The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient $C_6(2S;1S)$ describing the interaction of metastable atomic hydrogen ($2S$ state) with a ground-state hydrogen atom is resolved. In the the van der Waals range $a_0\ll R\ll a_0/\alpha$, where $a_0=\hslash /\alpha mc$ is the Bohr radius and $\alpha$ is the fine-structure constant, one finds the symmetry-dependent result $E_{2S;1S}\left(R\right)\approx (-176.75\pm 27.98)E_h{(a_0/R)}^6$ ($E_h$ denotes the Hartree energy). In the Casimir-Polder range $a_0/\alpha \ll R\ll \hslash c/\mathcal{L}$, where $\mathcal{L}\equiv E\left(2S_{1/2}\right)-E\left(2P_{1/2}\right)$ is the Lamb shift energy, one finds $E_{2S;1S}\left(R\right)\approx (-121.50\pm 46.61)E_h{(a_0/R)}^6$. In the the Lamb shift range $R\gg \hslash c/\mathcal{L}$, we find an oscillatory tail with a negligible interaction energy below ${10}^{-36}\mathrm{Hz}$. Dirac-$\delta$ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction or, expressed differently, the shift of the hydrogen $2S$ hyperfine frequency due to interactions with neighboring $1S$ atoms. The $2S$ hyperfine frequency has recently been measured very accurately in atomic beam experiments.

• Received 26 September 2016

DOI:https://doi.org/10.1103/PhysRevA.95.022703