  A physical model of Geant4-based simulation of galactic cosmic ray (GCR)
particles interaction with the lunar surface matter has been developed to
investigate the production rate of cosmogenic nuclei. In this model the GCRs,
mainly very high energy protons and $\alpha$ particles, bombard the surface of
the Moon and produce many secondary particles such as protons and neutrons. The
energies of proton and neutron at different depths are recorded and saved into
ROOT files, and the analytical expressions for the differential proton and
neutron fluxes are obtained through the best-fit procedure under the ROOT
software. To test the validity of this model, we calculate the production rates
of long-lived nuclei $^{10}$Be and $^{26}$Al in the Apollo 15 long drill core
by combining the above differential fluxes and the newly evaluated spallation
reaction cross sections. Numerical results show that the theoretical production
rates agree quite well with the measured data. It means that this model works
well. Therefore, it can be expected that this model can be used to investigate
the cosmogenic nuclei in lunar samples returned by Chinese lunar exploration
program and can be extended to study other objects, such as the meteorites and
the Earth's atmosphere.
