In this paper we apply to photoproduction total cross-section a model we have
proposed for purely hadronic processes and which is based on QCD mini-jets and
soft gluon re-summation. We compare the predictions of our model with the HERA
data as well as with other models. For cosmic rays, our model predicts
substantially higher cross-sections at TeV energies than models based on
factorization but lower than models based on mini-jets alone, without soft
gluons. We discuss the origin of this difference.Comment: 13 pages, 9 figures. Accepted for publication in EPJC. Changes
concern added references, clarifications of the Soft Gluon Resummation method
used in the paper, and other changes requested by the Journal referee which
do not change the results of the original versio