Table of contents

The collective approach to a Fermi gas is discussed by considering the wave functions of non-interacting Fermi gases in one and three dimensions, and of the interacting Fermi gas. It is shown how to write the one-dimensional case exactly in terms of collective coordinates, and how these have a well defined existence for long wavelengths even without interaction. This is extended as far as possible to three dimensions, and it is shown how the statistics affect the collective motion in the presence of interaction. A brief discussion is given of how calculations may be performed when redundant sets of coordinates are used.

Resonance charge transfer cross sections are calculated for protons in atomic hydrogen in the ground and first two excited states. The cross sections for an excited atom are nearly an order of magnitude larger than those for the ground state.

The adiabatic theory allows for perturbation of the atom by treating the colliding electron as a fixed point charge. The form of the wave functions obtained may be shown to be correct in the limit of large separations. Numerical results are discussed for the s- and p-phases in electron-hydrogen collisions. It is considered that the adiabatic theory over-estimates the effect of perturbations of the atom for separations of order 1 atomic unit. The error introduced for the s-wave may be particularly large.

From the theory of Eisenschitz (1949) on the steady non-uniform state of a liquid, a magnitude has been calculated for the anisotropy of flow in a liquid due to a distortion of the radial distribution function by a shearing force. The optical anisotropy has been obtained by using the Bragg (1924) method of calculating double refraction from the variation of the polarization due to the distorted distribution function. The value Δn=7.1 × 10^-8 (calculated for chloroform, for which the distribution function is known and of which the polarizability does not differ greatly from that of carbon tetrachloride) shows that the effect may be detected experimentally in a liquid normally isotropic.

The calculation also shows that the main contribution to the anisotropy arises from small values of the range r, and the magnitude of the anisotropy is independent of the precise way in which the distortion decreases at large distances. This implies that the ` strong ' condition of Eisenschitz cannot be supported by an appeal to the isotropy of flow.

Probabilities P_n have been determined for the emission of electrons in groups of n numbering from zero to eight occurring as a result of a single primary. Beryllium copper surfaces under different activation conditions have been studied for primary energies between 100 and 300 ev, P₀, having values between 0.5 and 0.2 falling to a minimum at intermediate energies, and P₁ with values 0.3 to 0.4 rising to a maximum at intermediate energies remain larger than any other probability. Probabilities above P₁ for constant primary energy fall off with number in two distinct curves, that for even numbers lying above and falling less steeply than that for odd numbers. Separation of these curves depends on surface treatment. For activated surfaces probabilities P₁ to P₆ show evidence of maxima in the energy range covered; P₇ and P₈ are still rising at the end of the range. For unactivated surfaces only P's for odd numbers of electrons show a clear decrease at higher energies; P'_s for even numbers of electrons, with the possible exception of P₂, are still rising at the end of the range.

Electron transmission measurements, using a collecting cup and galvanometers, have been made for homogeneous energy beams in the range 0.25-0.75 MeV in foils of Be, Al, Cu, Ag and Au. The discrepancy between the present measurement of extrapolated range in aluminium and the generally accepted range-energy relationship cannot be simply explained in terms of low energy secondary emission or geometrical effects. Transmission measurements through silver foils agree, however, with other published results. The angular distribution of electrons emerging from the exit side of a foil has been examined. This appears to approach a cosine distribution at low transmissions. Further information on range values, and some confirmation of voltage calibration have been obtained from ionization in depth measurements.

Measurements of the electrical conductivity, Hall coefficient, thermoelectric power and Nernst coefficient on specimens cut from zone melted Bi₂ Te₃ and on a single crystal are described. The current flow was parallel to the cleavage planes and the galvanomagnetic effects of the single crystal were measured with the magnetic field perpendicular and parallel to the cleavage planes. For the other specimens the Hall and Nernst coefficients were measured with the magnetic field perpendicular to the cleavage planes. The temperature range was 100°K to 600°K and specimens with a wide variation of impurity content were used. Analysis of the thermoelectric power and conductivity in the extrinsic range indicated that the specimens were partially degenerate, and when allowance is made for this, the temperature dependence of mobility is T^-1.63 for electrons and T^-1.94 for holes. In the high temperature range the conductivity measurements yield a value of the energy gap at 0°K of 0.21 eV. The temperature dependence of the Hall coefficient in the extrinsic range is anomalous and the explanation is not known. The Nernst coefficient Q exhibits the general behaviour expected for a semiconductor, and it is shown that it obeys a relation which can be derived from Moreau's relation, Q being proportional to TRσd²E/dT² (thermoelectric power = dE/dT, Hall coefficient = R, conductivity = σ).

The colours observed when white light is reflected from metals covered with a thin oxide film are considered, and a theory of selective transmission of light into the metal is developed. The Smith Chart is used to calculate the variation of the composition of the reflected light with the thickness of the oxide film.

A study is made of the possibility of increasing the response of an optical system to a given spatial frequency by means of apodization, when the wave front aberrations and defocusing are supposed to be known.

By the usual methods of the calculus of variations, the condition for maximization of frequency response for variation of transparency is expressed as a functional equation, which may be approximated to by a linear second-order eigenvalue problem, for the transparency. Some examples are discussed.

The magnetic susceptibilities and electrical properties of a series of quenched alloys of uranium with zirconium, niobium and molybdenum, metals which have four, five and six outer electrons respectively, were measured over the temperature range 90 to 300°K. The general features of the three systems are the same, with anomalies at about 0.5 and 2.0 atomic per cent of the solute. The first anomaly is of unknown origin, and the second suggests that alloys containing up to about 2 atomic per cent of the solute may be obtained in the α-form by quenching them from the γ-phase field, and that within this composition range the behaviour is consistent with the full Brillouin zone structure that has been proposed for α-uranium.

The conditions under which a reduction in the demagnetizing energy in a uniaxial crystal can be brought about by rotation of the magnetization vectors (μ^* effect) is examined and an expression for the energy reduction is obtained for materials with high anisotropy (K > 2πI₀²). The closure domain structure of cobalt has been examined by Bitter pattern technique on the curved surface of a disc, and the results give the conditions under which domains of reverse magnetization are preferred. Suggestions for future development are made.

This paper describes the extension of earlier work on the elastic scattering of neutrons by tritons and ³He to proton scattering over the energy range 1 to 14 MeV. Cross sections and phase shifts are calculated assuming central two body interactions, of various exchange types and of Gaussian radial form.

Comparison with experiment favours the Serber rather than the symmetrical type of exchange interaction. Detailed agreement between the calculated and experimental cross sections is however lacking at the lowest energies.

The spatial asymmetry of the positrons from polarized muon decay has been measured, with and without discrimination in favour of high energies. The high energy positrons were found to be more asymmetric than the average, and the effect is quantitatively consistent with the two-component neutrino theory.

An analysis has been made of the main excitation processes caused by an electron swarm passing through helium. Recent experimental studies of energy losses of monoenergetic electron beams in helium together with published theoretical excitation functions have been used to obtain approximate cross sections for the principal transitions leading to metastable and resonance states.

The energy balance for an electron swarm in helium is derived and compared with that found previously for molecular hydrogen.

The variation of the nuclear magnetic resonance absorption line of cyclopentene has been measured from 20°K to the melting point at 138°K. Below the specific heat transition temperature of 87°K the lattice is effectively rigid and there is no evidence corresponding to a reported specific heat anomaly at 54°K. Above 87°K the second moment of the absorption line is reduced and this is interpreted in terms of molecular motion about an axis perpendicular to the plane of the four co-planar carbon atoms of the molecule. Above 124°K a further reduction in the second moment is thought to be due to self-diffusion of the molecules through the crystal lattice. Information is also obtained which confirms the nonplanar structure of the cyclopentene molecule.

The ⁶³Cu resonance has been observed in copper-nickel alloys containing up to 9.2% Ni, at 3 Mc/s and 7 Mc/s in the temperature range 20°K to 290°K. The resonance shows a reduction in intensity and a shift to lower frequencies which are larger at the lower frequency and substantially independent of temperature. The line width is not much greater than in pure copper. These effects are interpreted as due to an interaction between the electric quadrupole moment of the ⁶³Cu nucleus and electric field gradients resulting from the difference in size between copper and nickel ions. Any magnetic effect of nickel ions is negligible. The resonance in copper-manganese alloys containing up to 6.1% Mn at the same frequencies and temperatures has a width proportional to the applied field and inversely proportional to the absolute temperature. The direct magnetic interaction with manganese ions is insufficient to account for the broadening. If the results are interpreted in terms of an indirect interaction through the conduction electrons, of the form proposed by Behringer and Yosida, an s-d exchange constant six times the Mn free atom value must be assumed. A large decrease in width on heat treatment is tentatively attributed to clustering of Mn ions.

A theory is suggested to account for the phase changes which have been observed by Barrett in lithium and sodium. The elastic constants for the face-centred and body-centred cubic structures have been calculated and from them the free energies determined. An interesting conclusion is that the electrostatic and ionic terms alone are not sufficient to account for the phase change. The Fermi energy of the conduction electrons is affected by shear, and hence this part of the total energy gives rise to a contribution to the elastic shear constants. The difference in this contribution between the two cubic structures was found to be adequate to account for the observed phase change. An estimation of the transition temperature indicated that it lies in the range 40°-100°K.

Electrical breakdown in air and in hydrogen for uniform high frequency and static fields was investigated using a pair of geometrically similar electrode systems. Static breakdown potentials for values of pd ⩽ 15 mm Hg cm were measured and high frequency data obtained over a range of frequencies f from 5Mc/s to 70Mc/s. The results support the view that there is only one mode of breakdown, contrary to the views proposed by many previous workers. The similarity relationship was found to be satisfied for certain pairs of frequencies provided that the discharge was confined to the regions of uniform field between the electrodes, and that the electrode surfaces were clean. On the other hand, when the electrodes were covered with oxide layers, the similarity theorem did not apply. This result indicates that at least one process of electron generation or loss was not a function of E/p; the most probable process, cold emission, was identified by correlating the results with those obtained under similar conditions with static fields.

In continuation of earlier work, measurements have been made of the attenuation of ultrasonics in a liquid containing globules of another liquid in suspension, viz. an emulsion. The effect of the viscosity of the continuous liquid and of the mean size of the globules of the other liquid on the attenuation is investigated and tested against a theoretical formula.

It is shown that besides viscous loss relevant factors are (a) scattering of the radiation out of the direct beam, (b) pulsation of the globules.

In the propagation of short duration trains of compressional waves in bounded solid media, secondary wave trains are generated as a result of the partial conversion of compressional waves to transverse waves at the boundaries of the media.

The phase relation between these secondary signals and the main compressional signal is analysed here, with reference to the propagation of waves of frequency of the order of 10 Mc/s in solid cylindrical specimens. The theoretical analysis is compared with experimental results.

The results are of importance in applications of the ultrasonic pulse technique to the accurate measurement of the velocity and absorption in solids, and also help to clarify certain characteristics of the propagation of continuous waves in bounded media.

The surface tensions of liquid argon and nitrogen have been measured over their complete liquid ranges, from triple point to critical point, using a capillary rise method. The experimental results are given and compared with values obtained theoretically. Agreement between theory and experiment is not good for temperatures near the critical point.

Ranges of solid solution have been investigated in systems composed of either two A₂^IIIB₃^VI compounds or one A^IIIB^V and one A₂^IIIB₃^VI compound. It is found that in practically all cases considered complete solid solution throughout the whole range of composition can be obtained, but that in some cases this equilibrium condition can only be reached under special conditions of temperature and time of annealing. The possibility of ordering and of the occurrence of low temperature miscibility gaps is investigated.

Eigenphaseshifts and eigenvectors of the nuclear scattering are constructed from the Wigner many level approximation, after separation of the potential scattering. The two level case is discussed in detail, and a simple approximation based upon the eigenphaseshift formalism is suggested.

The elastic photoproduction of neutral mesons from helium has been studied at centre-of-mass angles of 70°, 90°, 115° and 135° for the meson in the photon energy range 220-320 MeV. The reaction has been identified by detecting the recoiling ⁴He particles in a pair of gridded ionization chambers which discriminated against other particles by dE/dx and E measurements. The measured cross sections are compared with the predictions of an impulse approximation calculation with which they are in qualitative agreement. They are smaller by an order of magnitude than some of the previous measurements of this reaction.