We apply the dipole formalism that has been developed to describe low-x deepinelastic scattering to the case of ultra-high energy real photons with nucleonand nuclear targets. We hope that there will be future modeling applications inhigh-energy particle astrophysics. We modify the dipole model of McDermott,Frankfurt, Guzey, and Strikman (MFGS) by fixing the cross section at themaximum value allowed by the unitarity constraint whenever the dipole modelwould otherwise predict a unitarity violation. We observe that, underreasonable assumptions, a significant fraction of the real photon cross sectionresults from dipole interactions where the QCD coupling constant is small, andthat the MFGS model is consistent with the Froissart bound. The resulting modelpredicts a rise of the cross section of about a factor of 12 when the thephoton energy is increased from $10^{3}$ GeV to $10^{12}$ GeV. We extend theanalysis to the case of scattering off a $^{12}$C target. We find that, due tothe low thickness of the light nuclei, unitarity for the scattering offindividual nucleons plays a larger role than for the scattering off the nucleusas a whole. At the same time the proximity to the black disk limit results in asubstantial increase of the amount of nuclear shadowing. This, in turn, slowsdown the rate of increase of the total cross section with energy as compared tothe proton case. As a result we find that the $^{12}$C nuclear cross sectionrises by about a factor of 7 when the photon energy is increased from $10^{3}$GeV to $10^{12}$ GeV. We also find that the fraction of the cross section dueto production of charm reaches 30% for the highest considered energies with a$^{12}$C target.
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