  In this paper we consider a spatially flat Friedmann-Robertson-Walker (FRW)
cosmological model whit cosmological constant, containing a stiff fluid and a
classical Dirac field. The proposed cosmological scenario describes the
evolution of effective dark matter and dark energy components reproducing, with
the help of that effective multifluid configuration, the quintessential
behavior. We find the value of the scale factor where the effective dark energy
component crosses the phantom divide. The model we introduce, which can be
considered as a modified $\La$CDM one, is characterized by a set of parameters
which may be constrained by the astrophysical observations available up to
date.
