Unusual bound state of H₂⁺

The H2+ molecular ion has been studied over the years using various techniques, and in some unusual regimes it continues to display remarkable properties. One of the most dramatic predictions by Ref.[1] is the existence of a first excited state in the 2pσu potential with total orbital angular momentum, L=0. This state is extremely weakly bound, with a binding energy of 1.09 x 10-9 a.u. relative to the dissociation threshold, which correlates with a huge proton-hydrogen scattering length of about 750 Bohr radii. We explore adiabatic representations [2] to study the physics of ungerade states very close to the dissociation threshold, neglecting spin-orbit and hyperfine coupling and relativistic effects.

[1] J. Carbonell et al 2003 EPL 64 316

[2] B. D. Esry and H. R. Sadeghpour, Phys. Rev. A 60, 3604 (1999)