  An analysis is given of particlelike nonlinear bound states in the Newtonian
limit of the coupled Einstein-Dirac system introduced by Finster, Smoller and
Yau. A proof is given of existence of these bound states in the almost
Newtonianian regime, and it is proved that they may be approximated by the
energy minimizing solution of the Newton-Schr\"odinger system obtained by Lieb.
