Independent pair approximation for attractive bose condensates

A bosonic analog of the independent pair approximation is developed in the context of a zero-temperature assembly with a positive s-wave scattering length, but attractive interparticle interactions. By preferentially scattering any pair back into the condensate, we account for the effect that all other particles have on the two-body state inside the medium. Instead of the energy of a pair, the poles of the resulting T matrix now give the chemical potential of the system. One pole reveals a collapsing many-body ground state whereas the other gives a complex valued chemical potential, where the imaginary part quantifies the decay rate of the condensate. Both solutions are in close agreement with those obtained in a variational calculation.