SINGLE-PARTICLE CONDENSATE AND PAIR THEORY OF A HOMOGENEOUS BOSON SYSTEM

A canonical transformation which takes into account both pair correlations and the single-particle condensate is made on the full Hamiltonian for a system of interacting bosons, and the quasi-particle interactions are neglected. The theories of Bogoliubov, Valatin and Butler, Brueckner and Sawada, and Etters can be obtained as special cases of the theory under certain approximations which are critically examined. A delta function potential which describes a soft spherically symmetric shell around a particle is used to reduce the complicated coupled integral equations to coupled equations for parameters. The formula for the quasi-particle energy is used to fit the experimental excitation spectrum, and good agreement in both the phonon and roton regimes is obtained with three parameters. An effective mass approximation is made to derive the empirical formula used by Larsson and Otnes to fit their neutron scattering data. © 1968.