Threshold Behaviour of Cross-Sections in Atom–Ion Scattering

The scattering process for multi-particle Coulomb systems with initial two-cluster data has been studied in physics, both experimentally and theoretically. In particular, in the collision of a neutral cluster with a charged one (atom–ion scattering), physical pictures suggest that if the neutral sub-system has no static dipole moment, the total cross-sections would be finite. Its mathematical proof is subtle. In [ES], V. Enss and B. Simon put forward several open questions and the sixth one of them is the following