Relativistic and QED energy shifts in positronium ion

The leading relativistic and QED corrections to the ground state energy of the three-body system (epe) are calculated numerically using a Hylleraas correlated basis set. The accuracy of the nonrelativistic variational ground state wave function is discussed with respect to the convergence properties at the increase of the basis dimension and to the variance of the energy expectation value. Recent progress in the numerical procedure used to calculate expectation values for products of various physical operators is presented. It is shown that the nonrelativistic ground state energy can be calculated with an accuracy below the level width. The corrections to this energy include the lowest order Breit interaction, the vacuum polarization potential, one and two photon exchange contributions, the annihilation interaction, and spin-spin contact terms. The relativistic effects and the residual interactions considered here decrease the one electron binding energy from the nonrelativistic value of 0.012 005 070 232 980 10(3) a.u. to 0.011 981 051 246(2) a.u..