Comprehensive Study of Final State Interactions and Dirac Dynamics in Inclusive Quasielastic Electron Scattering.

The longitudinal and transverse response functions for the inclusive quasielastic (e,e^' ) reaction as well as the Coulomb sum rule are analyzed in detail. A theoretical framework is developed resulting in a one-body Green's function doorway approach, which includes many-body and inelastic final state processes by properly incorporating a nonhermitean optical potential. Final state interactions and Dirac physical degrees of freedom are thoroughly analyzed within this optical model formalism. Explicit momentum space calculations are performed permitting comparisons between relativistic plane wave approximations, nonrelativistic final state interaction and relativistic final state interaction results. Nonrelativistic final state interaction effects are described by a variety of complex optical potentials including phenomenology, local density models and microscopic impulse approximations. Optical potentials used to describe relativistic final state interactions span a similar range of models such as energy dependent global phenomenology and Dirac impulse approximation optical models. Relativistic calculations are performed in Dirac four-component space allowing no nonrelativistic reduction in {|vec p| /m}. Extensive calculations are performed for ^{40 }Ca at 410, 550 and 700 MeV/c momentum transfers, where there are no free adjustable parameters. Physical effects observed include large off-shell effects, significant relativistic suppression of R_{rm L} and large quantitative shape differences between various final state interaction predictions. In no case is simultaneous agreement found with both response functions. The large suppression of R_ {rm L} due to relativistic and Dirac sea effects is reflected in the Coulomb sum rule results providing reasonable predictions of the data, although continuing to overestimate the anomalous ^ {40}Ca data. Implications are that large additional transverse mechanisms are necessary for realistic descriptions of quasielastic electron scattering.