The radial wavefunction of a relativistic binary of two fermions bound by the Coulomb force

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. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA.Wmheim.