Table of contents

A spin-Hamiltonian approach to the theory of spin-lattice relaxation in paramagnetic salts is developed in which the orbit-lattice interaction is treated as a perturbation connecting states of the overall spin-Hamiltonian. The approach is much simpler than previous treatments where the spin-orbit and Zeeman effects were treated as perturbations, and is applicable to a wide range of salts including both the iron group and the rare earth group.

It is found that, for Kramers salts (ions with an odd number of electrons), many previous results apply quite generally, regardless of the relative size of the spin-orbit and crystalline field terms, but there are important exceptions. For the case of large crystalline field splittings, the relaxation rate (inverse of the relaxation time T₁) varies as H⁴T and T⁹ for direct and Raman processes respectively, as Van Vleck has previously shown. The so-called Van Vleck cancellation leading to these dependences is derived in a very simple and quite general manner. For small crystal field splittings δ, less than, or of the order of, the lattice Debye temperature, the relaxation rate varies as H⁴T and a exp (-δ/kT)+bT⁹ for direct and Raman processes respectively. The two coefficients a and b are such that the T⁹ term is important only at low temperatures where the exponential term is quite small. These results are in marked contrast with earlier theories.

The problem is formulated in terms of the radial exchange equations. The Schwinger method, with polynomial trial functions, is used to calculate the scattering length. With 3-term polynomials one obtains Λ⁺ = -9.72, Λ^- = -2.35 compared with Λ⁺ = -8.095, Λ^- = -2.350 from exact numerical integrations.

The polarization of 9 MeV protons, elastically scattered from C and Al, has been measured using a double scattering technique. The polarization was obtained from the left-right scattering asymmetry from helium as recorded in photographic emulsions. Angular distributions from the polarization and elastic scattering cross section are compared with predictions of optical model calculations. The general features of the scattering from aluminium are described by the optical model calculation, while the scattering from carbon appears to have strong contributions from sources other than the shape-elastic scattering.

A silver foil of 4.4 mg cm^-2 was bombarded with the internal 14₇N⁶⁺ beam from the 150 cm Birmingham cyclotron, and the reaction products were recorded in C2 emulsion. The energy and angular distributions of the emitted protons and α-particles were measured and the results at large angles have been compared with the predictions of evaporation theory. Good agreement was obtained by assuming that the Coulomb barrier is reduced at high nuclear excitations.

The presence of competing direct processes is discussed briefly.

A simple source of O^- ions suitable for accelerator applications is described. Negative atomic ion currents of over 2 μA can be directly extracted at 10 keV energy for a low-pressure cold-cathode oxygen discharge source which incorporates an electrostatic constrictor electrode. The input power is only 25 watts and the gas consumption 14 cm³ h^-1 of oxygen at atmospheric pressure.

Mass analysis of the beam has shown the primary components to be O^- and O₂^- ions whilst the main impurity ions are OH^-, Cl^- and NO₂^-.

A study has been made of the relationship between the negative ion yield and various source operating conditions. The O^- and O₂^- ion yields are shown to be related to the striated structure of the positive column. With a singly striated column the beam is composed mainly of atomic ions. Only when a doubly striated column is formed does the O₂^- yield become large. Ion production processes are discussed in terms of this relationship.

A broad range magnetic spectrograph has been used to analyse the deuterons emitted from targets of natural boron, carbon, silicon dioxide and aluminium bombarded with 5.5 MeV tritons. The angular distributions of the majority of the deuteron groups from the reactions observed in ¹⁰B, ¹²C, ¹³C, ¹⁶O, ²⁷Al and ²⁸Si have been measured and information has also been obtained on (t, d) reactions in ²⁴Mg, ²⁸Si, and ⁴⁰Ca because of the presence of these nuclei as impurities in the targets. In all cases the measured excitation energies of the final nuclei are in good agreement with the accepted values. The angular distributions have been compared with the stripping theory and also with published data on (d, p) transitions between the same initial and final nuclear states. Where possible the ratios of the yields of corresponding (t, d) and (d, p) reactions have been compared with the predictions of stripping theory to extract values of the proportionality constant of the momentum transform of the deuteron within the triton,|A₀|²N₁². The values obtained vary between 18.0 × 10¹² cm^-1 for the transition from ¹⁰B to the ground state of ¹¹B and 1.3 × 10¹² cm^-1 for the transitions from ¹⁶O to the ground state of ¹⁷O and from ²⁸Si to the 3.630 MeV excited state of ²⁹Si.

At 5.5 MeV triton bombarding energy, therefore, a constant value of|A₀|²N₁² cannot be used to extract values of nucleon reduced widths from studies of (t, d) reactions.

A simple diffusion method has been employed to measure the shape of the excitation probability curve above the threshold of the 2³S excitation in helium. The results are in substantial agreement with those of Schulz and Fox.

Luminescence excitation spectra have been obtained, at room temperature, for 13 natural diamonds comprising six of type I, three of type IIa, three of `intermediate' type and a single, semiconducting diamond. Excitation peaks, corresponding in detail to the well-known absorption bands at 5.250ev, 5.363ev and 5.391ev were detected in all except the semiconducting crystal, and indications of further structure in this energy region were seen. In the region of fundamental optical absorption, broad excitation bands with maxima at 5.51ev, 5.56ev and 5.73ev occur in all but the semiconducting crystal. The semiconducting diamond showed unique features consistent with the presence of an acceptor level within 0.35ev of the valence band. The luminescence emission spectrum appears to be independent of the quantum energy of the exciting radiation.

Luminescence decay times of 10 milliseconds have generally been found but for the semiconducting diamond, the decay time was six seconds.

A method for the determination of the fracture energy of brittle plastics is described. A crack is propagated down the length of a rectangular specimen under controlled conditions and the variation of crack opening with length determined. From these results the fracture energy may be calculated The method has been applied to determine the variation of fracture energy for polymethyl-methacrylate and polystyrene with temperature in the temperature range 20 to 80°C. The results of tests carried out at room temperature show good agreement with similar results obtained by other investigators.

A new tensor invariant is introduced into elasticity, viz. the work done by a system of fixed initial stresses in generating second-order dilatations. The effect of the latter can therefore be systematically accounted for, in a crystal of any symmetry class, when making lattice theory calculations of non-equilibrium elastic constants. Two examples of such calculations are included.

It is shown that a law of corresponding states exists amongst the inert gases in the solid phase even when quantum effects are large. The theoretical treatment is based on the Einstein model of a crystal modified to account for large vibrations of the crystal atoms. Using a Lennard-Jones 12-6 potential for the interaction energy between a pair of atoms, reasonable agreement is obtained between theoretical and experimental values for the equilibrium volumes and energies of the rare gas crystals at the absolute zero.

The instrument described measures alternatively the distribution of intensity in the image of a narrow slit (the spread function), or the frequency response function, which latter is the Fourier transform of the spread function. For the former use a slow scan with an exploring slit is used while for the direct determination of the frequency response curve a continuous scanning with a grating of slits arranged around the periphery of a variable speed drum is employed with a single frequency electrical detector.

The in-focus aberration-free image of a line source has been measured together with the axial variation of central intensity and good agreement with the theoretical curves has been obtained. The frequency response curves obtained by taking the Fourier transforms of four out-of-focus spread functions numerically agree well with the direct determinations of the frequency response with the scanning drum. Further the frequency response curves for a well corrected lens in different focal planes have been compared with results obtained by Hopkins theoretically.

Ferromagnetic resonance absorption has been measured in a series of nickel-copper alloys having compositions Ni 50% Cu 50%, Ni 45% Cu 55%, Ni 42% Cu 58% by weight. The temperature range over which measurements were made included the individual Curie points of the alloys. The experiments were carried out at 3.19 cm and 8.8 mm wavelength. Absorption lines were observed in both the ferromagnetic and paramagnetic phases, and the line-width was found to be a maximum at the Curie point. It was also frequency dependent, being roughly twice as great at 8.8 mm as compared with 3.19 cm. The g-factor had the value 2.22 ± 0.02 for the ferromagnetic phase of each alloy.

A new phenomenological coupling constant in the pion-pion interaction is introduced through an interaction Lagrangian of the form L_int = λ₁ (ϕ×ϕ_,μ)·(ϕ×ϕ^,μ). It is found that this type of interaction leads to a P-wave pion-pion resonance when summation is made over the `chain-diagrams'. The width of the resonance is adjusted by a cut-off and λ₁ is determined by the position of the resonance and the cut-off.

An apparatus has been developed by means of which nuclear resonance signals have been observed at temperatures up to 1300°K. The variation of the line shape and width of the ⁶³Cu resonance at high temperatures is found to follow quantitatively the predictions of Kubo and Tomita for motional narrowing. In conjunction with the theoretical value of the frequency factor D₀ (0.28 cm² sec^-1) in the expression D = D₀ exp (- E/RT) for the coefficient of self-diffusion, the results yield a value 48.1 ± 0.9 kcal mol^-1 for the activation energy for self-diffusion in copper, in agreement with the results of the most recent radio-tracer measurements. A similar change in shape and width of the ²⁷Al resonance cannot be used to determine the activation energy in aluminium because of the presence of a line-broadening mechanism of uncertain origin. The data are not inconsistent, however, with the theory and the known activation energy of about 31 kcal mol^-1.

If the only factors restricting the configurations of a polymer molecule are the constancy of the C-C-C bond angle, and the existence of a potential hindering free rotation about C-C bonds, stereospecific polymers of the type (CHX)_N are simple Markoff chains but the stereospecific vinyl polymers (CH₂CHX)_N are not. These vinyl polymers are examples of Markoff chains with a periodic transition probability. The eigenvalue theory of such chains is briefly discussed.