Elastic Scattering of 500-MeV Polarized Protons fromCa40,48,Zr90, andPb208, and Breakdown of the Impulse Approximation at Small Momentum Transfer

New 500-MeV $p_{\mathrm{pol}}$+${}_{}{}^{40,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic $\frac{d\sigma }{d\Omega }$ and $A_y\left(\theta \right)$ data are presented. The small-momentum-transfer data are not reproduced by the second-order Kerman-McManus-Thaler optical potential which uses free nucleon-nucleon amplitudes. The systematics of these results, taken together with previous 800-MeV results, suggest that medium modifications to the $\mathrm{NN}t$ matrix are required to obtain an accurate description of the 500-800-MeV proton-nucleus elastic data in general.