Microscopic theory of interacting excitations in Bose systems

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Abstract
A study of an interacting boson system is presented, which examines the internal consistency and validity of certain microscopic theories. Our formalism is based on density variables and follows closely the work of Bogoliubov and Zubarev, although the general features of the results apply to other approaches as well. First, we employ model potentials to calculate the excitation spectrum, the structure factor, the condensate fraction, and the scattering amplitude for two excitations. The results demonstrate new and stringent limitations of the model-potential approach, and suggest that this type of analysis may yield fortuitous and misleading agreement with experiment when applied to liquid helium. In particular, although the theory yields a good fit to the energy spectrum (in accord with previous work), the scattering amplitude is found to be extremely sensitive to the details of the model, so the potential approach cannot be considered as a reliable basis for calculations of the excitations in superfluid helium. As an alternative, we develop a first-principles theory of helium based only on the liquid structure factor Sk. To lowest order, the latter method gives results qualitatively similar to the strong-coupling calculations. This indicates a need to consider renormalization effects, which are briefly discussed.