A Benchmark Study of the Relativistic Plane Wave Impulse Approximation for Polarized (vec{p},2vec{p}\,) Reactions on the 3s_(1/2) state in ²⁰⁸Pb at 392 MeV

The Relativistic Plane Wave Impulse Approximation (RPWIA) is benchmarked against the established Relativistic Distorted Wave Impulse Approximation (RDWIA) for exclusive proton-induced proton knockout reactions ($\vec{p},2\vec{p}\,$) from the 3s$_{1/2}$ state in $^{208}$Pb at 392 MeV. While the RDWIA provides the proper description of the reaction, the RPWIA-which neglects nuclear distortion and absorption effects-fails dramatically for absolute cross-sections, requiring a scaling factor of $\frac{1}{26}$ to match the data. However, within $\pm10$ MeV of the recoilless condition, the RPWIA quantitatively describes the analyzing power ($A_y$) data and yields similar results as the RDWIA predictions for all polarization transfer observables (D$_{i'j}$). These polarization transfer observables are insensitive to the choice of the Relativistic Mean Field model used. The study establishes clear boundaries for the RPWIA's utility: computationally simple predictions for polarization observables near zero recoil, but essential reliance on the RDWIA for spectroscopic factor extraction.