Evaluation of the two-photon exchange graphs for the ${2p}_{1/2}-2s$ transition in Li-like ions

We present ab initio calculations of the complete gauge invariant set of the two-photon exchange graphs for the ${2p}_{1/2}-2s$ transition energy in Li-like high-$Z$ ions. The evaluation is carried out to all orders in $Z\alpha$ in the range $Z=20\mathrm{}–100.$ Results are compared with calculations based on relativistic many-body perturbation theory. All presently available contributions to the ${2p}_{1/2}-2s$ transition energy are collected. The resulting theoretical predictions are compared with experimental data.