O(m alpha^7 ln(alpha)^2) corrections to positronium energy levels

We present a calculation of the O(m alpha^7 ln(alpha)^2) corrections to positronium energy levels. The result is used to estimate the current uncertainty in theoretical predictions of the positronium spectrum.Comment: revtex, 12 pages, result correcte

Recoil Correction to Hydrogen Energy Levels: A Revision

Recent calculations of the order (Z\alpha)^4(m/M)Ry pure recoil correction to hydrogen energy levels are critically revised. The origins of errors made in the previous works are elucidated. In the framework of a successive approach, we obtain the new result for the correction to S levels. It amounts to -16.4 kHz in the ground state and -1.9 kHz in the 2S state.Comment: 15 pages, Latex, no figure