Table of contents

The energy distributions and absolute yields of photoprotons of energy greater than 10 MeV from silver have been measured for maximum bremsstrahlung energies between 16 and 32 MeV. The derived cross section for this component, which may be identified as arising from direct interactions, passes through a maximum at about 22 MeV, and the integrated cross section is found to be (36 ± 9) MeV mbn. This result is consistent with the idea that most of the emission arises from a 2p-2d transition at 22 MeV, and this interpretation is supported by the angular distribution measured at 30 MeV, which is strongly anisotropic.

The recent experimental data on the (³He, p) differential cross section showing forward and backward peaks are interpreted as due to the ³He particle stripping and heavy particle stripping respectively. Reasonable agreement is obtained between the derived theoretical formulae and the experimental data. Some (d, α) reactions are interpreted in a similar way.

A procedure involving a coupling parameter is described by which the pair distribution for a classical condensed system of particles can be calculated without the need for applying the superposition approximation to the triplet distribution itself, although it is still needed for the higher order distributions. For the special case of spherical particles interacting with central forces the approach takes on its simplest form and should provide a feasable means of deriving highly accurate information about the structure of a simple classical liquid under uniform conditions. An extension of the method is suggested for completeness by which all the lower order distribution functions can in principle be successively released from the restrictions of the superposition approximation.

The energy levels of ¹⁸F have been investigated using the reactions ¹⁶O(³He, p)¹⁸F and ¹⁹F(³He, α)¹⁸F. In both cases magnetic analysis was employed and the incident ³He energy was 5.9 MeV. The excitation energies of 40 levels have been determined below 7.493 MeV.

The reactions ¹⁶O(³He, α)¹⁵O, ²⁴Mg(³He, α)²³Mg and ²⁸Si(³He, α)²⁷Si have been investigated at an incident energy of 5.8 MeV by magnetic analysis. The following levels were observed: ¹⁵O, 5.174, 5.233 MeV; ²³Mg, 0.451, 2.048, 2.356, 2.712, 2.768, 2.904, 3.792, 3.856, 3.968, 4.353 MeV; ²⁷Si, 0.782, 0.958, 2.165, 2.651, 2.866, 2.908, 3.540, 3.800, (4.13) MeV.

The work function Φ of evaporated films of sodium chloride and the energy gap δ from the filled levels to the Fermi level have been determined by photoelectric measurements using the complete electrode substitution method. The values found are Φ = 5.12(3) ± 0.018 ev and δ = 1.55(0) ± 0.034 ev.

Isothermal and quasi-adiabatic Hall and Nernst coefficients were measured on n- and p-type Bi₂Te₃ over a temperature range 100°K to about 450°K. The current flow was parallel to the cleavage planes, and measurements were made with the magnetic field either parallel or perpendicular to the cleavage planes. The difference between the two Hall coefficients follows the expected variation with temperature. However, the Nernst coefficients do not, and the reason is not known. Results obtained with the magnetic field perpendicular to the cleavage planes have been used to calculate the Ettingshausen coefficient.

The exact formula for the electrical conductivity of a metal, derived by Kubo, Greenwood, and others, is evaluated using Van Hove's methods for quantum mechanical transport problems. The evaluation is restricted to the case of elastic scattering by impurities or lattice vibrations, but completely avoids the use of the customary random phase assumption. In the limit of weak coupling our method yields formulae for the conductivity that are identical with those derived from the Boltzmann equation. The accuracy of the weak coupling approximation is investigated and it is found to be accurate as long as h/τ<<η, where τ is the collision time and η is the Fermi energy. A general treatment of the conductivity in an anisotropic metal is given and an explicit expression for the conductivity is written down in terms of the eigenvalues and eigenvectors of an integral equation. A general and rigorous derivation of the conventional Boltzmann equation is given using Van Hove's results on the quantum mechanical master equation.

Measurements of ultrasonic relaxation in liquids and gases provide experimental data from which it is desired to obtain theoretically useful parameters such as heats of reaction and transition probabilities. It is shown here that even if full experimental results are available concerning the variation of the ultrasonic relaxation strength r with pressure and temperature it is still necessary to make at least three assumptions before thermodynamic reaction parameters can be evaluated.

The main purpose of the paper is to set out a logical theory which makes the nature of these assumptions explicit. It is first shown how the experimental results can best be analysed to yield the relaxation strength. The formula connecting the relaxation strength with the reaction parameters leads to a partial differential equation which is integrated in a form convenient for practical application.

The general implications of the theoretical work are discussed in relation to experimental observations and the need for further experimental work at high pressures is emphasized.

The problem of automatic lens designing by an electronic digital computer is considered in the light of existing aberration theory. Methods previously suggested are discussed, and a new iterative method of linear approximation is described.

A method of inferring the principal values and the directions of the principal axes of the g-tensor for a paramagnetic complex in a single crystal from measurements of the g-value variation in three different planes is described, and an ambiguity in the determination of the principal values that will often arise in practice is pointed out and discussed. An estimate of the root mean square error in the determination is given.

The reactions ²⁷ Al(p, p')²⁷ Al and ²⁷ Al(α, p)³⁰ Si have been studied at 5 MeV incident energy using a high resolution broad range magnetic spectrograph. Angular distributions of several of the proton groups from each of the reactions were determined and the results suggest that some of the final states are formed by direct processes. The excitations of the first four states of ³⁰ Si were found to be 2.258 ± 0.006, 3.518 ± 0.007, 3.798 ± 0.009 and 4.85 ± 0.01 MeV.

Solutions of the time-dependent Boltzmann equation for gases are considered. The Boltzmann equation is first linearized by considering only small deviations from equilibrium. From the solutions of the linearized equation, a variational principle is developed, which permits the estimation of the eigen-values by a method of successive approximations. In this paper we calculate the lowest non-zero characteristic rate of relaxation for spherically symmetrical distributions. The distribution function is assumed to be uniform in the configuration space. Eigenvalues have been evaluated for gases whose particles interact with a law of force of the form Q(a/r)^s where ^r is the distance between a pair of particles. The cases s=2, 5 and infinity have been considered in detail. In the cases s=2, the impact parameter is cut off at the Debye shielding distance. The calculations are extended to include the case of a two-component mixture of gases.

The effect of small quantities of copper, up to 1%, covering the eutectic at 0.7% Cu, on the photoelectric work function of liquid tin has been determined by measurement of stopping potential when the surface is irradiated with light from a tin spark. It is found that the apparent value of the work function obtained changes with composition, the change being greatest near the eutectic. The results are briefly discussed with reference to other published work on structure effects in liquids.

The effect of exchange forces on the wave functions of an atom resulting from the unpaired spin of a single electron outside closed shells is considered. Calculations were carried out for lithium and sodium starting from the usual self-consistent field wave functions using a modified type of perturbation theory. These yield an increase of 31% for Li and 5½% for Na in the value of the hyperfine coupling constant. In addition, the effect of this core polarization on the theory of the Knight shift in metals is developed in detail.