In chapter I of this thesis the Born series solution of the Schrodinger equation for the scattering of a structure less particle by a static potential is derived and known results about its radius and rate of convergence given. The derivation is generalised to electron-atom scattering in chapter II. It is proved that the second Born scattering amplitude satisfies relationships analagous to the optical theorem and the dispersion relation conjectured by Gerjuoy and Krall. Various approximate methods of evaluating the second born correction to the scattering amplitude are discussed. In chapter III the method used to reduce the second born correction to the scattering amplitude to a sum of known integrals is given and chapter IV contains the method of evaluating these known integrals. The results obtained from applying various forms of the simplified second born approximation to elastic and inelastic collisions of electrons with Helium and Hydrogen atoms are presented in Chapter V. At incident electron energies of up to twenty times threshold a correction of between 5% and 10% to the first Born total cross sections is obtained for the following collisions:- [diagram] For transitions between the ground state and excited d states of both Hydrogen and Helium atoms induced by electrons with impact energy of twenty times threshold the correction to the first Born total cross section is less than 3%, apart from the excitation of the 31D state of Helium when it is 15%. Differential and total cross sections are given for the excitation of model doubly excited states of Helium.

In the first part of this thesis an optical potential approach is applied to the problem of elastic electron-helium scattering at low energies. First the deficiencies in the second order calculation of Pu and Chang arc removed and then third order corrections to the phase shifts are considered. In Chapter I a short review of Brueckner-GoIdstone perturbation theory is presented and explicit expressions for the second order phase shifts are derived. The methods of computing these expressions are considered in Chapter II. Various other theoretical models are discussed in Chapter III where also our second order results for the s, p and d-wave phase shifts are given. Chapter IV comprises our calculation of the polarisability of helium, using a Brueckner-Goldstone approach. In Chapter V a method of determining all the distinct Feynmann diagrams of any order is given, and third order corrections to the d-wave phase shift are discussed. The aim of the work described in Part II of this thesis has been to test for electron-neon scattering the dispersion relation conjectured by Gerjuoy and Krall. An introduction to the dispersion relation and the technique of phase shift analysis is given in Chapter VI and previous work on electron-helium scattering is reviewed. In Chapter VII the various quantities which have to be calculated in order to test the validity of the dispersion relation for electron-neon scattering are discussed. In particular, the analysis involved is the calculation of the Born exchange scattering amplitude,S_B(O, k²) is given. A more accurate evaluation of this amplitude for zero energy, using a configuration interaction ground state wave function, is described in Chapters VIII and IX. Preliminary results for g_B(O, 0) are given in Chapter X.

The dispersion relations are expressions which relate the real and the imaginary parts of the scattering amplitude. The importance of the dispersion relations in collision theory lies in that they can be used to derive rigorous formulae for quantities directly related to the measured values; and can therefore serve as a criterion for the analysis of experimental data. This is done by connecting an integral over the total cross section with the scattering length, the consistency and accuracy of total cross section measurements can be assessed. The most extensive application so far, of the dispersion relations has been to the electron scattering by hydrogen (Gerjuoy and Krall, 1960) and helium (Lawson et al. 1966, Bransden and McDowell 1969, 1970). Part of the problem addressed in the following account is that of accurately calculating the Born exchange contribution at zero energy for electron scattering by helium and lithium in the forward direction using various wavefunctions. The corresponding dispersion relations have also been discussed.

The classical Hamiltonian describing the hydrogen atom in the presence of a static magnetic field of arbitrary strength for arbitrary angular momentum is derived. For this Hamiltonian the transition from the regular to the chaotic motion is observed by means of the Poincare mappings. Two different classes of non-planar periodic orbits are traced in both regular and irregular regions. The bifurcations and variation of the periodic motion with the change of the total energy parameter throughout the regular regime and into the chaotic regime are given together with the relevant frequencies. For both classes the stability/instability of the periodic orbits is studied by calculating the linearization matrix in the neighbourhood of the corresponding fixed points of the Poincare mappings. In one class, the class of orbits that approach very close to the nucleus, we have surprisingly found that a set of periodic orbits bifurcate from the same periodic orbit along the field at various values of the energy. These values are determined numerically. A repeated pattern of stability and instability of these orbits exists over decreasing intervals of energy until the escape energy is approached. All these periodic orbits are unstable beyond the ionization limit. On the other hand we have found that the bifurcation of the second class of orbits is, generally, generic. Three sets of the energy separation lines due to three types of periodic motions are given when B = 60 kG with m - 0. Other sets of lines are given for B = 42 kG with m = 0, m = -1 and m = -2. Many of these lines coincide with the spectral lines obtained experimentally by A. Holle et al (1986).The energy spacing 0.64 near the ionisation limit, which has been found recently in the experiments of Holle et al (1986) is due to one of the non-planar orbits. Other new predicted spacings arising from other orbits have been seen in high resolution experiments on atoms in external fields (Main et al 1986).

The present work has been carried out to investigate the dynamic properties of 3 He film adsorbed on an exfoliated graphite substrate, using pulsed NMR techniques. It has been found that the dipolar interaction is the dominant mechanism for the spin relaxation, although the effect of the grafoil local fields can not be ignored. The spin-lattice relaxation time T1 and the spin-spin relaxation time T2 which characterize the spin system were determined. The study has been concentrated on two phases. The registered phase and the solid phase. Some data were taken at the mixed phase which lies between them. Both relaxation times were determined as functions of monolayer capacity, frequency, temperature and spin orientations. For temperatures less than 2 K, the spins exhibit quantum motion behaviour. The frequency of this motion was determined and was found to be inversely proportional to the spin density. At the registered phase, the activation temperature was determined, where it was a maximum corresponding to perfect registry. Special attention was given to the T1 data at the minima in the solid phase since there the frequency of the motion is comparable to the Larmor frequency.

The interaction of HeII with a solid oscillating (20,34 and 48 MHz) boundary has been studied between 0.03K and T[lambda] by an experimental technique based on the measurements of the change in resonant frequency and Q factor of a shear-mode quartz crystal immersed in the liquid. The results show three separate aspects of this interaction. (i) Below 0.6K the measurements indicate a non-viscous mechanism which is attributed to the formation of a solid layer of 4He atoms on the crystal surface. Estimates of the total adsorbed areal density reveal it to be a monolayer, characterised by a thermal mobilisation energy of 0.15K. (ii) Measurements in the middle temperature region (0.6 T T[lambda]) are used to determine the (complex) transverse acoustic impedance and hence the effective viscosity of Hell. The data is at sufficiently high frequencies to observe the breakdown in hydrodynamics which occurs when the viscous wave penetration depth [delta] becomes comparable to the phonon and roton mean free paths. (iii) Very precise measurements of the change in Q factor near T[lambda] show that the viscous wave samples an enhanced normal fluid density next to the crystal surface when [delta] becomes smaller than [xi], the superfluid healing length. A simple model is developed for the viscous losses in this region which enables an estimate to be made of the amplitude and temperature dependence of [xi]. The results are found to be well described by a power law [xi] = [xi] = [xi]0 (1 - T/T[lambda])-2/3 where [xi]0 = 0.08 nm. The transverse acoustic impedance of a weakly interacting Fermi-liquid is derived from an exact solution of the Landau kinetic equation. Explicit computations for a Fermi-gas are presented.

D.Phil. (Chemistry) / In order to optimise the parameters for graphite tubes used for electrothermal atomic absorption spectrometry a good understanding of the factors that influence the efficiency of the atomisation process is necessary. The most important of these factors are the temperature surroundings of the analyte. Consequently, a model was developed to calculate the spatial and temporal variations of the wall temperature of the tube. Reliability of the calculations was ensured by determining some graphite parameters experimentally. Normal laboratory conditions could therefore be simulated precisely. There were some problems associated with the actual measurement of wall temperatures. After these had been investigated and solved, it was possible to correlate and verify the calculated temperat~re values with the experimentally measured ones. While it is likely that the analyte evaporates as such (or in modified forms) from the walls of the tube, the actual atomisation process most probably takes place in the gas phase. It is therefore the gas temperature that controls atomisation. In view of this a gas temperature model was developed by means of which spatial and temporal temperature data within the atomiser could be calculated. Together with the calculations of wall temperatures already mentioned, this presents for the first time the possibility of calculating temperatures, both spatially and temporally, at any point within the atomiser during the heating cycle. With the above information, the nature of atomisation processes can be studied. In this work, attempts were made to study the mechanism by which- the use of a platform placed within the atomiser eliminates interferences. Contrary to the literature, it was found that this can not be attributed to stabilized temperature surroundings.

M.Sc. (Instrumental Chemical Analysis) / An investigation was undertaken into the analytical procedures and the identification of problem areas, for the certification of a new biological standard reference material supplied by the International Atomic Energy Agency, namely, a human hair sample designated as HH-I ...

Alzheimer’s disease (AD), the most prevalent neurodegenerative disease, is characterized in part by disruptions in axonal transport. Axonal transport is a process by which motor proteins carry organelles and other cargo made in the neuronal cell body along microtubule tracks to distal regions of the axon. The microtubule-associated protein (MAP) Tau plays a crucial role in regulating axonal transport, and is implicated in the development of AD and other types of dementia collectively known as Tauopathies. Tau is a neuronal-specific MAP that has six isoforms alternatively spliced from a single gene. These isoforms differ by the presence of zero, one, or two N-terminal acidic inserts and three or four C-terminal microtubule binding repeats. Tau is also known to be an intrinsically disordered protein that undergoes a dynamic equilibrium between static and diffusive states on the microtubule surface. The dynamics of Tau are important in the regulation of motor protein mediated axonal transport in neurons. Isoform-specific differences in the dynamic behavior of Tau on the microtubule surface, however, are not yet fully understood. Diffusive Tau is thought to be stabilized by electrostatic interactions between its N- and C-termini while static Tau is proposed to be extended with its C-terminal repeats contacting the microtubule and the N-terminus projected away from the microtubule surface. Thus, the N-terminal inserts may help regulate Tau’s dynamic behavior and function during axonal transport. In this study, the dynamics of two different isoforms of Tau, both with three-microtubule binding repeats but a different number of N-terminal acidic inserts, were assessed using single molecule imaging techniques and novel data analysis methods.

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