We present an alternative organizational scheme for developing effective theories of 2- and 3-body systems that is systematic, accurate, and efficient with controlled errors. To illustrate our approach we consider the bound state and scattering prope
rties of the 2- and 3-nucleon systems. Our approach combines the computational benefits of using separable potentials with the improved convergence properties of potentials evolved with a renormalization group procedure. Long ago Harms showed that any potential can be expanded in a series of separable terms, but this fact is only useful if the expansion can be truncated at low order. The separable expansion provides an attractive organizational scheme that incorporates the two body bound state in the leading term while allowing for systematic corrections thereafter. We show that when applied to a renormalization group-evolved potential, the separable expansion converges rapidly, with accurate results for both 2- and 3-body scattering processes using only two separable terms.
We demonstrate the implications of Efimov physics in the recently measured recombination rate of Cesium-133 atoms. By employing previously calculated results for the energy dependence of the recombination rate of Helium-4 atoms, we obtain three indep
endent scaling functions that are capable of describing the recombination rates over a large energy range for identical bosons with large scattering length. We benchmark these and previously obtained scaling functions by successfully comparing their predictions with full atom-dimer phase shift calculations with artificial Helium-4 potentials yielding large scattering lengths. Exploiting universality, we finally use these functions to determine the 3-body recombination rate of Cesium-133 atoms with large positive scattering length, compare our results to experimental data obtained by the Innsbruck group and find excellent agreement.
