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We present an analytic model to calculate the atomic scattering length near aFeshbach resonance from data on the molecular binding energy. Our approachconsiders finite-range square-well potentials and can be applied near broad,narrow, or even overlapping Feshbach resonances. We test our model on Cs$_2$Feshbach molecules. We measure the binding energy using magnetic-fieldmodulation spectroscopy in a range where one broad and two narrow Feshbachresonances overlap. From the data we accurately determine the Cs atomicscattering length and the positions and widths of two particular resonances.

Determination of atomic scattering lengths from measurements of molecular binding energies near Feshbach resonances