A functional Analytic method which was first introduced by Larsen and Habetler for the one-speed isotropic case in 1973 is applied to full and half-space multigroup problems in one dimension with a constant and invertible transfer matrix. The Case-type eigenfunction expansion formulas for the solutions of these problems are explicitly obtained. For the half-space case, the formulas are expressed in terms of two matrices X and Y which provide the Wiener-Hopf factorization of the dispersion matrix. The method applied yields compact results avoiding the calculation of adjoint solutions and normalization integrals to determine the expansion coefficients. Since the method proves to be amenable to further generalization, the case of a degenerate transfer kernel is also considered along the same lines, yielding the expansion formulas for that problem in the full and half-space cases. The expansion formulas are shown to be valid at least for subcritical media, but an extension to critical problems is expected. / Doctor of Philosophy

We have undertaken to develop a method !or determining the resonance escape probability of homogeneous reactors containing aqueous solutions of a resonance absorber. TH(NO₃)₄ was selected as a salt since it is readily dissolvable in water. Even at the highest concentration, the atomic densities of thorium and nitrogen are small compared to hydrogen and oxygen. Only the latter two contribute significantly to the slowing down in the high energy range; therefore, a water Monte Carlo serves adequately as the neutron supply to the resonance region of thorium. In order to find an escape probability we determine the ratio of the number of neutrons that attain energies below the resonance region to the number that appear in the resonance region for the first time. The difference between the two numbers in the ratio occurs due to absorption by the resonance absorber, in this case thorium, and due to leakage. The initial source of neutrons comes from H²(d,n)He³ reaction where the deuteron beam strikes the deuterium target at the center of one face of the containing parallelepiped. Once the water Monte Carlo is run one has a set of data cards which can be used as the input data to a second Monte Carlo designed to calculate the resonance escape probability. Our prime concern is this second Monte Carlo. The resonance escape Monte Carlo is a direct analog type using known physical distributions and laws. The decisions about what events occur in the history of a neutron are based on these distributions and laws. The detailed effect of the thorium resonances on the number of neutrons absorbed is described by the cross-section as a function of energy. A Breit-Wigner Doppler broadened single level formulation gives the scattering and absorption parts of the cross-section as a function of energy. Given a neutron-thorium interaction, the neutron is either absorbed or scattered with probabilities σ_ab/(σ_ab+σ_sc) and σ_sc/(σ_ab+σ_sc). A new statistical weight is assigned the neutron by taking the latter fraction of the old weight. A new neutron is picked from the source supply only after the previous neutron has delivered a weight to low energy or to the exterior of the pile. The heart of the Monte Carlo method lies in the determination of a random variable, distributed according to some known probability function. This requires a source of random numbers which in our case is provided by the IBM-650 computer. The resonance escape probability as a function of thorium number density fits very closely to a straight line with small negative slope throughout the whole range of stable concentrations. The Monte Carlo statistics provides probable errors of less than 0.3% for all five points calculated. Each of the five points lies close enough to the straight line of least-squares fit to give an error less than 0.3%. A theoretical determination of the resonance escape probability based on resonance integral theory for the eight peaks used in the Monte Carlo calculation gives good enough agreement to make both methods plausible. Although other resonance escape calculations have been done by the Monte Carlo method, they have been for radically different systems. In all such cases the system was heterogeneous with "lumped" uranium for the absorber. Therefore comparisons between existing Monte Carlo calculations is impossible. We hope to be able to provide experimental verification for the applicability of the Monte Carlo model. / Ph. D.

The electrical potential differences which arise across the length of capillary tubes containing 1 N perchloric acid and mercury drops are studied experimentally and theoretically for constant acceleration and different lengths of the drops of mercury. A relatively simple theory explains many features of the voltage on the experimental parameters. The results suggest that surface modes exist on the mercury drops which, in association with the Gibbs-Thompson effect, is the coupling between the mechanical and electrochemical phenomena. / Ph. D.

The Jost function method is extended to study scattering phenomena produced by potentials having spheroidal symmetry. The spheroidal radial functions are constructed by taking the spherical wave functions as bases. The role of the Jost function in spherical potential scattering is reviewed. The relation between zeros of the Jost function and the formation of bound and resonant states is then established for spheroidal potentials. The domain of analyticity of the spheroidal Jost function is studied for three classes of basis functions: those belonging to spherical potentials having only a bounded first and second moments, those belonging to a Yukawa potential, and those belonging to truncated potentials. / Ph. D.

Many workers have attempted to determine neutron absorption cross sections and average resonance parameters with varying degrees of success. Values of the latter parameters for a given isotope often vary as much as a factor of two or three from one worker to another. This dissertation is an attempt to remove some of this uncertainty. Natural silver and the isotopes ¹⁰⁷Ag, ¹⁰⁹Ag, ¹¹⁵In, ¹²⁷I have been irradiated by the monoenergetic neutrons emitted at 90° to a proton beam striking a ⁷Li target. These samples were then counted for their β and γ activity and their absolute cross sections relative to the cross section of ¹²⁷I at 24 keV were calculated over the energy range of from 3 to 155 keV. These measured cross section versus energy curves were used to determine the γ-ray strength functions, (r_γ)/( D_o), the s-wave neutron strength functions, (r¹_n)/(D), and the p-wave neutron strength functions (r¹_n)/(D). Because of data limitations it has been assumed that the γ-ray strength function is the same for both s- and p-wave neutrons. The cross sections determined are in general good agreement with the values previously reported but differ somewhat in shape. This shape variance results in values for the average resonance parameters which are somewhat higher than values reported by other workers. / Ph. D.

For lunar satellites within a few hundred miles of the lunar surface the primary cause of disturbance from pure Keplerian motion is the disturbing force due to the moon's noncentral gravitational field which, unlike the earth's field, is unsymmetrical and rotating. This thesis presents a first-order approximation to the motion of lunar satellites under the forces resulting from this field. The results are a set of equations which give the short period, long period and secular variations of a slightly modified set of Delauney elements. A typical set of orbital characteristics are utilized to obtain an estimate of the order of magnitude of the variations in the various elements. / Master of Science

no abstract provided by author / Master of Science

A single crystal neutron spectrometer using a copper crystal has been designed and constructed for the purpose of studying the low energy (<1 ev) neutron spectrum from the V.P.I. reactor. The basic theory necessary for the design, the details of the spectrometer, calibration data and method of operation are presented in this thesis. A relation between angle of diffraction and neutron energy is obtained from the known lattice spacing of the copper crystal. A measure of the total cross section of cadmium from 0.01 to 1.0 ev has been obtained from transmission data for a thin cadmium sheet. The position of the low energy resonance peak confirms the computed calibration. The resolution of the instrument and the intensity of the diffracted beam as a function of energy were studied in order to ascertain the usable range of the spectrometer. / Master of Science

Thermodynamic properties are calculated for mixtures of ideal gases in equilibrium for temperatures up to 15,000° K. Results for air and a model Mars atmosphere are given. The equilibrium composition of a gas mixture at a given temperature and pressure is determined by minimizing the Gibbs free energy. Species of the following types are included in the mixture: atoms and atomic ions, diatomic and linear triatomic molecules and ions, and electrons. Quantum statistical mechanics is used to determine thermodynamic properties of each species. For the diatomic species, accurate evaluations of vibrational anharmonicity, vibration-rotation interaction, and rotational stretching corrections are carried out. Comparisons are made between results with and without the above corrections. / Master of Science

no abstract provided by author / Master of Science