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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 85Rb 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.

We have studied the scaling of the interaction in Bose-Einstein condensates of ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We find that the effective interaction in the metastable, open channel, gaseous phase scales well with the scattering length in the range analyzed. Based on this we show that for increasing scattering lengths, or equivalently increasing densities, the system becomes less correlated, and that at large scattering lengths Bragg scattering experiments can directly measure the effective two-body potential in momentum space. This work is motivated by the recent Bragg-scattering measurements in 85Rb by Papp et al. [Phys. Rev. Lett. 101, 135301 (2008)], where the results in the line shifts show clear deviations from the simple contact interaction. We show that those results are well described by a soft spheres potential with parameters chosen to scale in scattering length units. So far the resolution in the experiments does not reveal details on the frequency dependence in the dynamic structure function S(k,ω) and we show that the Feynman spectrum determines the measured line shifts. We also construct the effective atom-atom interaction from two coupled channels, open and closed, assuming that the Feshbach resonance dominates the closed channel. The resonance energy and the scattering length a of the system are tunable by magnetic fields. We derive the T-matrix of such a system and use renormalization to calculate the bound state energy as a function of the magnetic field and make comparison with available experiments. The s-wave phase shifts determine the local, effective open-channel interaction, but if no scaling is used in the cut-off parameters of the renormalization the phase shift resembles more and more the ones obtained from the contact interaction with increasing scattering length. This leads to clear deviations from the measured line shift experiments.