Simplified Model of Liquid Helium

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Abstract
A simplified version of a Bose gas with negative scattering length is studied with a model Hamiltonian similar to that used in the case of repulsive interactions. A new transformation is used which takes into account the attractive interactions in the system, and the ground-state energy is calculated from experimental values of the sound velocity in the system. Real values for the phonon energy spectrum are obtained, and the ratio of the effective mass to ordinary mass is deduced using experimental values of interparticle separation and core radius. A justification for using this modified Hamiltonian is attempted in the Appendix.