Black-body radiation shift of atomic energy-levels:The $ (Z \alpha)^2\alpha T^2/m $ correction

TL;DR

This paper investigates the next-to-leading order black-body radiation shift in atomic energy levels using NRQED, revealing that certain corrections are more significant than previously thought, especially in multi-electron or cold atoms.

Contribution

It introduces the first analysis of the $ (Z\alpha)^2\alpha T^2/m $ correction to BBR-shift, including quadrupole and two-loop contributions, using NRQED.

Findings

One-loop quadrupole contribution is stronger than previous estimates.

Two-loop thermal photon contribution is negligible.

Next-to-leading order BBR-shift can be comparable to leading order in complex atoms.

Abstract

The next-to-leading order black-body radiation(BBR) shift to atomic energy-levels, namely $ (Z\alpha)^2\alpha T^2/m $ correction, was studied by using the nonrelativistic quantum electrodynamics(NRQED). We also estimate the one-loop contribution of quadrupole and the two-loop contributions of BBR-shift of the thermal(real) photon. These corrections have not been investigated before. The order of magnitude BBR-shift indicates the one-loop contribution of quadrupole is stronger than the previous result. And the two-loop contribution of BBR-shift of the thermal(real) photon is tiny, but this next-to-leading order BBR-shift may be as significant as the leading order in the multi-electron atoms or cold ones.