Quantum-defect theory for ion-atom interactions

We present a quantum-defect theory\footnote{B. Gao, Phys. Rev. A \textbf{78}, 012702 (2008).} (QDT) for ion-atom systems that provides a systematic understanding of ion-atom interaction over a wide range of energies that includes the cold and ultracold regime. Ion-atom bound spectrum, ion-atom scattering at ultracold temperatures including ultracold shape resonances and quantum reflection and tunnelling, can all be understood systematically within the QDT framework. We will give a flavor of the theory, with an emphasis on the universal spectra for ion-atom systems up to $l=10$.