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/\ensuremath{\rho}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/\ensuremath{\rho}potential. The cross...