  We present a theoretical analysis of excitation modes in Bose-Einstein
condensates in ultracold alkali-metal gases for large scattering lengths and
momenta where corrections to the mean field approximation become important. We
assume that the effective interaction in the metastable, single channel,
gaseous phase has a well defined Fourier transform that scales with the
scattering length. Based on this we show that for increasing scattering lengths
or equivalently increasing densities the system becomes less correlated and
that at large values of the scattering length Bragg scattering measures
directly the Fourier transform of the effective two-body potential. We
construct model potentials which fit the recently measured line shifts in
$^{85}$Rb by Papp et al. (Phys. Rev. Lett. {\bf 101}, 135301 (2008)), and show
that they fix the low momentum expansion of the effective range function. We
find excellent agreement with the experimental data when the effective range is
$\ll 1$ and the coefficient of the $k^4$-term is $-7.5 \pm 0.5$ in scattering
length units. The resolution in Bragg scattering experiments so far does not
reveal details of the frequency dependence in the dynamic structure function
$S(k,\omega)$ and we show that the Feynman spectrum determines the measured
line shifts. We propose the possibility of a transition to a novel density wave
state.
