  The determination of the fractional electron abundance, Xe, in protostellar
cores relies on observations of molecules, such as DCO+, H13CO+ and CO, and on
chemical models to interpret their abundance. Studies of protostellar cores
have revealed significant variations of Xe from core to core within a range
10^-8<Xe<10^-6. The physical origin of these large variations in Xe is not well
understood, unless unlikely variations in the cosmic ray ionization rate or ad
hoc values of metal depletion are assumed. In this work we explore other
potential causes of these variations in Xe, including core age, extinction and
density. We compute numerically the intensity of the radiation field within a
density distribution generated by supersonic turbulence. Taking into account
the lines of sight in all directions, the effective visual extinction in dense
regions is found to be always much lower than the extinction derived from the
column density along a fixed line of sight. Dense cores with volume and column
densities comparable to observed protostellar cores have relatively low
mass-averaged visual extinction, 2mag <= A_V <= 5mag, such that
photo-ionization can sometimes be as important as cosmic ray ionization.
Chemical models, including gas-grain chemistry and time dependent gas depletion
and desorption, are computed for values of visual extinction in the range 2mag
<= A_V <= 6mag, and for a hydrogen gas density of 10^4cm^-3$, typical of
protostellar cores. The models presented here can reproduce some of the
observed variations of ion abundance from core to core as the combined effect
of visual extinction and age variations. The range of electron abundances
predicted by the models is relatively insenstive to density over 10^4 to 10^6
cm^{-3}.
