Relativistic calculation of two-photon bound-bound transition amplitudes in hydrogenic atoms

Using a representation of the (first-order) Dirac Coulomb Green function in terms of an expansion over a Sturmian basis, we have computed two-photon probability amplitudes for transitions in hydrogenic atoms from the ground state towards states in the [Formula Presented] and [Formula Presented] shells. The treatment takes care of the relativistic structure of the atoms according to the Dirac theory and of the fully retarded interaction with the electromagnetic field. We present in detail the Sturmian-like expansion for the Dirac Coulomb Green function and we discuss the relative importance of relativistic and retardation effects occurring for higher nuclear charge [Formula Presented]. Comparison is made also with the nonrelativistic Schrödinger treatment, retardation included or not.