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Keywords:

  • two-fermion Dirac equation;
  • radial wavefunction;
  • relativistic binary atom;
  • Coulomb force

Abstract

The exact radial eigenfunctions of a relativistic binary atom bound by the static Coulomb force are calculated. We consider the two-fermion Dirac equation for two distinguishable fermions (like, e.g., in positronium) including the static Coulomb potential but no radiative corrections. As shown in a previous paper and its addendum this problem can be solved exactly [1]. Here we provide the exact solution in terms of generalized hypergeometric functions for the radial eigenfunctions of the hamiltonian, which are determined through a matrix recursion relation. Also, an equivalent set of coupled first-order, or uncoupled second-order, differential equations that may be solved numerically is provided.