Analytical properties and numerical calculations of high transcendental functions involved in the relativistic amplitudes of two photon atomic processes

  • Authors:

  • Adrian Costescu;Sever Spanulescu;Cristian Stoica

  • Affiliations:

  • Department of Theoretical, Physics and Mathematics, University of Bucharest, Bucharest, Magurele, Romania;Department of Physics, Hyperion University of Bucharest, Bucharest, Romania;Department of Theoretical, Physics and Mathematics, University of Bucharest, Bucharest, Magurele, Romania

  • Venue:
  • WSEAS Transactions on Mathematics
  • Year:
  • 2009

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Abstract

The high transcendental functions that occur in the relativistic expressions of the amplitudes of the two photon atomic processes are analytically treated taking advantage of their specific parameters values. We present some identities and recurrence relationships that allow reducing the number of needed Appell functions and transform their imaginary part in terms of Gauss hypergeometric functions. If the physical model takes into account only the terms up till the fourth power in αZ in the real part and the seventh power in the imaginary part, some transcendental functions may be reduced to elementary functions. The numerical results obtained using the presented methods were compared with other's authors results, displaying a very good agreement.