulb by a cylindrical vessel.

Measurements are reported of reversible permeability and associated losses for a specimen of magnetically annealed Perminvar possessing a rectangular B-H loop. Measurements were recorded both as the hysteresis cycle was traversed and when a circular domain was nucleated and pushed into the centre of the specimen using a small pulsed field. Under these conditions the observed eddy current losses were twelve times those calculated from a uniform permeability model. A tentative explanation of the nature of the restoring force on the circular wall is given.

General formulae applicable to any model or any domain process are derived for the magnetic susceptibility χ and the magnetically dependent part of Young's modulus ΔE. From these formulae expressions are obtained for χ and ΔE in the initial magnetization regions for domain assemblies where magnetization proceeds by (a) rotation of domain magnetization vectors against internal strain anisotropy, (b) rotation against magnetocrystalline anisotropy characterized by one, three or four preferred axes and (c) simple movement of 90° and 180° boundary walls. It is then shown how the types and relative importance of the domain processes operative in the initial magnetization region may be determined from measurements of χ and ΔE. Examples of this procedure are given and include the case of annealed cobalt for which the ΔE effect is due entirely to rotations against uniaxial magnetocrystalline anisotropy energy, while the susceptibility arises mainly from 180° boundary wall movement. For annealed nickel, experimental values of ΔE and χ obtained by a number of workers vary widely and this is shown to be due to (i) differences in the relative proportions of 90° and 180° boundaries and (ii) the influence of the annealing process on the ease of boundary wall movement.

A discharge in a longitudinal magnetic field in which the plasma pressure is balanced by electrodynamic forces is considered. It is shown that the resulting current flow is helical about the axis of the discharge. The direction of the helix is such that the initial longitudinal field is amplified inside the discharge channel. Some experimental evidence supporting the theory is presented.

Electrons may be removed from the gas between a pair of plane parallel electrodes by being swept out by the field, by recombination, by attachment or by diffusion. At high enough frequencies diffusion is the most likely mechanism. This can be tested quantitatively by plotting the relation between EΛ and pΛ (E=electric field required to produce breakdown, p=gas pressure, Λ=`diffusion length' for the gap). It can also be tested qualitatively by observing the decrease of E with increasing gap width d. The electrodes must be properly profiled to avoid breakdown beginning at the edges.

The necessary observations of breakdown voltage, electrode spacing, electrode size and gas pressure are made for air, hydrogen, nitrogen and neon, at 9.5 Mc/s. The (EΛ,pΛ) plot gives a single line for ultra-high-frequency breakdown, and E decreases with increasing d in accordance with diffusion theory. Values of the ionizing efficiency η are calculated.

The mathematical theory of semi-rigid asymmetric top molecules is re-formulated by introducing a new set of operators for angular momentum. All matrix equations are thereby replaced by ordinary differential equations, and the necessity of solving a formidable secular equation for the determination of energy is dispensed with. An analytic expression for energy correct to the second order can be obtained by the methods delineated here.

A study is made of the thermal behaviour of solid mixtures, containing a component A with molecules having several orientation states whose co-operative interaction leads, in pure A, to a second-order transition with a discontinuity in the specific heat and a diluting component B with molecules of the same size. Regular models are used and it can be shown from previous work on ternary assemblies that if A has two equivalent orientation states and complete equilibrium is attained, then the curve of critical temperature against the mole fraction x_A of A passes through the origin. It is shown here that if A-B diffusion is forbidden in the temperature range concerned so that the distribution of A and B is fixed, though A molecules can change their orientation, then the specific heat is continuous below a critical value of x_A. This effect depends on short-range ordering and a first-order quasi-chemical approximation is used. Similar results are obtained when A has three available orientation states. A short investigation is also made of results when the interaction with B removes the equivalence between the two states of A. The effects here do not depend on short-range ordering, a random statistical approximation is used and it is found that even the smallest proportion of B renders the specific heat continuous with a maximum replacing the discontinuity. Finally, these various types of behaviour are briefly compared with some observed dilution effects.

The determination of the spatial frequency density in the image recorded by a film or a photographic plate is shown to be possible by the measure of the total flux transmitted when the film or plate is illuminated by a sinusoidal distribution of light superposed on the transparency. The sinusoidal light distribution is produced in the form of two-beam interference fringes. In the present instrument fringes of good contrast are obtainable at frequencies greater than 20 per millimetre. The apparatus has been used to determine the frequency spectra of slits, a line-grating and of different scenes taken by air photography.

Corrections to 1955 Proc. Phys. Soc. A 68 346

Corrections to 1958 Proc. Phys. Soc.72 353