The higher-order blackbody-radiation shift of atomic energy levels

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 (Z alpha)(2)alpha T(2)m-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 (Za)(2)alpha T-2(2)/morder. 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 T-4/Z(4), 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.