Table of contents

A formulation for scalar problems in physical optics is presented. Approximations involve the neglecting of the obliquity factor and the dependence of amplitude on distance and the replacement of spherical by paraboloidal wavefronts. Expressions are obtained for wave function in a multi-component system in terms of convolution integrals, the components of the system being described by functions of either direct or Fourier space.

The formulation is equally applicable to light optics, electron microscopy or electron diffraction and permits interchange in the techniques of these disciplines. Some elementary examples of the application to thin lenses, and to periodic objects are given.

An arbitrary centred optical system is followed by two aspherical mirrors which are such that the complete system is exactly aplanatic. It is shown that the equations specifying these mirrors can be reduced to a first order linear differential equation and so the solution involves two quadratures. If these integrals can be evaluated then the mirrors can be specified exactly. If the arbitrary optical system is axially stigmatic then a particular solution of the differential equation can be found by inspection and the solution then involves only one quadrature. As an example the combination of two aspherical mirrors following a parabolic reflector to form an aplanatic telescope is solved exactly.

Differential cross sections have been measured for the elastic scattering of neutrons with a mean energy of 351.5 ± 3 MeV by lead, tin, copper, aluminium and carbon. Measurements were made out to the first diffraction minimum The total elastic scattering cross sections subtracted from the total cross sections measured previously, give upper limit values for the absorption cross sections By comparison with other measurements the absorption cross sections are seen to be essentially constant from 140 MeV to 1.4 GeV. Values of the radius of the black disc, giving an angular distribution which, when normalized, fits the experimental points, are found to be in agreement with those deduced from measurements of high energy electron scattering. From the values of the forward scattering cross sections and the previously measured values of the total cross sections, it is found that within the accuracy of the measurement the forward scattering amplitude is purely imaginary.

The scattering of 350 MeV neutrons by lead and carbon is analysed using the optical model. The parameters of the latter are determined as well as possible. The problem of the unambiguous determination of optical model parameters is considered in detail for the high energy region.

The distorted wave method is applied to the calculation of the cross sections for excitation of the 2p state of hydrogen by impact of electrons with energies between 13.5 and 54eV. The polarization of impact radiation emitted from the 2p state when excited by an electron beam is also calculated.

Comparison of results obtained using the Born-Oppenheimer approximation shows that the effect of distortion on the total cross section is not as great as for the excitation of the 2s state. It is pointed out that coupling between the 2s and 2p states which has been neglected in all calculations may be important.

The motion of conduction electrons in a metal in an electric field, scattered by an irregular static potential, is considered; this model is applicable to the resistance due to lattice waves at high temperatures, and to imperfections at any temperature. In §2 the Boltzmann equation is re-derived without the customary perturbation theory, avoiding the usual necessity of averaging over phases of different electron states after repeated small time intervals. The assumption that the scattering centres are distributed at random in the crystal is alone sufficient. The theory is, however, still dependent on assuming that h/τ<<kT, where τ is the collision time, as is the usual perturbation theory. §3 gives a general formula for the conductivity of the model, not subject to any assumption. This helps to justify an argument by Landau according to which the usual theory is valid provided h/τ<<η, where η is the cut-off energy of the Fermi distribution. No direct evaluation of the formula has been achieved.

Measurements have been made of the thermal conductivity in the normal state of ten alloys of tin with from two to eight per cent indium, over the range from 2 to 20°K. The samples with less than 3% indium satisfy the relation W = ρ₀/L₀T + αT² except at the lowest temperatures where a small lattice term lowers the thermal resistance. The more impure samples show a large lattice conductivity over the entire range. This is roughly parabolic below 4°K, but is linear in T from 5 to 16 or 17°K. The linear dependence is ascribed to scattering of phonons either by the local disorder in the lattice at the boundaries of mosaic domains or by stacking faults.

The distortion of longitudinal pulses in elastic cylinders resulting from the effects of lateral inertia is discussed in terms of the Pochhammer treatment The experimentally observed displacement-time curve produced at one end of a steel cylinder when a small explosive charge is detonated at the opposite end is compared with that obtained theoretically using Fourier synthesis. It is found that only the fundamental mode of propagation need be considered in predicting the pulse shape under such conditions.

The ¹⁸¹Ta(γ, 3n) reaction has been studied by measuring the 9.5 min and 150 min activities of ¹⁷⁸Ta. The two ¹⁷⁸Ta isomers are produced in the effectively constant ratio A(9.5 min)/A(150min) = 3.0±0.6 by gamma rays of all energies between 24 MeV and 32MeV. The experimental results have been combined with previous determinations of the ¹⁸¹Ta(γ, n) cross section and of the photo-neutron yield to obtain the relative cross sections for the ¹⁸¹Ta(γ, n), (γ, 2n) and (γ, 3n) reactions from their thresholds to 31 MeV. The integrated cross sections for the (γ, n), (γ, 2n) and (γ, 3n) reactions to 31 MeV are (73±3)°₀, (24±3)%, and (3.0±1.2)% of the total integrated cross section, (3.3±1.2) MeV barns, for these three photo-neutron reactions.

The neutron deficient isotopes, ¹⁷⁸Ta, ¹⁷⁹Ta and radioactive ¹⁸⁰Ta have been produced by photodisintegration of ¹⁸¹Ta and studied with scintillation spectrometers used singly and in coincidence. The identification of each isotope is based on a knowledge of the (γ, n) threshold and an appropriate choice of bremsstrahlung energies. Radioactive ¹⁷⁸Ta is shown to comprise an isometric doublet with half-lives 9.5±0.1 min and 150±10 min. The 9.5 min activity populates levels in ¹⁷⁸Hf at 0, 91 and possibly 1480 kev, the first two by both electron capture and β⁺ emission and the last by electron capture, while the 150 min activity decays by electron capture to a level of ¹⁷⁸Hf at 1046 kev. A decay scheme is proposed based on the experimental results and the strong coupling collective model of Bohr and Mottelson.

Evidence is presented to support the recent contention that ¹⁷⁹Ta decays by electron capture to the ground state of ¹⁷⁹Hf.

The observed γ radiation from 8.15 hour ¹⁸⁰Ta is in general agreement with the decay scheme of Brown et al. except that there is no evidence for gamma radiation in the energy range 175-450 kev.

Recent experimental results make a new discussion of the mechanism of this reaction necessary. A classical discussion is presented and the conclusions confirmed by quantum mechanical calculations at rather low energies. The qualitative features of the reaction seem now to be understood.

The electrical conductivity and thermoelectric power of the semiconductor Bi₂Te₃ have been measured between 150°K and 300°K. n-type and p-type samples with a wide range of carrier concentration have been included. Most samples have shown extrinsic conduction and have been partially degenerate over at least part of the temperature range, so it has been necessary to use Fermi-Dirac statistics in interpreting the results. A few samples have exhibited mixed and intrinsic conduction at the higher temperatures. It has been possible to determine the variation of carrier mobility with temperature and to estimate the energy dependence of the relaxation time, as well as a number of the semiconductor parameters.

It is shown that the walls of edge dislocations which exist in germanium crystals grown on a deformed seed are regions of high electrical conductivity in both n- and p-type samples. By means of simple plotting of potential against distance at constant current or from point-contact rectification measurements the positions of such dislocation walls may be located, the results agreeing with the positions determined by etch pit examination of the surfaces at which dislocations emerge. Evidence of the p-type character of dislocations in n-type germanium is presented.

The improvement in the agreement between theory and experiment in the threshold region of π⁺-meson production from proton-proton collisions is shown to be independent of any detailed model of the meson-nucleon interaction in the final state. The distorted wave approximation applied to the resonant scattering state gives a marked increase in the production cross section over the cross section calculated in Born approximation.

A variational calculation of the binding energy of the ¹⁶O nucleus is presented. A two-body central Yukawa interaction with a hard core of radius a, and with Serber exchange is assumed and the parameters adjusted to fit the low energy data. A two-parameter trial function in the form of a product of harmonic oscillator shell model wave functions and correlation functions is assumed, and the Ursell-Jastrow cluster development is applied. The results show that the assumed two-body interaction with 0.2<a<0.6 is capable of reproducing the saturation of both binding and density of the ¹⁶O nucleus.

Stick-slip oscillations are normally analysed in terms of the kinetic friction-velocity and the static friction-time of stick characteristics of the rubbing surfaces. It is shown that, in addition, a critical distance, of the order of 10^-3 cm, enters into the calculations, being the minimum resolving power of the friction process. Stick-slip oscillations must normally have an amplitude greater than the critical distance, and thus increased spring stiffness is often effective in eliminating stick-slip. Using the critical distance concept, it is possible to deduce a simple relationship between the static and kinetic coefficients of friction, and this is confirmed by experimental data.

The dependence of electron and hole mobilities on carrier concentration has been determined for p-type indium antimonide with impurity concentrations ranging from 10¹⁴ to 2 × 10¹⁷ cm^-3. The method used was the analysis of the variation of Hall coefficient and resistivity with a magnetic field. Good agreement was obtained with a simple theory, which assumes that the carrier relaxation time is independent of energy. The decrease of electron mobility with acceptor concentration can be explained by assuming that in pure indium antimonide the important scattering mechanisms are polar scattering and electron-hole scattering.