Analytic description of atomic interaction at ultracold temperatures. II. Scattering around a magnetic Feshbach resonance

Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave l and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary l, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary l, (b) rigorous definitions of “broad” and “narrow” resonances of arbitrary l and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.