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

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.