Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 127-132). Also available via the Internet.

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An investigation of the problem of inelastic scattering process under the Coulomb Born approximation is given. Different approaches to calculate Coulomb wavefunctions in the momentum space representation are analyzed and a discussion of their existences in the generalized distribution sense is provided. Inokuti’s approach of finding the differential cross section in the momentum space representation under the Coulomb Born approximation is described and a different approach with an application of the Bremsstrahlung integral is developed and compared with Inokuti’s approach.

An investigation of the problem of inelastic scattering process under the Coulomb Born approximation is given. Different approaches to calculate Coulomb wavefunctions in the momentum space representation are analyzed and a discussion of their existences in the generalized distribution sense is provided. Inokuti’s approach of finding the differential cross section in the momentum space representation under the Coulomb Born approximation is described and a different approach with an application of the Bremsstrahlung integral is developed and compared with Inokuti’s approach.

Thesis (M.S. in Physics)--Naval Postgraduate School, December 2008. / Thesis Advisor(s): Borden, Brett. "December 2008." Description based on title screen as viewed on January 29, 2009. Includes bibliographical references (p. 83-84). Also available in print.

Cengiz Esmersoy, Michael L. Oristaglio, Bernard C. Levy. / Bibliography: p. 16-18. / "November, 1984."

Cengiz Esmersoy, Bernard C. Levy. / "June 1985." / Bibliography: leaves 23-24.

This thesis concerns the use of nuclear reactions to study the structure of neutron-rich light nuclei. Emphasis is placed on 11Be which has been identified as a nucleus with a single neutron halo and which offers a simple 2-body case for detailed analysis. Comparisons are made with experimental data for the break-up of 11Be on gold, titanium and beryllium targets. As a prelude to more detailed work a simple elastic break-up model calculation, using the Distorted Wave Born Approximation (DWBA), is attempted. The resulting theoretical cross-sections show good agreement with the shape of the experimental data but cannot predict the absolute magnitude. A major part of the break-up work is a more accurate model using the post-form DWBA. The formulation is built up from basic scattering theory and includes details of employing the Zero Range Approximation and the Vincent and Fortune method of integration. A Finite Range Correction is also applied. Cross-section calculations for a gold target agree closely with experiment but a problem arises for lighter targets. Here the Coulomb potential must be excluded from the calculation to obtain a result that matches the experimental data. A method for the calculation of inelastic break-up is presented which only requires a small modification to the methods used for elastic break-up. As it suffers from the same light target problem only calculations for a gold target give an inclusive cross-section, produced from the elastic and inelastic contributions, which matches the experimental data satisfactorily. To overcome the light target problem a full recoil calculation is introduced. Arguments and analysis are produced to show that this method is too demanding of both computing time and storage for practicable implementation. Future calculations are proposed using an analytical method for Coulomb break-up.

We analyze the Schrödinger equation i𝜖 ¬²â /â tΨ = H(𝜖)Ψ, where H(â ¬) = - f24 Î x + h(X) is the hamiltonian of a molecular system consisting of nuclei with masses of order 𝜖¬^-4 and electrons with masses of order 1. The Born-Oppenheimer approximation consists of the adiabatic approximation to the motion of electrons and the semiclassical approximation to the time evolution of nuclei. The quantum propagator associated with this Schrödinger Equation is exp(-itH(â ¬)/â ¬²). We use the Born-Oppenheimer method to find the leading order asymptotic expansion in â ¬ to exp(_it~(t:»Ψ, i.e., we find Ψ(t) such that: (1) We show that if H(𝜖) describes a diatomic Molecule with smooth short range potentials, then the estimate (1) is uniform in time; hence the leading order approximation to the wave operators can be constructed. We also comment on the generalization of our method to polyatomic molecules and to Coulomb systems. / Ph. D.

A three-dimensional parabolic equation (PE) and perturbation approach is used to invert for the depth- and range-dependent geoacoustic characteristics of the seabed. The model assumes that the sound speed profile is the superposition of a known range-independent profile and an unknown depth- and range-dependent perturbation. Using a Green’s function approach, the total measured pressure field in the water column is decomposed into a background field, which is due to the range-independent profile, and a scattered field, which is due to the range-dependent perturbation. When the Born approximation is applied to the resulting integral equation, it can be solved for the range-dependent profile using linear inverse theory. Although the method is focused on inverting for the sound speed profile in the bottom, it can also invert for the sound speed profile in the water column. For simplicity, the sound speed profile in the water column was assumed to be known with a margin of error of ± 5 m/s. The range-dependent perturbation is added to the index of refraction squared n2(r), rather than the sound speed profile c(ro). The method is implemented in both Cartesian (x,y,z) and cylindrical (r,q,z) coordinates with the forward propagation of the field in x and r, respectively. Synthetic data are used to demonstrate the validity of the method [1]. Two inversion methods were combined, a Monte Carlo like algorithm, responsible for a starting approximation of the sound speed profile, and a steepest descent method, that fine-tuned the results. In simulations, the inversion algorithm is capable of inverting for the sound speed profile of a flat bottom. It was tested, for three different frequencies (50 Hz, 75 Hz, and 100 Hz), in a Pekeris waveguide, a range-independent layered medium, and a range-dependent medium, with errors in the inverted sound speed profile of less than 3%. Keywords: Three-dimensional parabolic equation method, geoacoustic inversion, range-dependent sound speed profile, linear inversion, Born approximation, Green’s functions. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection