  We explore the zero-temperature behavior of an assembly of bosons interacting
through a zero-range, attractive potential. Because the two-body interaction
admits a bound state, the many-body model is best described by a Hamiltonian
that includes the coupling between atomic and molecular components. Due to the
positive scattering length, the low-density collection is expected to remain
stable against collapse despite the attraction between particles. Although a
variational many-body analysis indicates a collapsing solution with only a
molecular component to its condensate at low density, the expected atomic
condensate solution can be obtained if the chemical potential is allowed to be
complex valued. In addition to revealing two discrete eigenfrequencies
associated with the molecular case, an expansion in small oscillations
quantifies the imaginary part of the chemical potential as proportional to a
coherent decay rate of the atomic condensate into a continuum of collective
phonon excitations about the collapsing lower state.
