Quantum-defect theory of resonant charge exchange

TL;DR

This paper develops a quantum-defect theory approach for resonant charge exchange in ion-atom systems, enabling accurate predictions across energy ranges with minimal parameters, bypassing complex potential energy surface calculations.

Contribution

It introduces a simplified quantum-defect framework for $-1/R^4$ potentials that accurately models charge exchange using only three experimentally accessible parameters.

Findings

Accurately describes charge exchange over wide energy ranges.

Requires only three parameters: scattering lengths and polarizability.

Links ultracold and higher-temperature interactions.

Abstract

We apply the quantum-defect theory for $-1/R^4$ potential to study the resonant charge exchange process. We show that by taking advantage of the partial-wave-insensitive nature of the formulation, resonant charge exchange of the type of $^1$S+$^2$S can be accurately described over a wide range of energies using only three parameters, such as the \textit{gerade} and the \textit{ungerade} $s$ wave scattering lengths, and the atomic polarizability, even at energies where many partial waves contribute to the cross sections. The parameters can be determined experimentally, without having to rely on accurate potential energy surfaces, of which few exist for ion-atom systems. The theory further relates ultracold interactions to interactions at much higher temperatures.