Isotopic production cross sections in proton-16O and proton-12C interactions for energies from 10 MeV/u to 100 GeV/u

Proton interactions with ¹⁶O or ¹²C nuclei are frequent nuclear interaction leading to secondary radiation in tissues for space radiation and cancer therapy with protons or ion beams. The fragmentation of these ions by protons produces a large number of heavy ion (A>4) target or projectile fragments often with high ionization density. Here we develop an analytical model of energy dependent proton-¹⁶O and proton-¹²C cross sections for isotopic nuclei production. Using experimental data and a 2^nd order optical model an accurate formula for the absorption cross section from <10 MeV/u to >10 GeV/u is obtained. The energy dependence of the elemental and isotopic cross sections is modeled as multiplicities scaled to absorption cross section with average isotopic fractions estimated from experimental data. We show that this approach results in accurate analytic formulae for isotopic fragmentation cross sections over the full energy range in hadron therapy and space radiation protection studies.