Gravitational Tensor-Monopole Moment of Hydrogen Atom To Order $\mathcal{O}(\alpha )$

Abstract

We calculate the gravitational tensor-monopole moment of the momentum-current density $T^{ij}$ in the ground state of the hydrogen atom to order $\mathcal{O}(\alpha )$ in quantum electrodynamics (QED). The result is \begin{align} \tau_H/\tau_0 - 1 = \frac{4\alpha}{3\pi}\left(\ln\alpha^2-0.028\right) \nonumber \end{align} where ${\tau }_0={\hslash }^2/4m_e$ is the leading-order moment. The physics of the next-to-leading-order correction is similar to that of the famous Lamb shift for energy levels.

Comments: 22 pages, 9 figures. Typos corrected from v1