Particle-particle interaction is what makes a quantum system, especially a quantum few-body or many-body system, both interesting and difficulty to understand. Properly simplifying the description of interaction is a key component of building a few-body or many-body theory that is both systematic and more amenable to understanding.
For decades, the only systematic and simplified quantum theory for two-body interactions has been the effective-range theory and its derivatives. Partly due to the lack of alternatives, many of the limitations of such theories are often either not well understood, or simply ignored.
In this talk, I hope to briefly discuss the limitations of the effective-range theory for ultracold atomic interactions, and to present a better theory, what we call the QDT expansion [1-3], that is based on the quantum-defect theory (QDT) for interactions. For all cases other than the single-channel s wave interaction or s wave interaction around a broad Feshbach resonance, the QDT expansion is not just a more accurate option, but an absolute necessity for a proper description of atomic interactions.