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We calculate the contribution from the two-photon exchange on the neutron tothe hyperfine splitting of S energy levels. We update the value of the neutronZemach radius, estimate total recoil and polarizability corrections. Theresulting two-photon exchange in electronic atoms exceeds by an order ofmagnitude the leading Zemach term and has different sign both in electronic andmuonic hydrogen.

Two-photon exchange on neutron and the hyperfine splitting