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

Abstract

The one-loop correction and two-loop contribution to black-body radiation (BBR) shift are restudied. The S-matrix approach and nonrelativistic quantum electrodynamics (NRQED) are adopted in finite temperature case. The relativistic correction to one-loop BBR-shift has a (Zα) 2 αT 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 at (Zα) 2 α 2 T 2 /m order. We calculate the relativistic correction to one-loop BBR-shift in the ground state of hydrogen and ionized helium, which is larger than the leading term. As the leading term is proportional to T 4 /Z 4 . We estimate these higher-order corrections may be larger than the leading term, when the system is a highly ionized (large Z) or a cold (small T ) one.

Thermal QED theory for bound states

“…On example of thermal self-energy correction it was established that the regularization procedure suggested in this work gives a physical result. Namely, in opposite, for example, to the results of (Zhou et al, 2017) there are no 'adventitious' contributions besides the Stark shift and BBR induced level width. Latter have a simple analogy with the QM results and 'ordinary' zero vacuum QED case when the real part of one-loop self-energy correction represents the energy shift and the imaginary parts corresponds to the lifetime of atomic level, see (Labzowsky et al, 1993).…”

“…Moreover, the results arising from the one-loop thermal self-energy correction have a clear physics which originally was found within the Quantum Mechanical approach. This circumstance has a most significant conclusion: a) the renormalization or regularization procedure described in section III.C is justified in this case also; b) besides the Stark shift anf level broadening there are no other 'artificial' contributions depending on temperature, see for example (Escobedo andSoto, 2008, 2010;Zhou et al, 2017).…”

“…Recently, the rigorous quantum electrodynamic derivation of the Stark shift and depopulation rates of the atomic energy levels in presence of the blackbody radiation was performed in (Solovyev et al, 2015), where the perfect agreement between QED (in non-relativistic limit) and QM results was also demonstrated. An attempt to evaluate the relativistic correction to the one-loop BBR shift in the ground states of hydrogen and ionized helium was given in (Zhou et al, 2017). Another application of the QED description of thermal effects in atoms was given in (Solovyev et al, 2015) with the use of the 'QED regularization' of the self-energy correction.…”

Analytical expressions of non-relativistic static multipole polarizabilities for hydrogen-like ions*

“…The BBR is isotropic and thus it can be described by the scalar polarizability. Some studies on BBR shifts to atomic energy levels can be found in [11,[14][15][16][17], including relativistic and QED corrections. Here we only focus on the nonrelativistic energy shift due to the BBR, which is given by…”

“…In the nonrelativistic limit, the BBR shift acts as T 4 /Z 4 ; whereas the relativistic correction acts as (ZαT ) 2 . Therefore, the relativistic correction becomes more important for high Z and/or low T [11,17].…”