Energy-momentum tensor of a hydrogen atom: stability, D-term, and the Lamb shift

TL;DR

This paper investigates the properties of the $D$-term in the energy-momentum tensor of a hydrogen atom, revealing it can be positive or negative in stable systems and identifying a state-dependent logarithmic correction enhancement.

Contribution

It clarifies the sign ambiguity of the $D$-term in stable systems and uncovers a state-dependent logarithmic enhancement of the $ ext{ extalpha}$ correction in hydrogen.

Findings

$D$-term can be positive or negative in stable systems

Logarithmic enhancement of $ ext{ extalpha}$ correction in hydrogen states

Contrast between $D$-term behavior and Lamb shift effects

Abstract

We clarify two issues related to the so-called $D$-term in matrix elements of the energy-momentum tensor. First, we show that in a stable system, the $D$-term can have either sign, contrary to claims that it must be negative. Second, we demonstrate a logarithmic enhancement of the $\mathcal{\alpha}$ correction to the $D$-term in any state of the hydrogen atom. We contrast this enhancement with the Lamb shift where it is present only in S-states.