Abstract The angular distributions and total cross sections of 20 BeV protons scattered by eight target nuclides ranging from Li to U are analyzed by means of the strong absorption model of Frahn and Venter. The analysis accounts for contributions from both coherent and incoherent (quasi-elastic) scattering. Good agreement with all the data is obtained for a consistent set of parameters. The main result of this investigation is conclusive evidence for a sizable negative real part of the coherent scattering amplitude. In high-energy approximation this corresponds to a real part of the central proton-nucleus potential which is repulsive in the nuclear surface.