INFLUENCE OF BOSE-CONDENSATION ON THE EXCITATION SPECTRUM OF LIQUID-HE-4

It is shown that the presence of delta functions in the dynamic struct ure factor S((q) over bar,omega) of a Bose fluid at zero temperature T implies the presence of a Bose-Einstein condensate (BEC). Thus, the d elta function phonon and roton peaks observed in liquid He-4 as T --> 0 imply the presence of a BEC. It is suggested that rotons are density oscillations, which are well defined at wavelengths less than the ave rage interparticle separation in the superfluid, due to the existence of a long range structure in the many particle wave function.