Corrections to Hyperfine Splitting and Lamb Shift Induced by the Overlapping Two-Loop Electron Self-Energy Insertion in the Electron Line

Contributions to HFS and to the Lamb shift intervals of order $\alpha^2(Z\alpha)^5$ induced by the graph with the two-loop overlapping electron self-energy diagram inserted in the electron line are considered. Explicit expression for the overlapping two-loop self-energy diagram in the Fried-Yennie gauge is obtained. Contributions both to HFS and Lamb shift induced by the diagram containing such subgraph are calculated.