The Effective Two-Particle Interaction of Cold Atoms as Derived from Bragg Scattering

We study the dynamic structure function of ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We compare our result with the Bragg-scattering measurements in Rb-85 by Papp et al. (Phys. Rev. Lett. 101:135301, 2008) and show that these experiments set very strict limits to the shape of the effective two-particle interaction ruling out the contact and hard spheres potentials. Using the Feshbach resonance approximation we derive the effective interaction, which turns out to be very similar to the soft spheres potential in momentum space. At large scattering lengths the interaction becomes universal and could be directly measured by Bragg scattering. We also discuss the experimental conditions needed for the appearance of the maxon-roton structure in the excitation spectrum and finally show that when the scattering length becomes larger than 2000 Bohr radii the uniform gas phase undergoes a phase transition into the density wave state.