Using the Moyer Model at energies less than 1 GeV

Although many shielding calculations are today done using sophisticated Monte Carlo codes there is still often a need to do quick estimates for simple geometries. Such estimates are usually made using the so-called 'Moyer Model'. Among the model's limitations is that it is of limited validity for proton beam energies less than about 1 GeV. One reason is that although above a few GeV almost all protons undergo a nuclear interaction, this is not true at energies below 1 GeV. At lower energies Coulomb interactions and ionization losses predominate and fewer protons participate in non-elastic nuclear interactions. We have modified the Moyer source term, multiplying it by the nuclear interaction probability for protons at the energy of interest. These interaction probabilities have been previously tabulated but we have recalculated them for thick targets using the Monte Carlo code FLUKA. Except for hydrogen, the nuclear interaction probability is very nearly independent of the target material. One can prepare a simple table as a function of energy that can be used for all targets except hydrogen. We present a comparison of estimates made using this modified Moyer model and detailed Monte Carlo calculations for a simple geometry as a function of incident proton energy below 1 GeV. The model has been used successfully in the design of the shielding for ISAC a high intensity accelerated ion beam facility at TRIUMF. This facility uses a 0.5 GeV proton beam incident on a thick target to produce the radioactive atoms. Some comparisons between the estimates made using the Moyer model and measurements made during the commissioning of this facility are also presented. (author)