Collisions near threshold in atomic and molecular physics

TLDR

We review current topics in electronic, atomic, and molecular scattering near thresholds. Using phase‑space arguments, quantum‑defect and semiclassical theories, the authors analyze how Coulomb, dipolar, and dispersion potentials, external fields, and many‑body breakup processes modify the Wigner law and produce diverse threshold behaviors. The authors highlight that hyperspherical coordinate methods are central to elucidating threshold laws, including those in low dimensions, and illustrate their application to specific collision processes.

Abstract

We review topics of current interest in the physics of electronic, atomic and molecular scattering in the vicinity of thresholds. Starting from phase space arguments, we discuss the modifications of the Wigner law that are required to deal with scattering by Coulomb, dipolar and dispersion potentials, as well as aspects of threshold behaviour observed in ultracold atomic collisions. We employ the tools of quantum defect and semiclassical theories to bring out the rich variety of threshold behaviours. The discussion is then turned to recent progress in understanding threshold behaviour of many-body break-ups into both charged and neutral species, including both Wannier double ionization and three-body recombination in ultracold gases. We emphasize the dominant role that hyperspherical coordinate methods have played in understanding these problems. We assess the effects of external fields on scattering, and the corresponding modification of phase space that alters the Wigner law. Threshold laws in low dimensions and examples of their applications to specific collision processes are discussed.