Analytic descriptions of two atoms in a trap and around a magnetic Feshbach resonance

We present an analytic description of two atoms in a trap and around a magnetic Feshbach resonance. It is achieved by combining a multiscale quantum-defect theory for two atoms in a symmetric harmonic trap\footnote{Y. Chen and B. Gao, Phys. Rev. A \textbf{75}, 053601 (2007).}, with a new analytic description of ultracold atomic interactions around a magnetic Feshbach resonance. The theory is applicable to both broad and narrow resonances, or anything in between, and is applicable to Feshbach resonances of arbitrary $l$. It will be illustrated for sample alkali-metal resonances of experimental interest.