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The radiative transfer equations are solved for an electron-scattering stellar atmosphere as formulated by Chandrasekhar. The solution employs a transformation of the integro-differential form of the transfer equations into singular integral equations for the angular intensities of the radiation field. The Milne problem is solved to illustrate the method. In addition, the relationship is found between the above method of solution and Case's normal mode expansion method. This leads to an alternate procedure for finding the normal mode expansion coefficients. As an example of the method the constant, distributed source problem is solved for a half-space medium. / Master of Science

Electron scattering by a single or multiple impurities affects the quantizaton of conductance of a semiconductor nanochannel. The theoretical model of electron transport in a hardwall nanostructure with an impurity requires an analysis of the electronic transverse energy levels, eigenfunctions and hopping integrals resulting from cross channel or transverse confinement. Theoretical equations for the electronic transverse energy levels, wavefunctions and hopping integrals in the case of a repulsive, finite strength rectangular barrier arbitrarily positioned in the nanochannel are presented. The effects of size, strength and location of the impurity are discussed.In order to find the electronic transverse energy levels, wavefunctions and hopping integrals, two FORTRAN computer programs were developed. The first, called Program Data Input, writes the computational parameters to a data file. The second, Program Single Impurity, uses this data file in performing the calculations of the electronic transverse energy levels, eigenfunctions and hopping integrals. / Department of Physics and Astronomy

iii, 135 leaves : ill. ; 26 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics, 1974

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 1977 / Vita. / Includes bibliographical references. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Physics

In this work, the method of streaming rays have been expanded to two spatial dimensions (three phase space dimensions, x, y, and s) and was used as a basis for the development of the electron transport computer code SR2D. The streaming ray algorithm is an Eulerian-Lagrangian hybrid. Electrons are followed as they traverse the medium along specified streaming rays. Fluxes, however, are computed at the centers of the fixed cells. The development of the SR2D code required the specification of a Lagrangian streaming ray network overlaying a three dimensional Eulerian grid. In contrast to its one dimensional predecessor, the SR2D code accommodates non-uniform cell sizes and allows for arbitrary quadrature sets (S₂, S₄, S₆, S₈, S₁₂, or S₁₆). The critical aspect of the streaming ray method is the determination of the pathlengths of each and every streaming ray through all of the Eulerian cells. These values must be precalculated and stored because of the iterative nature of the solution scheme. Although the number of pathlengths may be exceedingly large, computer memory requirements are minimized, however, in the two dimensional algorithm by the symmetry of the geometry in each pathlength increment. The SR2D code was used to calculate the energy deposition profile for two kinds of sources, an isotropic point source and a monodirectional point at the periphery of a two dimensional medium. For each case, we chose aluminum with dimensions 0.01g/cm² thick by 0.02g/cm² wide as the medium and specified a grid of 5 by 10 uniform cells, respectively. The pathlength increment was 0.002g/cm² with 25 pathlength increments chosen. An S₈ quadrature set was selected for the monodirectional point source while an S₁₂ quadrature set was used for the isotropic point source. Both sources were normalized to one incident particle with an energy of 200 keV. SR2D results were compared with those from the electron/photon Monte Carlo code TIGER. The total energy deposited in the medium and peak cell was selected to facilitate the comparison. For the monodirectional point source SR2D results were within 1% for total energy deposited into the medium and peak cell energy. The total energy deposited for the isotropic point source was within 1%, but peak cell energy varied by 4%.

[Truncated abstract] This work investigated electron correlation and spin-dependent effects in electron scattering from zinc for incident electron energies from the lowest excitation threshold at 4.003 eV to 50 eV. Experiments were performed using a crossed-beams electron impact spectrometer, which included an unpolarised electron gun, and also a spin-polarised electron gun. The apparatus was tested, and shown to be operating well, by repeating past studies of electron scattering from helium and argon. Emission cross sections for the 4s4p 3P1, 4s4p 1P1, 4s5s 3S1, 4s4d; 5d; 6d 3D1;2;3 and 4s4d; 5d 1D2 states were measured from the respective thresholds to 50 eV. These were compared with Convergent Close-Coupling (CCC) and B-spline R-matrix (BSRM) calculations of the 4s4p 3P1, 4s4p 1P1, 4s5s 3S1, 4s4d 1D2 and 4s4d 3D1;2;3 emission cross sections. There are serious discrepancies between the theories, and between the theories and experiment, which indicates strong continuum coupling and innershell excitation effects in the electron excitation of zinc. The differential elastic scattering signal at scattering angles of 30 , 54 , 90 and 110 was measured for incident electron energies from just below the lowest excitation threshold at 4.003 eV, to the ionisation threshold at 9.394 eV. Some assignments given by Sullivan et al [1] and Zatsarinny and Bartschat [2] were confirmed by the present experiment. An area of disagreement in the literature concerning the nature of a feature observed at the 4s4p 1P1 threshold at 5.796 eV was resolved in favour of Zatsarinny and Bartschat, who assign the feature as a cusp. ... Below the ionisation threshold, the 4s4p 3P1 photon excitation function supports the assignment of the near-4s4p 1P1 threshold feature as a cusp. Some of the overlapping negative-ion resonances which were observed near 7.5 eV in the 4s4p 3P1, 4s4p 1P1 and 4s5s 3S1 photon excitation functions were assigned with the assistance of the BSRM calculations of Zatsarinny and Bartschat. However, continuum coupling effects above 8 eV seem to cause the theoretical negative-ion resonance predictions to break down. Above the ionisation threshold, the near-11 eV negative-ion resonance effects depend on the configuration n, L and S of the neutral state excitation observed. This may be due to the properties of the mixed negative ion component states. Postcollision interaction (PCI) effects the 4s5s 3S1, 4s4d; 5d; 6d 3D1;2;3 and 4s4d; 5d 1D2 photon excitation functions. The PCI mechanism can populate the 4s4d; 5d; 6d 3D1;2;3 and 4s4d; 5d 1D2 states because the scattered and ejected electrons have a similar energy, and can thus exchange a large amount of orbital angular momentum. The present work demonstrates that electron correlation effects, especially those associated with innershell excitation, are very significant in electron scattering from zinc. Existing theoretical models of electron scattering from zinc inadequately treat electron correlations, and as a result of this are inaccurate, as shown here. The studies presented here should guide the development of models that accurately describe the innershell excitation effects, which are important for zinc and a great many other atoms.

For thin epitaxial metal films, when the thickness is on the order of the Fermi wavelength, [lambda subscript F], quantum confinement can dramatically alter the physical properties of the film. These so-called Quantum Size Effects (QSE) can dramatically alter the morphology of thin films by an intricate interplay between kinetics and surface energy driven thermodynamics. These effects lead to rich growth-related phenomena in Pb(111) films grown on semiconductor substrates such as Si(111). For example, QSE can drive flat film formation when growth is dominated by surface energy oscillations. This is rather surprising for Pb/Si systems because of a rather high lattice mismatch. However, these films are not defect free, but rather show common occurrences of three defect types. Low Temperature Scanning Tunneling Microscopy (LT-STM) was utilized to characterize these defects on the atomic scale. Furthermore, these defects create modulations in the electron density resulting in fluctuations in QWS near defect sites. Another topic of recent interest is how QSE affect adsorption of as well as how adsorbates modify QSE for these Pb films. In this thesis, LT-STM and first principles calculations were utilized to study Cs adsorbates on Pb film surfaces, defects, and step edges. Cs adsorption is intricately related to the electronic structure of the surface, especially the defect sites which can act as surface traps. These Cs adsorbates, which are assumed to be ionized, enhance elastic surface scattering of empty-state electrons. This results in observable wave interference patterns near Cs impurities. Furthermore, Cs adsorbates, by an overall step energy reduction, can promote QSE-related nanostructures, which are otherwise too weak when kinetic effects cannot be ignored. This enhancement of "quantum stability" is driven by favorable Cs step binding and can be explained within the contexts of Density Functional Theory (DFT). / text