Londergan There are two major topics to be studied in this proposal. The first deals with the quark sub-structure of protons and neutrons, and related baryons. We are studying the validity of charge symmetry, which states that up quarks in the proton and down quarks in the neutron should behave in identical ways. This approximate symmetry is very well preserved in nuclear physics, but we showed that previous experiments appeared to require significant deviations from charge symmetry at the quark level. A re-analysis of the experimental data suggests that charge symmetry is valid to a high degree of precision in high energy physics. We also propose to investigate the process by which quarks produced at high energies ``fragment'' into baryons. We want to see whether these processes depend on the type, or ``flavor,'' of quark which produces the baryon. We are developing a model for this process, and looking at the production of Lambda hyperons. The simplest model for the Lambda particle consists of an up, down and strange quark. It is customary to assume that up, down and strange quarks contribute equally to the fragmentation leading to a Lambda particle. Our preliminary investigations suggest significant differences from this simple ``flavor symmetric'' model. We can explain in simple qualitative terms why this model should be wrong, and we predict where large flavor symmetry violation should occur. We also propose to investigate bound state and scattering properties for particles in two dimensional systems. We are particularly interested in systems whose transverse dimensions are of the same order as the particle wavelength. In these cases, binding and scattering are dominated by wave effects. We have recently published a book on this subject ("Binding and Scattering in Two-Dimensional Systems", Londergan, Carini and Murdock, Springer-Verlag, 1999). We have shown that our work is relevant to the properties of electrons in quantum wires, confined electromagnetic modes in waveguides, and confined and propagating states in optical systems called ``photonic crystals.'' In this proposal we will focus on the properties of ``defect states,'' which are found when one starts with a finite periodic system, and then changes the properties of one or more of the cells producing the periodic system. The principal investigator is Director of the Indiana University Nuclear Theory Center.