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

TL;DR

This paper derives an analytical quantum correction to the resonant-exchange cross section, accounting for phase-shift locking and unlocking at various energies, improving understanding of low to moderate energy scattering processes.

Contribution

It introduces a generalized analytical expression for the resonant-exchange cross section that includes quantum effects of phase-shift locking and unlocking at higher energies.

Findings

Analytical expression matches quantum calculations well.

Phase-shift locking influences cross section over broad energy ranges.

The model applies to resonant charge-transfer in ion-atom collisions.

Abstract

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 detail for the case of resonant charge-transfer in ion-atom collisions.