Table of contents

The probability distribution p(n, T) of the number of counts n from a photoelectric detector illuminated by coherent light for a time T is studied, by associating photons stochastically with Gaussian random waves. The cumulants of the distribution are derived and it is shown to be of the expected form for a boson assembly in a limited volume of phase space. The distribution depends strongly on the degeneracy of the light beam. It approaches the Poisson form for classical particles at low degeneracies and the distribution characteristic of classical waves at high degeneracies. The analysis leads, incidentally, to an expression for the extent of the unit cell of phase space in the direction of the beam. It is argued that this should be adopted as the measure of coherence length.

The production of specimens of alloys in the GaSb-InSb system suitable for electrical and optical work is first discussed. X-ray data are given to show the variation in composition and the degree of homogeneity of specimen sections cut from long rod ingots produced by very slow directional freezing techniques. The results of measurements of infra-red transmission on such specimens are presented together with a graph of the variation of wavelength for onset of transmission, interpreted as optical energy gap, as a function of composition. The form of this graph is briefly discussed.

Electron spin resonance in a single crystal of LaF₃ containing 0.01% Gd³⁺ shows three magnetically distinguishable ions per unit cell in a rhombic crystalline electric field which is consistent with a hexamolecular unit cell of symmetry C6/mcm. This is in disagreement with recent crystallographic measurements, but in agreement with the interpretation of the Faraday rotation given by Van Vleck and Hebb. The parameters of the spin Hamiltonian are given in table 1. The crystal field splitting in zero magnetic field is of the order of 0.3 cm^-1 which makes this a possible salt for maser operation in low magnetic field.

The multiple scattering of fast electrons and positrons within the energy range of 7 to 17 MeV in xenon has been measured using a cloud chamber. A study has been made of the errors involved and also the use of the technique of overlapping intervals. At the higher energies the multiple scattering agrees, within the experimental errors, with the theoretical values predicted by Molière but at energies of less than 10 MeV the experimental values tend to be lower. The measured scattering for the mean energy values agree with the predicted values of Molière but are higher than the values given by the theory of Williams. There is no significant difference between the multiple scattering of electrons and positrons.

It is shown that the scalar representation of electromagnetic fields introduced in an earlier paper leads to a new model for energy transport. The energy may be considered to be carried by two mutually incoherent scalar waves, each of which arises from contributions of circularly polarized components of the same helicity. In a monochromatic field the energy density and the energy flow of each of these two partial waves are time-independent and the energy flow is at every point of the field in the direction of the normal to the surface of constant phase of the wave. Mathematically, the two partial waves are represented by `analytic signals' (containing spectral components of only positive or negative frequencies) into which the complex potential of the field may be decomposed.

As an immediate consequence of these results, a new representation of an unpolarized quasi-monochromatic electromagnetic field is obtained and it is shown that, under usual conditions, the `complex disturbance' of the classical scalar diffraction theory of optics may be identified with the complex potential of this representation.

The transformation properties of the single complex quantity, introduced by Green and Wolf to describe the electromagnetic field, are investigated and the physical energy-momentum tensor of this field is derived in terms of the scalar theory. In particular, it is found that the energy density, as defined in the previous paper, is identical with that given by the physical energy-momentum tensor; and that the energy flow density differs from the one given by this tensor only by a divergence-free vector.

Measurements are reported on the magnetic and other properties of alloys of chromium with small quantities of iron. The results show, as expected, that each iron atom carries a moment of 2β, but it is surprising to find that the moments are freely orientable in a matrix of chromium, which is presumably antiferromagnetic. The implications of this are discussed and further experiments are suggested.

Electron attachment coefficients were measured in oxygen, dry air, air saturated with water vapour at room temperature and in water vapour. An electron filter type apparatus was used. The results have been compared with those of other workers. An approximate evaluation has been made of the influence of humidity on the breakdown voltage of air gaps in a uniform field using the present results and the known ionization coefficient data.

Investigations are reported, based on a study of the mark left on the anode by a spark in air, which give information about the distribution of conductivity across a spark channel during the first microsecond after initiation. These indicate (a) that the spark channel becomes `hollow' after a few tens of millimicroseconds, with maximum conductivity towards its periphery, (b) that the diameters of the conducting channel, of the mark left on the anode, and of the shock front generated by the spark are approximately coincident for about one hundred millimicroseconds, and (c) that the energy which generated the shock is all supplied to the channel during the first few tens of millimicroseconds.

The method of Successive Linear Approximation at Maximum Steps, described in the previous paper, has been applied to automatic lens designing on an electronic digital computer. A description is given of the form of programme used and the results of applying the method to three design problems are quoted.

It is shown that many simple relations exist between various reduced matrix elements of the form (fⁿ WUSL || U^k || fⁿW'U'SL'), where W = (w₁w₂w₃) and U = (u₁u₂) are irreducible representations of R₇ and G₂ respectively. This is done by using the fact that for k = 2, 4 and 6, the components U_q^k of the tensor operators U^k, when multiplied by (2k + 1)^1/2, transform among themselves as the irreducible representations (200) of R₇ and (20) of G₂. The number of linearly independent sets of matrix elements for a given W and W' is equal to the number of times the identity representation (000) of R₇ occurs in the reduction of the product (w₁w₂w₃) × (200) × (w₁'w₂'w₃'); similarly, the number of times the identity representation (00) of G₂ occurs in the reduction of the product (u₁u₂) × (20) × (u₁'u₂') determines the number of linearly independent sets of matrix elements that can exist with U = (u₁u₂) and U' = (u₁'u₂'). These two numbers, which are denoted by c(WW'(200)) and c(UU'(20)), are tabulated for all W, W', U and U' which occur in fⁿ, and the use of the tables in calculating the splittings induced in the levels of rare earth ions by the surrounding crystal lattice is illustrated with a number of examples.

A perturbative method, which is gauge invariant in infinite order, is employed to investigate whether the Bardeen, Cooper and Schrieffer-Bogoliubov treatment of the theory of superconductivity leads to the Meissner effect. It is found that the theory does not reveal, in any finite order of perturbation, the long range correlations between the electronic momenta that are necessary for the Meissner effect.

Though simple qualitative arguments imply that the electron coincidence spectra for two-neutrino, and for no-neutrino double β-decay are broadly peaked at ½E₀ and infinitely sharply peaked at E₀ respectively (E₀ is the energy release), a recent calculation has shown that in some circumstances the two-neutrino case spectrum may also be broadly peaked in the region of E₀. A simple model, in which only one state of the intermediate nucleus gives a non-zero contribution to the matrix element, is used to recalculate these spectra. Two extreme approximations are considered: the energy of the intermediate state is equal to, or much greater than, that of the initial state. In both cases, the qualitative result is confirmed, and the recent calculation mentioned above is regarded as incorrect. The model is applied to the double β-decays of ⁹⁶Zr and ⁴⁸Ca. The relation between the conservation of lepton `charge' and the shape of the spectrum is also considered in some detail.

The Hall coefficient and transverse magnetoresistance of two type II-b semiconducting diamonds (p-type) were measured as a function of magnetic field from 500 gauss to 20 000 gauss at fixed temperatures between 0°C and 100°C. These diamonds have Rσ values of about 1000 cm²v^-1sec^-1 at room temperature. The Hall coefficient increases monotonically with increasing field, the total variation being about 10 per cent. This behaviour is similar to that which has been reported for p-type silicon at liquid nitrogen temperature, and it suggests a warped valence band. The transverse magnetoresistance is proportional to H² at low fields, but deviates from this behaviour at fields above 4000 gauss. The magnetoresistance is larger than would be expected for a spherical band but can be explained if a warped valence band is assumed. A warped band is also suggested by the longitudinal magnetoresistance which is about one-third the transverse value.

Generally, a body immersed in a fluid is surrounded by an electric double layer at least part of which resides in the fluid. In a previous paper (which contains an error corrected in the present paper), it was found that the double layer must satisfy certain conditions of macroscopic theory in order to be in equilibrium. In this paper it is shown that the conditions can be simultaneously satisfied, but not uniquely so, so that they do not determine the structure of the double layer, although in certain circumstances, they determine it partially.

A discussion is given of the relationship of the present theory to the microscopic theory, and its role in relation to that theory.