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A rigorous evaluation of the two-photon exchange corrections to the hyperfinestructure in lithiumlike heavy ions is presented. As a result, the theoreticalaccuracy of the specific difference between the hyperfine splitting values ofH- and Li-like Bi ions is significantly improved. This opens a possibility forthe stringent test of the many-electron QED effects on a few percent level inthe strongest electromagnetic field presently available in experiments.

Test of many-electron QED effects in the hyperfine splitting of heavy high-Z ions