Abstract
A new vibrational level of the H2+ molecular ion with binding energy of 1.09 × 10−9 a.u. ≈ 30 neV below the first dissociation limit is predicted, using highly accurate numerical non-relativistic quantum calculations, which go beyond the Born-Oppenheimer approximation. It is the first-excited vibrational level v = 1 of the 2pσu electronic state, antisymmetric with respect to the exchange of the two protons, with orbital angular momentum L = 0. It manifests itself as a huge p-H scattering length of a = 750 ± 5 Bohr radii.