A new vibrational level of the H _ { 2 } ^ { + } molecular ion with binding energy of 1.09 \times 10 ^ { -9 } a.u . \approx 30 neV below the first dissociation limit is predicted , using highly accurate numerical nonrelativistic quantum calculations , which go beyond the Born-Oppenheimer approximation .
It is the first excited vibrational level v = 1 of the 2p \sigma _ { u } 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 \pm 5 Bohr radii .