Differential cross sections and analyzing powers for scattering of 135-MeV protons by /sup 16/O have been measured for all narrow states below 12.1 MeV of excitation up to a momentum transfer of 3.2 fm/sup -1/. Calculations that employ accurate transition densities fitted to electroexcitation data are used to study medium modifications to the two-nucleon effective interaction with little residual uncertainty from nuclear structure. Definitive evidence for strong density dependence in the isoscalar spin-independent central component of the two-nucleon effective interaction has been found. The differential cross sections show that as the density increases, the strength of the central interaction is suppressed at low momentum transfer and enhanced at high momentum transfer. The analyzing powers exhibit strong negative excursions near 2.5 fm/sup -1/, which support enhanced repulsion at high density. The data are well described by the local-density approximation, which employs the nuclear-matter effective interaction appropriate to the density in the vicinity of the interacting nucleons. We find that the qualitative results are insensitive to ambiguities in the local-density prescription, the local-exchange approximation, and the choice of distorted waves. However, effective interactions based upon the Paris, Bonn, and Hamada-Johnston potentials do give substantially different results. Of these, the Paris-Hamburg effective interactionmore » provides the best description of normal-parity isoscalar transitions. The analysis also supports a rearrangement contribution to the effective interaction for inelastic scattering.« less