On the pairing theory of the bose superfluid

Abstract

In analogy to the BCS theory of superconductivity, a self-consistent pairing theory of the Bose superfluid is developed along lines closely resembling the original Bose pairing model of Valatin and Butler. A new treatment of the zero-wave-vector terms is given which necessitates an attractive part to the interaction in order that a nontrivial solution for the (k-dependent) coherence parameter can exist. It is emphasized that the superfluid phase is best identified with a nonvanishing coherence parameter rather than with the presence of Bose-Einstein condensation, for, in systems with repulsive interactions, condensation can exist in our model without coherence. However, the coherent (superfluid) phase is shown to possess a macroscopic condensation which vanishes at the same temperature,Tλ, that marks the vanishing of coherence. The superfluid spectrum is manifestly gapless and initially linear. Numerical solutions to the self-consistent integral equations atT=0 have been obtained for various pseudopotentials, some of which yield dispersion curves qualitatively resembling helium. The quasi-particle spectrum, condensed fraction, specific heat and sound velocity have been computed as functions of temperature for the complete range 0→Tλ for an attractive Gaussian pseudopotential whilst for more realistic pseudopotentials our numerical techniques were powerful enough only to yield solutions in a range nearT=0 not extending up toTλ. The appropriateness of the model to account for the properties of superfluid helium is discussed and various extensions of our numerical work suggested.