Energy Dependent Model of Isotopic Production Cross Sections from Proton-$^{16}$O Interactions

Proton interactions with $^{16}$O nuclei are the most frequent nuclear interaction leading to secondary radiation in tissues for space radiation and cancer therapy with protons. In addition, $^{16}$O has the largest fluence of galactic cosmic rays, and interacts with hydrogen in tissue or water and polyethylene shielding. The fragmentation of oxygen produces a large number of heavy ion (A>4) target fragments (TF) with high ionization density. Here we develop an analytical model of energy dependent proton-$^{16}$O cross sections. We introduce corrections to measurements of total charge changing cross sections to extend data on nuclear absorption cross sections. Using experimental data and a 2nd order optical model an accurate formula for the p-$^{16}$O absorption cross section from <10 MeV/n to >10 GeV/N is obtained. The energy dependence of the isotopic cross sections is modeled as multiplicities scaled to absorption cross section resulting in an accurate model over the full energy range.