Table of contents

A proportional-counter scintillation-counter telescope technique was developed to measure the energy distribution and angular distribution of alpha particles emitted from a thin (1.56 mg cm^-2) target of ²⁷Al bombarded with neutrons of 14.8 MeV from the (D, T) reaction. The energy distribution was obtained with good statistics by minimizing the neutron source-²⁷Al target distance, the alpha particles detected being those emitted in the forward hemisphere at a weighted mean angle of 55° with respect to the direction of the incident neutrons. A modified telescope geometry with improved angular definition (± 10°) was used in the measurement of the energy distributions at 5° and 90° (c.m.) and the differential cross sections at 5°, 38°, 90°, 130° and 139° (c.m.).

The energy distributions at different angles are very similar, with the characteristic shape of an evaporation process. Conventional analysis of the statistically good 55° spectrum gave `nuclear temperatures' of 1.35 MeV and 1.40 MeV, corresponding to two differents sets of σ_c (the cross section for the inverse reaction) based on the continuum (r₀ = 1· fermi) and optical models respectively.

The angular distribution, strongly peaked in the forward direction, is in agreement with that obtained by Kumabe et al. in 1957, who used the photographic emulsion technique.

A proportional-counter scintillation-counter telescope was used to measure the energy distributions of alpha particles emitted from thin (similar 1.8 mg cm^-2) separated isotope targets of ⁵⁴Fe, ⁶³Cu, ⁶⁴Zn and ¹⁰⁷Ag bombarded with neutrons of 14.8 MeV from the (D, T) reaction. The alpha particles detected were emitted over a wide angular interval (0°-110°), the weighted mean angle of emission being 55° with respect to the direction of the incident neutrons.

The energy spectra have been analysed conventionally in terms of the statistical theory of nuclear reactions, and values of `nuclear temperature' T, level density parameter a and differential cross sections for the (n, α) and (n, nα) reactions are obtained. The differential cross sections are in agreement with those obtained by other methods, and are larger than those usually predicted from the statistical theory. The values of T similar 1 MeV and a similar 5 MeV^-1 obtained for the residual nuclei ⁵¹Cr, ⁶⁰Co and ⁶¹Ni are in agreement with comparable data; for ¹⁰⁴Rh we obtain T = 1.2 MeV.

The differential cross sections at 55° for the (n, α) and (n, nα) reactions in target nuclei ⁵⁴Fe, ⁶³Cu, ⁶⁴Zn are, respectively, ⁵⁴Fe 6.47 ± 0.65, 0.43 ± 0.1; ⁶³Cu 5.65 ± 0.55, 0.65 ± 0.15; ⁶⁴Zn 4.62 ± 0.45, 6.28 ± 1.0; for ¹⁰⁷Ag(n, α)¹⁰⁴Rh the relevant differential cross section is 0.96 ± 0.1. All cross sections are expressed in millibarns per steradian.

Calculations of the energy and angular dependence of the polarization of 1 to 2 keV electrons elastically scattered from mercury agree qualitatively with experiment, a maximum 90° polarization occurring at 1.5 keV as found experimentally.

The impulse approximation is used to calculate the cross section for the reaction H⁺ + He(1s²) → H(1s) + He⁺(1s), for the range of incident proton energies 25 keV to 1 MeV. The results are compared with those given by Mapleton in 1961 using the Born approximation and are found to differ significantly especially in the predicted angular distributions. By estimating the probability for capture into excited states the total capture cross section is calculated and found to be in fair agreement with experimental results.

The relation between the calculated total reaction cross section and the optical model parameters is investigated for 17 Mev protons on copper. For both the real and imaginary central potential a Saxon-Woods form factor is used with a Thomas-type spin-orbit potential. A semi-automatic search procedure to find the parameters corresponding to the optimum fit to the elastic scattering is developed. A method is described for the derivation of the optimum adjustments of some or all of the parameters to produce a required change in the predicted reaction cross section with minimum departure from the optimum fit to the elastic scattering results. A 3% change in the reaction cross section can be accommodated for the reaction studied. The scattering of 17 Mev protons by carbon is also briefly considered.

Nuclear emulsions have been exposed at a depth of 58 m.w.e. underground to study stopped mesons, the rates for muons and pions being (73±3)10^-3 and (2.7 ± 0.6)10^-3 cm^-3 day^-1 respectively. The positive-negative ratio for the numbers of stopped muons is 1.1 ± 0.2, and the negative-positive ratio for stopped pions is 2.3 ± 0.9. The data on the stopped muons are consistent with the momentum spectrum of the cosmic ray muons at sea level. The pion data are not inconsistent with a mechanism of muon-nucleus interaction through the Coulomb field, but imply that pions are also produced by neutron secondaries from muon interactions.

The electrical resistance of the heavy rare earth metals shows strong anomalies at the temperatures where the magnetic order changes. These are most marked in measurements made along the hexagonal axis. A simple theory of the effect is given on the basis of two mechanisms. The spiral spin structures found in these materials cause an exchange field at the conduction electrons with a lower symmetry than that of the lattice. This introduces new boundaries in the Brillouin zone and distorts the Fermi surface. This distortion and the scattering of the conduction electrons by the spin disorder in these materials is calculated. The order of magnitude of the effect agrees with that calculated for a simple spherical Fermi surface. Agreement between experiment and theory is improved by assuming that the Fermi surface lies inside a boundary of the original zone and is cut by a new superlattice boundary near its extremity. Further improvement is made by including the variation of the spiral pitch with temperature.

Using a simple nuclear model it is shown that some of the low-lying resonances in the scattering of neutrons by ¹²C are possibly consequences of the virtual excitation by the neutrons of the 2⁺ first excited state at 4.43 MeV in ¹²C.

Rapid rotation of an assembly of dipolar coupled nuclei has a profound effect on the nuclear magnetic resonance absorption spectrum. In turn, this affects the broadening caused by random fields even when the correlation frequency greatly exceeds the rotation rate. This broadening is considered for a rotating pair of I = ½ nuclei and it is concluded that rotation may reduce the broadening due to very rapidly fluctuating fields. In this case the broadening depends on the degree of overlap of the frequency spectra of off-diagonal elements of the density matrix. When the angle between the rotation axis and the external magnetic field is 54.7° a continuous transition from almost no overlap to complete coincidence is obtained with rising rotation speed. For slowly varying fields, on the other hand, broadening may be increased by rotation.

The reduction of a relativistic wave equation for any atom to an approximately relativistic form is completed by considering the close approach of particles. The non-hyperfine structure electronic Hamiltonian is given as far as terms in 1/c² and m/M_A. The contact interactions differ from those found previously, expressions for one- and two-electron atoms being given explicitly. Some new isotope shift terms are derived as a correction to the normal mass effect. A relation satisfied by the wave function is obtained.

The problem of the uniqueness of solutions of the Boltzmann equation is studied. It is shown that if the kernel possesses certain symmetry properties (which it usually does in the absence of magnetic fields) the equation can be reduced to a form which is non-singular in an algebraic sense, and therefore has a unique solution. This solution also minimizes a functional which is equivalent to the standard variational expression.

Detailed and careful measurements have been made of the light output L_γ from NaI(Tl) and CsI(Tl) for energies E_γ from 6 kev to 200 kev, employing filtered characteristic x rays and γ rays from radio-active sources; an accuracy of 0.3% for L_γ/E_γ is claimed. The measurements have been extended, in less detail, to 2.6 MeV. The scintillation efficiency for single electrons, in the energy range 1 keV to 100 keV, calculated from the observed values of L_γ/E_γ, has been found to be a maximum at 15 keV and at lower energies shows a marked falling off. The results for single electrons are in good agreement with the diffusion theory of Meyer and Murray.

A small (<1%) component of delayed fluorescence has been observed from the sublimates of pyrene, 3,4-benzpyrene, 3,4-benztetraphene, chrysene and coronene excited by ultra-violet light in vacuo at room temperature. The spectrum of this component is similar to that of the total luminescence emitted at room temperature, but it persists for some milliseconds after excitation cut-off. The failure to observe the delayed fluorescence in the presence of air and the increase in intensity of the delayed component with the state of subdivision of the solid particles indicates that the emission originates at the crystal surface. The decay of the fluorescence in the millisecond region is virtually exponential for 3,4-benzpyrene and 3,4-benztetraphene, but is non-exponential for the other compounds.

Emission spectra from a King's furnace containing mixtures of Cu-Te and Au-Te respectively have been recorded. New bands appear with the Cu-Te mixture at about 1800 °C in the region λλ6965-6110, and with the Au-Te mixture they appear at about 2100 °C in the range λλ6940-6155. In both cases the bands are degraded to the red. They are attributed to diatomic CuTe and AuTe respectively. Vibrational analyses which include all the observed bands give the following constants:

	νe	ωe'	ωe'χe'	ωe"	ωe"χe"
CuTe	15988.8	198.0	0.50	254.0	1.01 cm-1
AuTe	15481.1	156.1	0.10	212.5	0.50 cm-1

Series solutions are presented for the problem of the numerical design of generalized aplanatic lenses zoned, or stepped in thickness, and extremized in the sense of having maximum aperture or minimum volume for fixed values of the other lens parameters, including the zone angular apertures or f/numbers, some of which also may be required to be minimal or nearly minimal in some sense. The solutions are developed by the method of limits or Cauchy-Kovalevsky process which in turn leads to the establishment of an existence and convergence theory for the problem. Applications to both classical optics and contemporary microwave and acoustic lens antenna problems are illustrated.

Observations were made of the domain structures on (001) surfaces of grains in 3% silicon-iron sheet when stresses were applied to the sheet. The changes produced by the application of a compressive stress along the [011] surface direction are described and discussed in terms of an extension of the theory proposed by Chikazumi and Suzuki in 1955. The effect of compressive stress was also investigated on surfaces which were inclined at angles of a few degrees to a (001) surface and an interpretation of the domain patterns is suggested.

Deformation potentials associated with the conduction band edge in Si are calculated using a pseudo-potential rigid ion model and the results of the band structure calculation made by Kleinman and Phillips in 1960. This simple method should give a good estimate for Θ_u, the shear component, but not necessarily for Θ_d. The calculated value of Θ_u, 8.4±0.3 eV, agrees well with experiment but there is no agreement for Θ_d.

A rigorous derivation is given of the conventional Boltzmann equation for a metal in an inhomogeneous electric field E(x, t). It is assumed that the electrons are scattered elastically by static impurities. The equation is shown to be valid provided the following conditions hold: (i) hτ << η, where τ is the scattering time and η the Fermi energy of the system, (ii) λ << λ_F, r0 where λ is the smallest wavelength present in E(x, t), λ_F is the Fermi wavelength of the electrons and r0 is the range of the scattering potential, (iii) hω << E_a, where ω is the largest frequency in E(x, t) and E_a is an energy of the order of magnitude of the Fermi energy.

Absolute pair cross sections in the elements Cu, Zr, Rh, Sn, Ta, Pt, Au and Pb for gamma rays of energy 1.119 MeV are determined, using a scandium 46 source of intensity 1 curie and a coincidence scintillation spectrometer. The results are found to support the general viewpoint that Bethe - Heitler theory fails at energies of this magnitude. Good agreement is observed between the present experimental value for lead and the value reported by previous investigators. The usual Z dependence formula valid at high energies is, however, found to be inadequate at this energy. A modified formula of the type

σ = σ_BH[1 + dZ² exp(-bZ)]

for the Z dependence of the pair cross section is found to give a better fit of the experimental data.

The theoretical discussion of Worthington and Tomlin published in 1956 has been modified to allow for electron scattering within the target, and the results of the two theories are compared with those of an extensive series of measurements of the absolute intensities of emission of characteristic K α radiation from thick targets of copper, silver and chromium. Good agreement was found between various methods of intensity measurement and the experimental results are in satisfactory accord with the modified theory.

In agreement with Schulz, resonance has been observed in the elastic collision cross section for electrons in helium. This occurs at approximately 0.5 eV below the 2³S excitation threshold and leads to a temporary decrease of 6% in the value of the cross section. A compound He^- ion state may be involved.