Abstract
The sum rules for the dynamic liquid-structure factor are investigated for the pair-correlation theory of many-boson systems, which allows a pair of particles to scatter with each other an infinite number of times above the condensate. In the long-wavelength limit the sum rules are not satisfied, and unphysical behavior develops. However, in the short-wavelength limit the sum rules are satisfied, but the energy spectrum for the quasi-particles becomes that for free particles. In the intermediate-wavelength region good agreement is obtained with the experimental single-quasi-particle contribution to the structure factor. The momentum distribution is obtained and shown to behave likek−1 for small momentumk. The pair amplitude is also obtained.
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