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It is well-known that cold atoms near s-wave Feshbach resonances haveuniversal properties that are insensitive to the short-range details of theinteraction. What is less known is that atoms near higher partial wave Feshbachresonances also have remarkable universal properties. We illustrate this with asingle atom interacting resonantly with two fixed static centers. At a Feshbachresonance point with orbital angular momentum $L\ge1$, we find $2L+1$ shallowbound states whose energies behave like $1/R^{2L+1}$ when the distance $R$between the two centers is large. We then compute corrections to the bindingenergies due to other parameters in the effective range expansions. Forcompleteness we also compute the binding energies near s-wave Feshbachresonances, taking into account the corrections. Afterwards we turn to thebound states at large but finite scattering volumes. For p-wave and higherpartial wave resonances, we derive a simple formula for the energies in termsof a parameter called "proximity parameter". These results are applicable to afree atom interacting resonantly with two atoms that are localized to twolattice sites of an optical lattice, and to one light atom interacting with twoheavy ones in free space. Modifications of the low energy physics due to thelong range Van der Waals potential are also discussed.

Universality in s-wave and higher partial wave Feshbach resonances: an illustration with a single atom near two scattering centers