Europhys. Lett.
Volume 64, Number 3, November 2003
Page(s) 316 - 322
Section Atomic and molecular physics
Published online 01 November 2003
DOI: 10.1209/epl/i2003-00176-1
Europhys. Lett., 64 (3) , pp. 316-322 (2003)

A new vibrational level of the $\chem{H_{2}^{+}}$ molecular ion

J. Carbonell1, R. Lazauskas1, D. Delande2, L. Hilico2, 3 and S. Kiliç2, 3

1  Institut des Sciences Nucléaires - 53 Av. des Martyrs, 38026 Grenoble, France
2  Laboratoire Kastler Brossel - Case 74, 4 place Jussieu, 75252 Paris, France
3  Université d'Evry Val d'Essonne - Boulevard F. Mitterrand, 91025 Evry cedex, France

(Received 24 July 2003; accepted 25 August 2003)

A new vibrational level of the $\chem{H_{2}^{+}}$ molecular ion with binding energy of $1.09\times 10^{-9}\un{a.u.}\approx 30\un{neV}$ 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 $2p\sigma_u$ electronic state, antisymmetric with respect to the exchange of the two protons, with orbital angular momentum L=0. It manifests itself as a huge $\chem{p}$- $\chem{H}$ scattering length of $a=750\pm
5$ Bohr radii.

31.15.-p - Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations).
03.65.Nk - Scattering theory.
03.65.Ge - Solutions of wave equations: bound states.

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