#### Date of Award

1-2011

#### Degree Name

Doctor of Philosophy

#### Department

Physics

#### First Advisor

Dr. Dean Halderson

#### Abstract

We have developed a relativistic coupled{channel reaction theory in which binary break-up channels satisfy a relative Dirac equation. This theory is developed by extending the R-matrix formalism of Lane and Thomas to the relativistic case and implementing the Dirac oscillator basis. The motivation for this project is testing po- tentials for the dense matter calculations and generating relativistic wave functions for the nal states in the knockout reactions. As an example of the formalism we have calculated observables for the proton scattering on light-to-medium weight nuclei in the relativistic impulse approximation using the relativistic Love-Franey amplitudes of Horowitz. The R-matrix procedure allows the nonlocal exchange terms to be calculated exactly and compared with the local density approximation. These calculations demonstrate that the local density approximation is not suitable due to the rela- tivistic e ects. Thus the wave functions with exact exchange would be preferred in distorted wave calculations. Also, calculations involving pseudoscalar π - N coupling provide a better agreement with experimental data than previously determined. In order to investigate relativistic e ects in the bound states and scattering reactions, we have applied the theory to the quantum hadrodynamics (*Q H D*) in the continuum Tamm-Danco approximation with the classical meson elds replaced by one-meson exchange potentials. The results show that the published *Q H D* parameters do not provide a decent t to the ^{15}N+*p* elastic cross section or reproduce the *Q H D* single-particle energies, and hence, are not appropriate for structure calculations. We have found more suitable parameters by fitting meson coupling constants and masses to produce single-particle energies and employed them in the structure calculations for ^{16}O. The results showed that the fitted single-particle energies have too large spin- orbit splitting. Our conclusion is that *π, σ, ω* and* ρ *meson exchange is inadequate for relativistic structure and reaction calculations. Unlike the conclusions of previous authors, the calculations indicate that the pseudoscalar *π* - *N* coupling gives better agreement to experimental data than the pseudovector *π* - *N* coupling. In addition, we calculated inelastic electron scattering form factors for the Dirac spinors and for the upper components of the Dirac spinors. The calculations indicated signi cant relativistic e ects.

#### Access Setting

Dissertation-Open Access

#### Recommended Citation

Grineviciute, Janina, "Relativistic R-Matrix Theory" (2011). *Dissertations*. 411.

http://scholarworks.wmich.edu/dissertations/411