[en] A relativistic multiple scattering theory is formulated in the context of meson exchange. The elastic scattering amplitude for a fermion projectile satisfies a Dirac equation with an optical potential derived from a relativistic multiple scattering series. It is shown that two-body t-matrix associated with the optical potential is the one with the projectile on its mass-shell in all intermediate states. 8 refs., 3 figs

[en] This is the proceedings of the 6th consecutive Hampton University Graduate Studies (HUGS) at the Continuous Electron Beam Accelerator Facility (CEBAF). These proceedings are composed of articles produced by graduate students. The participants were divided into smaller groups. Each group chose a lecturer's presentation to focus on and write up for these proceedings. There were some cross over students; that is there were students who participated in more am one group. In addition, there were participants who pursued topics considerably further than being confined to the scope of a given lecture; these participants contributed additional articles which can also be found here. All of the HUGS at CEBAF participants worked very hard and had a good time doing it. The students lived on the Hampton University campus and attended lecture sessions at CEBAF. The atmosphere of the river front campus of Hampton and the stimulation readily available at CEBAF made for a wonderful mix. These proceedings are divided into two sections: Section 1 contain articles that were generated by the HUGS participants from lecturers' notes and discussions among the student groups and lecturers, and Section 2 contains original work generated by the HUGS participants. Section 3 contains the contributions from the lecturers. Some of the articles were reviewed by the lecturer more closely connected to the particular subject matter. The appendices contain a list of the HUGS enrollment, lecturers, schedule, and lecture assignment

[en] This report contains papers on the following topics: Construction of hall C drift chamber prototype; a construction of the N-N potential; electron scattering; investigating lightcone QCD at CEBAF; lattice gauge theory; low energy NNbar interactions; photo and electroproduction of Baryon resonances in the potential quark model; D-state admixture and tensor force in deuteron; and, notes for a talk at HUGS at CEBAF 1990: Is light cone physics merely a change of coordinates?

[en] Using split-quaternions, we find explicit SDYM SU(1,1) instanton solutions in S_-² x S₊² which is the conformal compactification of the semi-Euclidean 4-spacetime R2+2 of split-signature (-,-,+,+). It is also shown that SDYM and ASDYM fields in S_-² x S₊² can be described as simple split-quaternionic 2-forms

[en] The Gaussian, exponential and Laguerre basis functions are examined in a variational calculation of energies and wavefunctions. The Laguerre basis set is already orthonormal and complete, but the Gaussian and exponential basis sets are not orthonormal. We used the linear and Coulomb potentials to test these basis functions. Calculations are performed in both position and momentum space. We also present the results with relativistic kinematics in the momentum space calculation. The Gram-Schmidt procedure is used to orthonormalize the Gaussian and exponential basis sets before using them in the calculations. We show that in the case of a pure linear potential, the orthonormal basis constructed from the Gaussian functions performs much better than the exponential and Laguerre basis for the same number of orthogonal functions. For Coulomb-like potentials, the exponential basis performs better than the other two for the same number of basis functions. The advantage of using these simple basis functions is that for the potentials that we examined, one can approach the lower bound of the low-lying states with very few basis functions.

[en] A numerical Gram-Schmidt orthonormalization procedure is presented for constructing an orthonormal basis function set from a non-orthonormal set, when the number of basis functions is large. This method will provide a pedagogical illustration of the Gram-Schmidt procedure and can be presented in classes on numerical methods or computational physics.

[en] It is shown that a relativistic multiple scattering theory for hadron-nucleus scattering can be consistently formulated in four dimensions in the context of meson exchange. We give a multiple scattering series for the optical potential and discuss the differences between the relativistic and non-relativistic versions. We develop the relativistic multiple scattering series by separating out the one-boson exchange term from the rest of the Feynman series. However, this particular separation is not absolutely necessary and we discuss how to include other terms. We then show how to make a three-dimensional reduction for hadron-nucleus scattering calculations and we find that the relative energy prescription used in the elastic scattering equation should be consistent with that used in the free two-body t-matrix involved in the optical potential. We also discuss what assumptions are involved in making a Dirac relativistic impulse approximation (RIA)

[en] Nuclear cross section calculations are often performed by using the partial wave method or the Eikonal method through Glauber theory. The expressions for the total cross section, total elastic cross section, and total reaction cross section in the partial wave method involve infinite sums and do not utilize simplifying approximations. Conversely, the Eikonal method gives these expressions in terms of integrals but utilizes the high energy and small angle approximations. In this paper, by using the fact that the lth partial wave component of the T-matrix can be very accurately approximated by its Born term, the infinite sums in each of the expressions for the differential cross section, total elastic cross section, total cross section, and total reaction cross section are re-written in terms of finite sums plus closed form expressions. The differential cross sections are compared to the Eikonal results for ¹⁶O+¹⁶O,¹²C+¹²C, and p+¹²C elastic scattering. Total cross sections, total reaction cross sections, and total elastic cross sections are compared to the Eikonal results for ¹²C+¹²C scattering