How the collisions of a laser-cooled neutral atom with a trapped ion can be described analytically instead of by brute-force close-coupling: the long-range r^-4 polarization potential admits exact solutions in terms of Mathieu functions, and a frame transformation between the asymptotic hyperfine basis and the short-range singlet/triplet molecular basis compresses all short-range physics into just three parameters -- the singlet and triplet s-wave scattering lengths and the C4 dispersion coefficient. A student learns how quantum-defect functions stay analytic across channel thresholds, how an angular-momentum-dependent correction to the short-range phase extends the description to high partial waves and mK temperatures, and how the resulting model predicts bound-state spectra, magnetic Feshbach resonances and radiative charge-transfer rates.
This 2011 arxiv paper develops a theoretical framework for ultracold atom-ion collisions using multichannel quantum-defect theory. It covers inelastic scattering through charge-transfer processes and…