Total and Jet Photoproduction Cross Sections at HERA

We show that the recent measurements of the total photoproduction cross section at HERA energies [1] are in agreement with our earlier prediction based on high-energy hadronic structure of the photon in the QCD minijet-type model [2]. We discuss an improved calculation of the photoproduction cross section, in which the soft part, motivated by the Regge theory, is taken to be energy-dependent and the semi-hard hadronic part is carefully eikonalized to take into account for the multiple scatterings and to include the appropriate hadronic probability of the photon [3]. We show that the extrapolation of our cross section to ultra-high energies, of relevance to the cosmic ray physics, gives significant contribution to the ``conventional'' value, but cannot account for the anomalous muon content observed in the cosmic ray air-showers associated with astrophysical point sources [4]. (invited talk presented at QCD Recontres de Moriond 1993)