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

TL;DR

This study investigates the adiabatic and post-adiabatic hyperspherical methods to accurately describe the scattering properties of the ungerade H₂⁺ ion, demonstrating minimal nonadiabatic effects and effective modeling of its large scattering length.

Contribution

It introduces an optimal hyperspherical adiabatic framework for the ungerade H₂⁺ system, highlighting the small role of nonadiabatic effects and validating postadiabatic corrections.

Findings

Hyperspherical adiabatic description captures main physics effectively.

Nonadiabatic corrections are small and well-described by postadiabatic theory.

Calculated scattering length aligns with known large value (~750 bohr).

Abstract

While the hydrogen molecular ion is the simplest molecule in nature and very well studied in all of its properties, it remains an interesting system to use for explorations of fundamental questions. One such question treated in this study relates to finding an optimal adiabatic representation of the physics, i.e. the best adiabatic description that minimizes the role of nonadiabatic effects. As a test case explored here in detail, we consider the ungerade symmetry of H$_2^+$, which is known to have a huge scattering length of order 750 bohr radii, and an incredibly weakly bound excited state. We show that a hyperspherical adiabatic description does an excellent job of capturing the main physics. Our calculation yields a competitive scattering length and shows that nonadiabatic corrections are small and can even be adequately captured using the postadiabatic theory of Klar and Fano.