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While the hydrogen molecular ion is the simplest molecule in nature and verywell studied in all of its properties, it remains an interesting system to usefor explorations of fundamental questions. One such question treated in thisstudy relates to finding an optimal adiabatic representation of the physics,i.e. the best adiabatic description that minimizes the role of nonadiabaticeffects. As a test case explored here in detail, we consider the ungeradesymmetry of H$_2^+$, which is known to have a huge scattering length of order750 bohr radii, and an incredibly weakly bound excited state. We show that ahyperspherical adiabatic description does an excellent job of capturing themain physics. Our calculation yields a competitive scattering length and showsthat nonadiabatic corrections are small and can even be adequately capturedusing the postadiabatic theory of Klar and Fano.

Adiabatic and postadiabatic hyperspherical treatment of the huge ungerade proton-hydrogen scattering length