A unified description of classical and quantal scattering is presented. This description is unified both in the mathematical language and in the conceptual pictures that are used. Statistical states and observables, represented in phase space, are emphasized while both the time dependent trajectory and stationary state beam pictures are used. Semiclassical-type approximation schemes to the generalized differential cross section are presented for the single and double potential cases. Connection is made with the Born and distorted wave Born approximations, for both quantum and classical mechanics. A similar semiclassical-type approximation scheme for the double potential internal state kinetic cross section is presented. Connection is also made with the 'constant acceleration approximation' of Oppenheim and Bloom. Zwanzig's projection operator method is used to express the kinetic cross sections in terms of memory effects for the interacting observables. / Science, Faculty of / Chemistry, Department of / Graduate

The large fluxes of positive and negative pions available in meson factories over the last few years have lead to an accumulation of precise n-nuclear data over wide ranges in energy and atomic number. Little nuclear structure information has been extracted from the data since a microscopic model for the pion interaction in the nucleus is not fully developed. However the elastic scattering differential cross sections for. low energy pions are predicted well over a wide range of atomic mass using a potential in which some parameters are empirically derived., since the potential is semi-empirical some nuclear structure information can not reliably be derived directly from the data. Measurement of differences in the nuclear structure between neighbouring nuclides, however, should be reliable if the potential produces the correct variation of differential cross section in this mass region. In the experiment reported here the differential cross section ratio for elastic scattering of 29 MeV π- on ¹³C/¹²C is measured using scintillator range telescopes. Solid carbon targets of pressed powder were used. Since a relative measurement is made the errors in the ratio are only statistical. A large peak in the distribution of the cross section ratio is produced by changes in the s-p interference minimum between ¹²C and ¹³C. The cross section ratio is sensitive to the neutron distribution of ¹³C because of the large s-wave interaction of the pion with neutrons in the nucleus. A measurement of the neutron rms. radius of ¹³C and some tests of dependence on the shape of the neutron distribution and optical potential parameters are made. The neutron distribution rms. radius of ¹³C is found to be 2.365±.025 fm. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In this work, we present rigorous and efficient methods for analyzing scattering from the following structures • Tandem Slit loaded with homogeneous material • Eccentrically loaded cylinder with multiple slits • Semicircular cylinder and slit • Dielectric loaded Wedge shaped cylinder • Circular cylinder with resonant cavities and resonant cavities on circular arc. For analyzing the material loaded tandem slit configuration, the boundary value problem is formulated into a pair of simultaneous Wiener-Hopf equations via Fourier transformation. After decoupling these equations by elementary transformation, each modified Wiener-Hopf equation is reduced to a Fredholm integral equation of the second kind. The integral equations are then solved approximately to yield the Fourier transform of the diffracted fields. The inverse transform is evaluated asymptotically to obtain the far field expressions. Measurements and numerical simulations are also performed for several different geometric and material configurations. The analytic solutions compare well with measured and simulated results. The possibility of reducing beamwidth and increasing power coupled through the loaded tandem slit is explored. The analysis of the eccentrically loaded cylindrical cavity with multiple slits under plane wave illumination is formulated using two distinct approaches: (1) an integral equation/combined boundary condition (IE/CBC) formulation and (2) an integral equation/Neumann series expansion (IE/NS) formulation. The IE/NS formulation is shown to converge faster than the IE/CBC formulation based on the proper edge behavior exhibited by the Neumann series current expansion functions. Results for the backscattered radar cross section (RCS) of several geometries are presented, and the relationships between the RCS and the scatterer characteristics are explored. The applicability of the Neumann series method to find a fast method for evaluating scattering from a metallic strip and semicircular cylinder is presented. The Neumann series of different periodicity is used for studying scattering from wedge shaped cylinder. The Neumann series is also applied to study scattering from a circular cylinder with resonant cavities and resonant cavities on a circular arc. These resonant cavities on a circular arc have superdirective properties, which are useful for high gain antenna design.

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Semiclassical scattering theory can be summarized as the study of connections between classical mechanics and quantum mechanics in the limit ℏ → 0 over the infinite time domain -∞ < t < ∞. After a brief discussion of Semiclassical Analysis and Scattering Theory we provide a rigorous result concerning the time propogation of a semiclassical wavepacket over the time domain -∞ < t < ∞. This result has long been known for dimension n ≥ 3, and we extend it to one and two space dimensions. Next, we present a brief mathematical discussion of the three body problem, first in classical mechanics and then in quantum mechanics. Finally using an approach similar to the semiclassical wave-packet construction we form a semiclassical approximation to the solution of the Schrödinger equation for the three-body problem over the time domain -∞ < t < ∞. This technique accounts for clustering at infinite times and should be applicable for researchers studying simple recombination problems from quantum chemistry. / Ph. D.