Quantisation rule for highly excited vibrational states of H +2

Alexander Kaiser, Tim Oliver Muller, Harald Friedrich

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5 Scopus citations


We analyse the influence of the attractive tail of the p-H two-body potential on the energy progression of the near-threshold rotationless bound states of the H+2 molecular ion. For the 1sρg configuration we study different definitions of the reference potential describing the potential tail. In each case, the scattering length consistent with the energies of the highly excited vibrational states, as calculated by Hilico et al. [Eur. Phys. J. D 12, 449 (2000)], is found to lie in the range between -30.5 and -31 au. In the 2pρu configuration, for which there is an extremely weakly bound v=1 vibrational state [Carbonell et al., Europhys. Lett. 64, 316 (2003)], we obtain a scattering length near 762.8 au. In contrast to previously conveyed impressions, the weakly bound v = 1 state can be satisfactorily described as the excited state in a distant shallow potential well of the p-H two-body potential, provided that a sufficient number of terms is included in the representation of the large-distance behaviour of this potential.

Original languageEnglish
Pages (from-to)878-887
Number of pages10
JournalMolecular Physics
Issue number7
StatePublished - 2013


  • H molecular ion
  • Long-range interaction
  • Near-threshold quantization
  • Scattering length
  • Weakly bound states


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