Recoil Corrections of Order $(Z\alpha)^6(m/M)m$ to the Hydrogen Energy   Levels Revisited
  The recoil correction of order $(Z\alpha)^6(m/M)m$ to the hydrogen energy levels is recalculated and a discrepancy existing in the literature on this correction for the 1S energy level, is resolved. An analytic expression for the correction to the S-levels with arbitrary principal quantum number is obtained. 
Michael I. Eides (Petersburg Nuclear Physics Institute, Russia, and   Pennsylvania State University, USA) and Howard Grotch ...