Long-range interactions between two $2s$ excited hydrogen atoms

The doubly excited ${}^1{\Sigma }_g^{+}$ and ${}^3{\Sigma }_u^{+}$ states of the ${\mathrm{H}}_2$ molecule converging to the $\mathrm{H}\mathrm{}(n=2\mathrm{})+\mathrm{H}{(n}^{\prime }=2)$ limit have been calculated using explicitly correlated basis functions, giving accurate results out to a nuclear separation sufficiently large to apply asymptotic expansions for the potential energy. The autoionization widths have been obtained using the complex-scaling method. For nuclear separations larger than 22 a.u., asymptotic expressions for the interaction energies have been obtained from perturbation theory.