  In the majority of population synthesis calculations of close binary stars,
the common envelope (CE) phase is modeled using a standard prescription based
upon the conservation of energy, known as the alpha prescription. In this
prescription, the orbital separation of the secondary and giant core at the end
of the CE phase is taken to be the orbital separation when the envelope becomes
unbound. However, recent observations of planetary nebulae with binary cores
(BPNe), believed to be the immediate products of CE evolution, indicate orbital
periods that are significantly shorter than predicted by population synthesis
models using the alpha prescription. We argue that unbinding the envelope
provides a necessary, but not sufficient, condition to escape a merger during
CE evolution. The spiral-in of the secondary must also be halted. This requires
the additional dynamical constraint that the frictional torque on the secondary
be reduced to approximately zero. In this paper, we undertake a preliminary
examination of the effect of adding this dynamical constraint in population
synthesis calculations of BPNe. We assume that the frictional torque will be
sufficiently reduced when the secondary enters a region within the giant where
the mass-radius profile is flat. We crudely estimate the location of this
region as a function of the core mass based upon existing stellar models of AGB
stars between 1 and 7 solar masses. We calculate a theoretical orbital period
distribution of BPNe using a population synthesis code that incorporates this
dynamical constraint along with the alpha prescription.
