HYPERSPIN FORMULATION OF A MODIFIED PAIRING TREATMENT OF BOSE FLUID

A modified pairing treatment is developed for handling the N-boson problem with repulsive particle-particle interaction. The nonpairing portion of the many-boson Hamiltonian is eliminated, to first order, by a canonical transformation. The resultant Hamiltonian contains an additional attractive particle-particle interaction, whenever there is a Bose condensation in the k=0 single-particle state. The Bose condensate plays the same role in mediating this interaction that the phonon field does in mediating the attractive interaction between electrons in a superconductor. The strength of the condensate-induced attractive interaction is approximately double that of the direct repulsive interaction. The region of k space over which the attractive interaction operates depends on N0, the number of bosons in the condensate, this region vanishing when N0 does. For convenience, the problem is formulated in terms of hyperspin, in analogy with the isospin treatment of superconductivity. The ground state is characterized by two order parameters Δ1 and Δ2, and an energy Γ (proportional to N0), which can be obtained by solving a set of coupled integral equations. It is shown that there is no gap, at low energies, in the single-particle excitation spectrum. Aside from these single-particle excited states, there are no other collective oscillations. The hyperspin formulation is extended to finite temperatures. There are, however, certain difficulties with this extension. © 1968 The American Physical Society.