Relativistic description of inclusive quasielastic proton-nucleus scattering with relativistic distorted-wave impulse approximation and random-phase approximation

Abstract

We present a fully relativistic model for polarized inclusive quasielastic proton-nucleus scattering that includes relativistic distorted waves for the projectile and ejectile (RDWIA), as well as the relativistic random-phase approximation (RPA) applied to the target nucleus. Using a standard relativistic impulse approximation treatment of quasielastic scattering and a two-body Scalar, Pseudoscalar, Vector, Axial vector, Tensor (SPVAT) form of the current operator, it is shown how the behavior of the projectile/ejectile and target can be decoupled. Distortion effects are included via a full partial-wave expansion of the relativistic wave functions. Target correlations are included via the relativistic RPA applied to mean-field theory in quantum hadrodynamics. A number of novel analytical and numerical techniques are employed to aid in this highly nontrivial calculation. A baseline plane-wave calculation is performed for the reaction $^{40}\mathrm{Ca}$$(\mathrm{pP\vec},\mathrm{pP\vec} {}^{\ensuremath{'}})$ at an energy of 500 MeV and an angle ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}={40}^{\ifmmode^\circ\else\textdegree\fi{}}$. Here it is found that the effect of isoscalar correlations is a quenching of the cross section that is expected to become more pronounced at lower energies or for higher-density targets. A RDWIA calculation shows additional reduction and if isoscalar target correlations are included this effect is enhanced.