Table of contents

Cosmologies separate sharply into those which predict that a definite origin of the whole universe occurred a precise finite time ago, and those which require no such origin to have taken place. Observational methods exist for arriving at a decision between these two forms of theory. In particular, these are:

1. Geometrical tests

   Proposed differences between the present state of the universe (determined by the observer's immediate locality) and the past condition of the universe (determined by observation of very distant objects) are investigated under this heading.

2. Local evolutionary tests

   The past history of the universe must have been such as to lead to the present state. When applied to the formation of galaxies, the ages of galaxies, to the generation of cosmic rays and cosmic radio waves, this simple condition turns out to have far-reaching implications.

The current status of tests under these headings will be reviewed.

An investigation of both the linear and non-linear parts of the photographic process has been carried out using the concept of optical frequency response for the description of the contrast degradation resulting from diffusion of light in the emulsion which is the linear part of the process. An analogy between the operation of a low-pass passive filter and valve and photographic image recording is established and a simple theory for calculating the resulting opacity in a photographic image is described. This latter introduces the idea of harmonic distortion to describe the non-linear part of the process. The experimental results obtained by means of an optical Fourier analyser for transparencies were found to be in good agreement with the theory. A description of the instrument is given in the first part of the paper. Some other applications of the theory are considered.

The anisotropy of relaxation time for both ¹⁹F and ⁷Li has been examined in a pure single crystal of lithium fluoride, and is satisfactorily accounted for in terms of Bloembergen's spin-diffusion theory of relaxation. Confirmation is provided by the reduced anisotropy observed in two single crystals of lithium fluoride containing enhanced concentrations (50% and 90%) of ⁶Li. The lack of anisotropy of the ²³Na relaxation time found in sodium chloride accords with the predictions of the theories of quadrupolar relaxation. A similar observation for the ⁷⁹Br and ⁸¹Br relaxation times in potassium bromide is not inconsistent with van Kranendonk's theory and suggests that covalency does not make a strong contribution to the quadrupolar relaxation process.

The four-nucleon reaction has been formulated using the resonating group method and including the three groupings dd, n³He, and pt. The central potential used is of Gaussian shape with exchange dependence (Serber and symmetrical exchange have been mainly investigated). The wave functions for the nuclear ground states are double Gaussian for deuteron and single Gaussian for t and ³He, the parameter being determined by variational methods to fit the binding energies.

Coupled integro-differential equations have been derived for each value of the total spin and angular momentum of the corresponding system.

Preliminary results have been obtained by including only one channel for dd and are given here.

Using the distortion approximation the cross sections for the collision processes H(1s) + H⁺ (or He²⁺) → H(2s) + H⁺ (or He²⁺) are evaluated at H⁺energies between 10kev and 100√10kev (or He²⁺ energies between 40 kev and 400√10 kev). It is found that the effect of distortion is not as much as in the case of H(1s) + H⁺ (or He²⁺) → H(2s) + H⁺ (or He²⁺). Optically allowed transitions are in general likely to be less influenced by distortion than are optically forbidden transitions.

Absolute differential cross sections have been measured for the ⁹Be(p,d)⁸Be(0) and ⁹Be(p,p)⁹Be(0) `reactions at incident proton energies of 4.85 and 5.49Mev, and for the <sup>9</sup>Be(d,t)<sup>8</sup>Be reaction at 5.86Mev; the pick-up reactions have been analysed in terms of the Butler theory. A comparison of the (p,d) results with those at higher proton energies gives the ranges of validity of the Butler theory and the `transparent-nucleus' Born approximation pick-up theory for the reaction; the neutron reduced width is also deduced from these results. A comparison of the (d,t) results with those at higher deuteron energies shows consistency over a wide energy range: a comparison with the (p,d) reaction gives the triton form-factor|A₀|²N₁². Excitation functions have been measured for the reaction products of ⁹Be+p for bombarding energies between 3.5 Mev and 6.0 Mev and for the reaction products of ⁹Be+d for bombarding energies between 3.8 Mev and 6.3 Mev.

A lead-glass Cerenkov counter has been used as a gamma-ray spectrometer to redetermine the Panofsky ratio for negative pions stopped in hydrogen. The ratio was found to be 1.56±0.05.

In the surface region of a nucleus the nucleon density is lower than in the interior, and it might be expected that this will reduce the effect of the Pauli principle in suppressing correlations. Since in light nuclei the surface region is more important, one expects perturbation theory to work less well and correlations to be more important, than in uniform nuclear matter.

Calculations with a simple model for ¹⁶O show that the second-order correction to the energy is almost exactly the same as for uniform nuclear matter, but that two-body correlations are indeed enhanced considerably.

The rate of energy loss of carbon and oxygen ions passing through carbon, aluminium, nickel, silver, and gold absorbers has been measured in the energy interval of 0.36 to 3.2 MeV. Ranges of the carbon and oxygen ions in these stopping materials were obtained by numerical integration of the rate of energy loss against energy curve. The relative accuracy of the results is to about 2% and the absolute accuracy is to better than 5%.

The abnormal intensity of some `forbidden' hyperfine transitions in the paramagnetic resonance spectra of ions with S = 1 or more is shown to be due to cross terms in the spin Hamiltonian. These arise from off-diagonal terms in the electronic and nuclear interactions, and the computed transition intensities agree closely with measurements on vanadium fluosilicate. In a powder an apparent doubling of the hyperfine transitions is shown to be due to the combined effect of these terms and others due solely to the electronic splitting.

The estimation of the interaction energies between the magnetic ions in antiferromagnetic crystals is investigated and it is shown that they may be obtained from measurements of the magnetic susceptibility in the paramagnetic phase.

High temperature power series expansions of the zero-field susceptibility - well known in connection with ferromagnetic systems - are analytically continued by means of the transformation 1/w = 1/z - θ so that the series no longer diverge at the ferromagnetic Curie point and the domain of convergence is extended towards lower temperatures.

Analytically continued high temperature power series expansions developed in the preceding paper are applied to the susceptibilities of the polymorphic forms of MnS, all three of which are known to be antiferromagnetic. An isotropic Heisenberg interaction is assumed between nearest neighbours only.

Estimates of the exchange interaction are obtained using experimental data from the region above the Néel temperature but below the Curie-Weiss region. It is found that|J|/k is (12.4 ± 0.5)°K for β-MnS (zinc blende) and (10.7 ± 0.5)°K for β-MnS (wurtzite). In the case of α-MnS difficulty occurs, using g = 2, because general arguments show that it is not possible to fit the experimental susceptibility. A fit can be obtained with g = 1.8, but as this is an arbitrary assumption it seems that a full understanding of the properties of α-MnS must await further experiments.

Measurements have been made of the intensity of the recoilless resonance absorption of the 24 kev γ-ray from the decay of ¹¹⁹Sn^m in metallic tin from 120°K to the melting point. Values of the Debye-Waller factor deduced from these results tend towards the values calculated for a Debye Θ of 142°K at low temperatures; the behaviour of the Debye-Waller factor at higher temperatures indicates considerable anharmonicity of the lattice vibrations. Comparison with evidence from the thermal expansion and specific heat suggests that the quartic term in the interatomic potential is positive, and that the ratio of quartic to cubic terms is of the same order as the ratio of cubic to quadratic terms.

In the last few degrees below the melting point the resonance absorption shows a rapid drop accompanied by an increase in line width. It is suggested that this effect is due to enhanced self-diffusion in the solid, and it is estimated that the diffusion coefficient reaches a value of 10^-8cm²sec^-1 about 0.6°K below the melting point.

A set of simple theoretical criteria are established for the occurrence of the Meissner effect in a many-electron system. The criteria are of a qualitative nature and involve only the single- and two-particle excitations of the system.

Two new band systems in absorption have been observed in the quartz ultra-violet region (λλ2190-2450) by vaporizing tellurium in a vacuum along with the sulphide of a group II b element. The bands, which are degraded to the violet, have been classified and attributed to a new molecule TeS.

The optical absorption of single crystals of sodium chloride containing calcium as impurity has been measured. Results are given which show a new band at 345 mμ and from measurements of the bandwidth of the F-band it is deduced that the Z₁-band is present in specimens, x-ray coloured, at room temperature.

The growth of the Z-bands on bleaching in samples containing differing amounts of calcium impurity and the effect of quenching was also studied. Rate equations are used to discuss the coloration of NaCl and are also applied to the complex (Ca²⁺. plus sign in box. 2plus sign in box minus sign in box) to explain the coloration of the crystals containing Ca²⁺.

Fine structure in the ¹²C(γ,n)¹¹C activation curve has been examined in great detail. Eighteen breaks were found between threshold and 23 Mev. The positions of these breaks and the integrated cross sections of the corresponding levels for the (γ, n) reaction are listed. Independent measurements in other laboratories have indicated that resonance photon absorption into discrete levels may also be present for the (γ, p) reaction. The failure to observe structure in the (p, γ) inverse reaction thus remains unexplained.

Optically allowed transitions have long-range interaction potentials, behaving asymptotically as s₁/r² where s₁ is proportional to the dipole matrix element. In calculating cross sections many angular momentum states l must therefore be considered. When the coupling is strong the usual Born approximation leads to violations of conservation conditions which are serious for the smaller values of l. Three variants of the first Born approximation are considered: I is the Born approximation for the total scattering amplitude, II the Born approximation for the reactance matrix and III (suggested by Percival) the Born approximation for the proper phase of the scattering matrix. Approximations II and III satisfy conservation conditions and make some allowance for processes such as a → a' → a, a → a' → a" and of a → a" competing with a → a'.

Considering the case of exact resonance, and replacing the potentials by their asymptotic forms, one obtains equations for which exact analytic solutions may be obtained. The exact solutions are compared with those obtained using approximations I, II and III.

The Born partial wave integrals may be evaluated on making a harmonic analysis of the integrals occurring in the Born total scattering amplitude. This provides a convenient method for numerical evaluation of the partial wave integrals.

The paper includes the proofs of an addition theorem for solid harmonics and a multiplication theorem for spherical Bessel functions.

Using methods described in a companion paper by Seaton, the partial wave integrals are calculated for transitions involving the states 1s, 2s and 2p.

In a companion paper Lawson, Lawson and Seaton have calculated the Born R matrix for H 1s, 2s and 2p. Using these results the transmission matrix is calculated from T=-2_iR/(I-_iR). In another companion paper Seaton has shown that this should give results which are better than those obtained from the Born approximation for the total scattering amplitude.

The following cross sections are calculated: elastic (1s-1s, 2s-2s, 2p-2p); momentum loss (1s-1s, 2s-2s, 2p-2p, 2s-2p); inelastic (1s-2s, 1s-2pm_l); transitions between fine structure levels (2s_1/2-2p_1/2, 2s_1/2-2p_3/2, 2p_1/2-2p_3/2). Comparison with experiment shows our results for 1s-2p to be much better than those obtained from the usual Born total amplitude.