Multichannel quantum-defect theory for ultracold atom-ion collisions

TL;DR

This paper introduces an analytical multichannel quantum-defect theory for ultracold atom-ion collisions, simplifying complex interactions into three key parameters and improving accuracy for higher partial waves, aiding the understanding of resonances and charge transfer.

Contribution

It presents a novel analytical model based on quantum-defect formalism for ultracold atom-ion interactions, incorporating corrections for higher partial waves and enabling efficient predictions of resonances and collision processes.

Findings

Accurately describes atom-ion interactions with three parameters.

Improves quantum-defect model for higher order partial waves.

Analyzes bound states, charge transfer, and Feshbach resonances.

Abstract

We develop an analytical model for ultracold atom-ion collisions using the multichannel quantum-defect formalism. The model is based on the analytical solutions of the r^-4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of the atom-ion interaction in the ultracold domain in terms of three parameters only: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce corrections to the scattering lengths that improve the accuracy of our quantum-defect model for higher order partial waves, a particularly important result for an accurate description of shape and Feshbach resonances at finite temperature. The theory is applied to the system composed of a 40Ca+ ion and a Na atom, and compared to numerical coupled-channel calculations carried out using ab initio potentials. For this particular system, we investigate the spectrum of bound states, the rate of charge-transfer processes, and the collision rates in the presence of magnetic Feshbach resonances at zero and finite temperature.