Analytic basis set for high-Z atomic QED calculations: Heavy He-like ions

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Abstract
A relativistic Sturmian analytic basis set representation for the Coulomb-Dirac Green function, previously studied by Zapryagaev, Manakov, and Pal'chikov [Opt. Spectrosc. 52, 248 (1982)], is investigated for application to high-Z atomic QED calculations. This pseudoeigenfunction representation follows from exact identities starting from the Whittaker function representation. It eliminates the radial ordering problem of that representation, and so is particularly useful for numerical calculation of the perturbation theory Feynman diagrams with more than one electron Green function. While the Green function represents discrete bound states, and both positive and negative energy continuum states, the Sturmian (bound-state-like) form for the pseudoeigenfunctions makes it possible to more analytically calculate matrix elements for full photon exchange, reducing numerical problems for high photon frequency. For He-like Fm (Z=100) we calculate the perturbation theory equivalent of the Dirac-Fock-Breit ground-state energy, agreeing well with the Grant code and with the numerical B-spline basis set approach results of Blundell, Mohr, Johnson, and Sapirstein [Phys. Rev. A 48, 2615 (1993)]. Preliminary results on the relativistic and QED correlation are also reported.