Abstract
We restudy the one-loop correction and two-loop contribution to the blackbody-radiation (BBR) shift. The S-matrix approach and nonrelativistic quantum electrodynamics (NRQED) are adopted in the finite temperature case. The relativistic correction to the one-loop BBR shift has a -order contribution. In the two-loop case, the pure thermal (real) photon part is too tiny to be detected, while the corrections induced by the thermal and virtual mixing diagram are of the order. We calculate the relativistic correction to the one-loop BBR shift in the ground states of hydrogen and ionized helium, which is larger than the leading terms. As the leading term is proportional to , we estimate that these higher-order corrections may be larger than the leading term when the system is a highly ionized (large Z) or cold (small T) one.
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