Proton-beam energy diagnostics by color-center photoluminescence imaging in LiF crystals: Implementation of multiple Coulomb scattering into an analytical Bragg-curve model

Lithium fluoride crystals are used to assess proton-beam energy spectra. Proton irradiation induces laser-active color centers in the crystal, whose density correlates with the absorbed dose. The spatial distribution of photoluminescence emitted by these color centers is exploited to estimate the proton-beam energy spectrum using an analytical Bragg-curve model. This study integrates the effects of multiple Coulomb scattering (MCS) into the model. At high enough energies, MCS leads to proton leakage through the crystal faces with a reduction in absorbed dose along the crystal length. The model incorporates MCS using an empirical approach based on Monte Carlo simulations.