Using Glauber's multiple scattering theory, closed form expressions for the volume integrals and rms radii of different components of the optical potential for intermediate energy protons are obtained. Applying these expressions to the available optical-model parameters for proton scattering energies between 0.1 and 1 GeV, the corresponding parameters of the effective nucleon–nucleon interactions are extracted and compared with the information obtained from nucleon–nucleon scattering. Corrections due to Pauli principle, short-range correlations, and centre-of-mass recoil are considered.