Spallation is induced in a heavy material by 72 MeV protons. The hereby produced neutrons with essentially an evaporation spectrum with a peak energy of less than 2 MeV are moderated in two steps, first in iron, and then in carbon. Results from neutron fluence measurements in a perspex phantom placed close to the moderator are presented. Monte Carlo calculations of neutron fluence in a water phantom are also presented under some chosen configurations of spallation source and moderator. The calculations and measurements show a good agreement and also show that useful thermal neutron fluences are attainable in the depth of the brain, at proton currents of less than 0.5 mA. 3 refs., 5 figs., 4 tabs