  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.
