Accurate calculations of weakly bound state energy and scattering length near magnetically tuned Feshbach resonance using the separable potential method.

We present a theoretical model for investigating the magnetically tuned Feshbach resonance (MTFR) of alkali metal atoms using the separable potential method (SPM). We discuss the relationship and difference between the SPM and the asymptotic bound state model. To demonstrate the validity of the SPM, we use it to calculate the weakly bound state energy and magnetically tuned scattering length for the Li-K, Li, and Li systems with narrow and broad Feshbach resonances. The results of the SPM calculations are in good agreement with those of coupled channel calculations and with experimental measurements for all three systems. The SPM, by simplifying the calculation of the two-body MTFR, is expected to simplify numerical computations for three-atom collisions in a magnetic field and the Feshbach-optimized photoassociation process.