The ultraviolet convergence of the electromagnetic correction to the ground-state energy of hydrogen

Temporal behavior and quantum Zeno time of an excited state of the hydrogen atom

“…which are the Fermi "Golden Rule" (yielding the lifetime τ E = γ −1 ≃ 1.595 · 10 −9 s) and the second order correction to the level energy E 2 . Notice that ∆E is not the Lamb shift, but only the shift of the 2P level due to its interaction with the ground state [23,17]. Observe that for hydrogen-like atoms of nuclear charge Z, τ E ∝ (χω 0 ) −1 scales like Z −4 , so that the ratio τ Z /τ E has the favorable scaling Z 2 .…”