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Bethe-Heitler cross-section for very high photon energies and large muon scattering angles

The cross-section for the process $γ+ A \to μ^+ + μ^- + X$ is studied where the photon energy is of the order of several hundreds of GeV and where one of the leptons is scattered to large angles. This is of practical importance for muon shielding calculations at future linear electron colliders. In addition to the photon pole contribution which was previously considered especially by Y.S.Tsai, we identify another component due to the muon pole (equivalent photon and equivalent muon approximation). This is discussed following the usual Bethe-Heitler formula. Then we give practically useful formulae for inclusive lepton (muon) production along with some numerical examples.