: We have investigated the influence of different nonlinear relativistic mean-field models (NL, NL{rho}, and NL{rho}{delta}) on spallation neutrons for p+Fe and p+Pb reactions at 0.8,1.2, and 1.6 GeV by means of a relativistic Boltzmann Uehling Uhlenbeck (RBUU) approach plus a statistical multifragmentation (SM) decay model. We find that the 'evaporation shoulder', that is, the neutron energy spectrum from 3 to 30 MeV, almost for any emission angle is quite sensitive to the isospin part of the mean field. For the more neutron-rich Pb target the evaporation component can be directly related to the low-density behavior on the symmetry energy in the thermal expansion phase of the excited compound system. It turns out that the spallation data for the reactions under study are shown to be more consistent with RBUU+SM employing the NLrho effective Lagrangian.