In this paper we present the results of GEANT4 simulations of the production of surface muons as a function of energy of the incident protons on a graphite target. A validation of the GEANT4 hadronic physics models has been performed by comparing the results with experimental data from the Lawrence Radiation Laboratory, United States. Considering the ISIS muon target as a reference, simulations have been performed to optimise the pion and muon production. Of particular significance we predict that optimal surface muon production occurs at a relatively modest proton energy of 500 MeV. This will be of importance for the development of future μSR facilities.
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