Table of contents

A résumé of the treatment of image formation from the standpoint of the theory of passive linear systems is given, it being shown that image formation for an incoherent object satisfies the basic postulates of superposition and stationarity. It then follows that the spatial frequency response of an optical system will be given by the Fourier transform of its impulse response, this latter being simply the distribution of intensity in the image of a narrow self-luminous line. There follows an account of work done in the author's image-assessment group at Imperial College. This includes the diffraction theory of optical frequency response, aberration tolerance theory and the numerical evaluation of frequency response and diffraction integrals together with examples of the response curves for particular cases. A number of methods for the measurement of frequency response are described, and the theory of these methods and results showing the comparison of theoretical and measured response curves are discussed. The final section describes methods for the measurement of the Fourier spectra of photographic images, and their application to the study of the influence of the detector properties on recorded images.

A formula is developed which corrects for self-interaction in the Thomas-Fermi statistical theory of the atom. By its aid it is possible to write down an effective Schrödinger equation for any separate orbital. This equation is solved for the 4f and 5f series of atoms. The results show the expected sudden contraction in mean radius at about Z = 61 and Z = 91 respectively. A short discussion is given showing the difficulty in making adequate allowance for exchange in a one-electron scheme of this kind.

The internal friction of 5 Mc/s shear waves in AT-cut synthetic quartz resonators has been measured over a temperature range of 4°-400 °K as a function of the rate of growth of the parent quartz crystal. It is found that the peak in the region of 25 °K decreases somewhat with increasing growth rate, whilst the 50 °K peak increases by two orders of magnitude for a fourfold increase in growth rate. Furthermore, the internal friction in the range 250°-400 °K rises exponentially in the faster grown material. Tentative explanations of these effects are given in terms of the current theories of the interaction of phonons and imperfections in dielectric crystals.

A neutron-diffraction study of polycrystalline samples of gold-manganese alloys near the composition AuMn has correlated the crystallographic and magnetic-structure changes as the composition and temperature are varied. The interlayer spacing between the antiferromagnetically arranged ferromagnetic sheets is retained practically unaltered. It is concluded that the magnetic moment on the manganese atoms is 4.2 μR.

By considering the symmetry operators (table 1) of the various crystallographic magnetic point groups, the forms of property tensors in magnetic classes are related to those in the classical crystal classes. The resulting schemes of tensor components are presented in tabular form for tensors of ranks 1, 2, 3 and 4 possessing no intrinsic symmetry. The use of this table (table 2) is exemplified by a brief discussion of piezomagnetism, pyromagnetism (i.e. the occurrence of spontaneous magnetization) and the magneto-electric effect in antiferromagnetic chromic oxide.

Accurate measurements have been made of the ²³Na nuclear magnetic resonance spectrum of sodium nitrate single crystals from -190 °C to 300 °C in an applied magnetic field of 6000 Oe. The nuclear electric quadrupole coupling constant has a magnitude which is convenient for the separation of first- and second-order shifts of the resonance lines. The separation of the two satellite lines, to which second-order perturbations do not contribute, follows the theoretical first-order variation closely. The frequency of the central line, and the mean frequency of the satellite lines to which first-order perturbations do not contribute, accurately follow the theoretical behaviour using the parameters determined from the first-order examination.

The magnitude and angular variation of the second moment of the central line at room temperature is in excellent agreement with the theory of Kambe and Ollom and provides the first experimental test of their theory. At all orientations of the crystal the second moment is approximately 10% smaller than would be expected if the quadrupole coupling constant were zero, when Van Vleck's expression would be applicable. The width of the line decreased over the range 200° to 280 °C to a small value; this reduction is ascribed to diffusion of the sodium ions.

The quadrupole coupling constant was found to decrease by a factor of ten over the whole range of temperature, with a discontinuity in the temperature dependence at the second-order phase transition, 276 °C. This unusually large decrease is much greater than can be explained by the effects of lattice expansion or the tendency of the crystal structure to become somewhat more nearly cubic. The behaviour must clearly be associated with the changes in the crystal which lead to the second-order phase transition.

Experimental information bearing on the nature of the phase transition is reviewed. It is shown that the evidence can be reconciled by a dynamic-disorder model in which the nitrate groups reorient about their threefold axes with increasing rapidity as the temperature rises. Although this motion does not become free it encourages the disordering of orientation of the nitrate groups leading to a phase-transition of the order-disorder type. This motion does not however directly account for the reduced electric field gradient experienced by the sodium nuclei. It is proposed that this reduction arises from the oscillation of the sodium ions predominantly in directions perpendicular to the triad axis of the unit cell, and that this motion is a secondary consequence of the mechanism of the phase transition. Calculations have been made of the electric field gradient, and these support the proposed mechanism of dynamic disorder.

Bitter figure and electron-micrograph studies have been made of (i) field-cooled, (ii) optimum and (iii) over-aged specimens of Alcomax III cut from the same test block and subjected to the appropriate thermal treatments. The photographic records taken during the description of a hysteresis loop with each specimen have been compared.

The general domain structure of all three specimens consists of 180° domains and spikes of reverse magnetization, and is superficially typical of a uniaxial material like cobalt. Significant differences between the structures of the three specimens are discussed; in particular, in the optimum specimen there are no marked changes in domain directions across grain boundaries, the domain walls are less clear than in the other specimens, and the domains are narrower. On planes perpendicular to the field applied during cooling, normal Lifshitz closure domains are formed in case (i), complex free pole structures in case (ii) and coarser free pole structures in case (iii).

An interpretation of the observed phenomena is suggested in terms of magnetic interaction domains.

The magnetostriction of dysprosium metal has been measured at 20.3 °K and from 90 °K to 206 °K. At the lowest temperature, at which the metal is ferromagnetic, the magnetostriction constant λ_s defined by λ = 2λ_s(cos² ϕ-½) is found, by extrapolation, to be 3.4 × 10^-2. The magnetostrictive behaviour of dysprosium in the antiferromagnetic region can be qualitatively accounted for in terms of the deformation of a helical spin system.

Microwave resonance has been studied in polycrystalline spheres of nickel ferrite in the temperature range 20 to 500°c at wavelengths close to 3.13, 1.25 and 0.87 cm. The internal field H_i was then calculated, on the assumption of a frequency-independent g-value, and compared with known contributions to H_i arising from the finite sizes of the samples, from their porosity and from their crystalline anisotropy. A residual contribution to H_i of over 100 oersteds is attributed to the presence in the samples of hair-like defects or fissures, which would not be accounted for in the usual `porosity' correction.

The diamagnetic shielding of nuclei by Bloch electrons in a metal is considered. The shielding may be divided into a Lorentz correction arising from a uniform magnetization and a part due to the induced volume currents. An exact expression in the Bloch model is derived for the volume current density induced in a metal by a uniform magnetic field. This permits in principle the calculation of the shielding. Certain special cases are discussed.

The correlation energy of a charged Boltzmann gas at absolute zero is calculated. The result is exact at high density in the same sense as the result of Gell-Mann and Brueckner for the Fermi gas. Investigation of the magnetic properties reveals that at absolute zero this system exhibits a Meissner effect of the London type. At any finite temperature the system is diamagnetic. Consideration of the effect of the Coulomb interaction on the Meissner effect leads to the conjecture that the London constant is independent of the particle interactions. The results are also applicable to a charged boson gas at absolute zero.

Assuming the electrons to move in a common perturbing potential, which is to be determined self-consistently, a general theory is given for the evaluation of charge and potential distributions round perturbations in an originally uniform electron gas at elevated temperatures. The results reduce to those given recently by the writers for perturbations in metals in the limit as the temperature T → 0.

In the non-degenerate case, and to first order in the perturbing potential, our results lead to a treatment which supersedes the Brooks-Herring theory of ionized impurity centres in semiconductors. However, a numerical application we have considered verifies that their treatment will often represent a very good approximate solution of the new equation.

We have also examined the low-temperature problem in a high-density gas and results are presented which indicate how the long-range density oscillations round a perturbation are damped out by the temperature effect in this case. Some tentative conclusions about the effect of electron interactions on the long-range oscillations are thereby suggested.

Finally it is pointed out that, when a slowly varying potential assumption is valid, the perturbation series may be summed, and the theory of Sakai and of Feynman, Metropolis and Teller is regained.

The present paper describes an experiment designed to measure the angular asymmetry of the neutrons emitted when polarized muons are captured by nuclei. The nuclide used was sulphur. After correcting for the depolarization of the muon beam we obtained a value of -0.22 ± 0.07 for the asymmetry parameter. The non-zero result confirms the violation of parity conservation in the muon capture process, and the magnitude of the effect suggests the presence of an effective pseudoscalar term in the transition amplitude for the fundamental process μ^- + p → n + v.

The reaction ⁷Li(α, γ)¹¹B has been studied at the three resonances found at 951, 815 and 401 keV. The decay schemes have been established, and it is shown that at the two upper resonances the decay via the 6.76-6.81 MeV doublet involves only the 6.76 MeV member. The analysis of the experimental data on angular correlations establishes the resonance spins, and also shows the 6.76 MeV and 4.46 MeV levels to have spins 7/2^- and 5/2^- respectively. The transition from the 4.46 MeV state to ground is found to have an E2/M1 mixing amplitude of +0.20±0.02.

The properties of the 6.76 MeV level are not as predicted by the independent particle model.

Thick targets of ¹⁰B, ¹⁴N, ¹⁶O, ¹⁹F, ²³Na, ²⁷Al, ⁵¹V, ⁵⁵Mn and ⁵⁹Co were irradiated with ¹⁹F ions with energies up to 43 MeV. The yield of ¹⁸F from the neutron transfer reactions with these nuclides was measured by separating and counting fluorine from the irradiated targets. All the neutron transfer cross sections were found to increase from a lower limit of detection of about 0.2 mbn to several mbn at 43 MeV. The shapes of these excitation functions have been compared with that expected from the theory of Breit for neutron transfer between the ground states of the interacting nuclei.

Thin targets of ²⁷Al were irradiated with 42.3 and 34.2 MeV ¹⁹F ions and the angular distribution of ¹⁸F was measured in each case over the range 0° to 178° in the laboratory system. A pronounced peak in the angular distributions was observed corresponding to neutron transfer from Rutherford orbits at the closest distance of approach. The value of the reduced radius R₀ at this distance for both energies was found to be 1.7±0.05 fermis.

The experimental results for elastic electron scattering from ⁶Li are fitted using a cluster model. The value obtained for the r.m.s. radius of the alpha cluster is very close to that for a free alpha particle. This is in contrast to previous calculations using a shell model which indicated that in this model the alpha core in ⁶Li is considerably larger than the alpha particle. Electron scattering data do not distinguish between the two models.

A classical impenetrable sphere treatment of the collision of a proton and a single orbital electron is found to lead to limiting proton impact energies E_p between which the ionization cross section function reaches its maximum value: 1.46E_i ⩽ (m/M)E_p ⩽ 2.25E_i, with ionization potential E_i, proton and electron masses respectively M and m. This is consistent with available experimental data.

From the experimental emitted electron energy distributions, due to Blauth, the classical treatment yields electron angular distribution functions, which have been computed at representative electron energies.

Determinantal equations are given for the accurate determination of the energy shifts in the rotational levels (J = 1 and J = 2) of sodium chloride from precision measurements on the quadrupole hyperfine structure of the transition line J = 2 → J = 1. The significance of the precise evaluation of the energy shifts for an understanding of the electronic structure of diatomic molecules is pointed out.

The effective masses of conduction electrons in PbS, PbSe and PbTe have been found from room temperature measurements of Faraday rotation. The equivalent isotropic masses obtained for PbS and PbSe are 0.17(5)m₀ and 0.11(4)m₀ respectively. In PbTe, the value is 0.08(6)m₀ for our purest material, with a marked increase in highly doped material.

General expressions are derived on the basis of Bayer's theory for the temperature dependence of the nuclear quadrupole resonance frequency for the case of iodine. This variation is studied in CH₃I and CD₃I and compared with experimental observations. This method may prove useful in estimating the torsional frequency, at least where it is not known from other observations.

Correction to Proc. Phys. Soc.78, 1393