Previously reported neutron spectra resulting from the ($p, n$) reaction all showed one strong neutron group at an energy corresponding in excitation in the final nucleus to the isobaric counterpart (analog state) of the target ground state, i.e., the $Q$ value for the reaction is the usual Coulomb displacement energy. Using time-of-flight techniques and the higher proton energies available from the 90-in. cyclotron after recent modifications, we have measured the angular distributions of the neutrons from the isobaric ($p, n$) reaction for 18.5-MeV protons on 19 targets between ${\mathrm{Be}}^{9}$ and ${\mathrm{Nb}}^{93}$. The optical model, with the inclusion of the isospin term as suggested by Lane, is capable of explaining the diffractive nature of the ($p, n$) angular distributions and the absolute magnitude of the cross sections. The strength of the isospin potential (${V}_{1}$) obtained from the quasielastic ($p, n$) reaction (${V}_{1}\ensuremath{\approx}70\ensuremath{-}90$ MeV) is in agreement with the magnitude calculated from the proton potential anomaly (${V}_{1}\ensuremath{\approx}100$ MeV).