Nonperturbative Calculation of the Two-Loop Lamb Shift in Li-Like Ions

A calculation valid to all orders in the nuclear-strength parameter is presented for the two-loop Lamb shift, notably for the two-loop self-energy correction, to the $2p\mathrm{\text{−}}2s$ transition energies in heavy Li-like ions. The calculation removes the largest theoretical uncertainty for these transitions and yields the first experimental identification of two-loop QED effects in the region of the strong binding field.

Figure 1

Two-loop one-electron QED corrections. Gauge-invariant subsets are referred to as SESE (a)–(c), SEVP (d)–(f), VPVP (g)–(i), S(VP)E (k).

Figure 2

Nonperturbative results for the higher-order remainder $G^{\mathrm{h}.\mathrm{o}.}(Z)$ for the differences ${\Delta }_s$ (squares) and ${\Delta }_p$ (dots) and their limiting values at $Z=0$, denoted by the cross for ${\Delta }_s$ and by the diamond for ${\Delta }_p$.