Physics Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2800
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Item Energy Dependence of the Effective Interaction for Nucleon-Nucleus Scattering(1990) Seifert, Helmut; Kelly, James J.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)We have measured cross sections and analyzing powers for 40, 42, 44, 48Ca and 16O at IUCF using the new high-resolution K600 spectrometer for 100 and 200 MeV protons. Measurements at 318 MeV for 40, 42, 44 ,48Ca and 32 ,34S were done at LAMPF using the HRS spectrometer. In this work, we obtain empirical effective interactions by fitting inelastic scattering data for many low-lying normal-parity isoscalar excitations of the self-conjugate nuclei 16O and 40Ca, assuming a local tp folding model. One-nucleon transition densities are from (e, e') . The fitted interactions are iterated to generate optical potentials self-consistently. We find that the fitted parameters are essentially target independent, which supports the validity of the local density hypothesis. Elastic scattering is predicted by extracting the rearrangement factor (1 + pd/dp) from the fitted in elastic interactions. Below 300 MeV the strength of the empirical interaction is reduced at zero density and the general density dependence is weaker compared to the theoretical interaction. Above 300 MeV we find the density dependence is stronger than expected. The empirical interactions provide better descriptions of elastic and inelastic data than IA calculations or LDA calculations using theoretical G-matrices, and can be used for nuclear structure studies of other nuclei . Fitted optical potentials above 300 MeV are comparable to equivalent Schrödinger potentials from the relativistic IA2 model.Item Lie Algebraic Methods for Treating Lattice Parameter Errors in Particle Accelerators(1986) Healy, Liam Michael; Dragt, Alex J.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Orbital dynamics in particle accelerators, and ray tracing in light optics, are examples of Hamiltonian systems. The transformation from initial to final phase space coordinates in such systems is a symplectic map. Lie algebraic techniques have been used with great success in the case of idealized systems to represent symplectic maps by Lie transformations. These techniques allow rapid computation in tracking particles while maintaining complete symplecticity, and easy extraction of analytical quantities such as chromaticities and aberrations. Real accelerators differ from ideal ones in a number of ways. Magnetic or electric devices, designed to guide and focus the beam, may be in the wrong place or have the wrong orientation, and they may not have the intended field strengths. The purpose of this dissertation is to extend the Lie algebraic techniques to treat these misplacement, misalignment and mispowering errors. Symplectic maps describing accelerators with errors typically have first-order terms. There are two major aspects to creating a Lie algebraic theory of accelerator errors: creation of appropriate maps and their subsequent manipulation and use. There are several aspects to the manipulation and use of symplectic maps. A first aspect is particle tracking. That is, one must find how particle positions are transformed by a map. A second is concatenation, the combining of several maps into a single map including nonlinear feed-down effects from high-order elements. A third aspect is the computation of the fixed point of a map, and the expansion of a map about its fixed point. For the case of a map representing a full turn in a circular accelerator, the fixed point corresponds to the closed orbit. The creation of a map for an element with errors requires the integration of a Hamiltonian with first-order terms to obtain the corresponding Lie transformation. It also involves a procedure for the complete specification of errors, and the generation of the map for an element with errors from the map of an ideal element. The methods described are expected to be applicable to other electromagnetic systems such as electron microscopes, and also to light optics systems.Item Topics in Nonlinear Wave Theory With Applications(1984) Tracy, Eugene Raymond; Chen, Hsing Hen; Physics; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Selected topics in nonlinear wave theory are discussed and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasiperiodic solutions to several nonlinear wave equations which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schrodinger equation, an equation with general applicability in one dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in our numerical studies, and the numerical work of other authors. The method of solution (related to the Inverse Scattering Method) is then analyzed within te context of Hamiltonian dynamics where we show that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation which appears here and in the work of other authors is shown to be a special form of Liouville's Transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's Inversion Problem, is surveyed briefly.