A numerical investigation of the doubly excited states of ${\mathrm{H}}_2$ converging to the $\mathrm{H}(n=2)+\mathrm{H}(n^{\prime }=2)$ limit was performed. Special emphasis was put on the accurate description of the range of intermediate internuclear distances in order to correctly connect the short range with the asymptotic van der Waals regime where perturbation theory is applicable. The present nonperturbative calculation extends to internuclear separations $R=200a_0$ and is sufficiently accurate to achieve a connection between the two extreme regimes without any need for an interpolation procedure. The high precision of the ab initio results revealed a long range dipole-quadrupole interaction that had been omitted in two earlier calculations. In addition to revised first-order perturbation theory results the leading second-order term varying as $R^{-6}$ was obtained. The impact of the present findings for cold $\mathrm{H}(n=2)$ collisions is briefly discussed.

• Received 16 November 2006

DOI:https://doi.org/10.1103/PhysRevA.73.062706