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

Haakon A. Olsen, Yuri Kunashenko

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)527-537
Number of pages11
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume56
Issue number1
Publication statusPublished - 1997

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electron-positron pairs
pair production
high energy electrons
photons
cylindrical waves
strings
crystals
wave functions
electrons
continuums
cross sections
periodic variations
positrons
perturbation
expansion
matrices

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

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AU - Olsen, Haakon A.

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N2 - 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.

AB - 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.

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