Quantum correction to the Langevin cross section in resonant-exchange processes

Resonant-exchange scattering plays a key role in many-body dynamics and transport phenomena (such as spin, charge, or excitation diffusion) at low and moderate temperatures. Recent investigations have shown that the locking of phase shifts is central to resonant-exchange scattering at low energies. Moreover, phase-shift locking causes an unexpected behavior, namely the resonant-exchange cross section over a broad range of energies is largely dictated by s-wave scattering, whose influence extends high above the s-wave Wigner regime. Here, we generalize our previous treatment to higher energies and derive an analytical expression for the resonant-exchange cross section which depends on a few parameters and accounts not only for the locking of phase shifts, but also for their gradual unlocking with increased energy. We find good agreement between the computed (fully quantal) cross sections and those obtained with our expression, which we illustrate in great details for the case of resonant charge-transfer in ion-atom collisions. We also apply the treatment to resonant spin and excitation exchange and discuss the limits of applicability of the expression.