Phase-shift locking and unlocking in resonant-exchange scattering

Resonant exchange is an important process in many-body dynamics and transport phenomena (such as spin, charge, or excitation diffusion). The underlying dynamics is described by the resonant exchange cross section. We show that the s-wave scattering, generally thought to contribute mainly in the ultracold (or Wigner) regime, dictates the overall cross section (and rate coefficient) over a broad range of energies. We derive an analytical expression and explain its applicability high above the Wigner regime. In particular, we demonstrate its relationship to the classical capture (Langevin) cross section and apply it to resonant charge transfer, and explain the large variations found for different isotopes. We explain the behavior through a “locking” and gradual “unlocking” of phase shifts with increasing energy. We illustrate the agreement between our expression and the full quantum mechanical cross section using the case study of Yb ion-atom collisions.