Three-Loop Reducible Radiative Photon Contributions to Lamb Shift and   Hyperfine Splitting
  Corrections of order $\alpha^3(Z\alpha)^5m$ to the Lamb shift and corrections of order $\alpha^3(Z\alpha)E_F$ to hyperfine splitting generated by the insertions of the three-loop one-particle reducible diagrams with radiative photons in the electron line are calculated. The calculations are performed in the Yennie gauge. 
Michael I. Eides (University of Kentucky, USA, and Petersburg Nuclear   Physics Institute, Russia), and Valery A. Shelyuto (...