Relativistic distorted-wave analysis of quasielastic proton-nucleus scattering

A relativistic distorted-wave impulse approximation formalism is presented for the calculation of quasielastic proton-nucleus scattering. It is shown that the double differential cross section may be written as a contraction between the hadronic tensor (describing the projectile and ejectile) and the polarization tensor (describing the nuclear target) and that this mathematical structure also holds for the case where distortions are included. The eikonal approximation is used to introduce distortions in the wave functions, and the nuclear response is described using a Fermi gas model. The highly oscillatory nine-dimensional integrand contained in the expression for the double differential cross section is computed using a novel technique based on combining traditional Gaussian integration methods with the powerful fitting functions in the matlab programming language. This work has successfully calculated the distorted-wave quasielastic differential cross section for proton-nucleus scattering within a fully relativistic framework. It is found that the distortions lead to a reduction in the double differential cross section and have a negligible effect on the computed spin observables.