Dirac states of relativistic electrons channeled in a crystal and high-energy channeling electron-positron pair production by photons

Dirac wave functions for high-energy electrons channeled in crystals are obtained for crystal string potentials. Specifically, we study partial cylindrical wave expansions for “cylindrical constant and 1/ρ potentials. The periodicity along the crystal axis is taken into account as a perturbation to the cylindrical wave functions. We also find a Sommerfeld-Maue-like solution for the 1/ρ potential. The cross section for channeling electron-positron pair production in continuum states is obtained for the crystal string potential. For two-dimensional Sommerfeld-Maue-like electron and positron wave functions, matrix elements and cross section are obtained for unpolarized photons. The fact that channeling continuum pair production can only occur when the photon is hitting the crystal string at a small, finite angle is taken into account.