  We explore the zero-temperature statics of an atomic Bose-Einstein condensate
in which a Feshbach resonance creates a coupling to a second condensate
component of quasi-bound molecules. Using a variational procedure to find the
equation of state, the appearance of this binding is manifest in a collapsing
ground state, where only the molecular condensate is present up to some
critical density. Further, an excited state is seen to reproduce the usual
low-density atomic condensate behavior in this system, but the molecular
component is found to produce an underlying decay, quantified by the imaginary
part of the chemical potential. Most importantly, the unique decay rate
dependencies on density ($\sim \rho ^{3/2}$) and on scattering length ($\sim
a^{5/2}$) can be measured in experimental tests of this theory.
