The ionization fraction in OMC-2 and OMC-3
  The electron density ($n_{e^{-}}$) plays an important role in setting the
chemistry and physics of the interstellar medium. However, measurements of
$n_{e^{-}}$ in neutral clouds have been directly obtained only toward a few
lines of sight or they rely on indirect determinations. We use carbon radio
recombination lines and the far-infrared lines of C$^{+}$ to directly measure
$n_{e^{-}}$ and the gas temperature in the envelope of the integral shaped
filament (ISF) in the Orion A molecular cloud. We observed the C$102\alpha$ and
C$109\alpha$ carbon radio recombination lines (CRRLs) using the Effelsberg 100m
telescope at ~2' resolution toward five positions in OMC-2 and OMC-3. Since the
CRRLs have similar line properties, we averaged them to increase the
signal-to-noise ratio of the spectra. We compared the intensities of the
averaged CRRLs, and the 158 {\mu}m-[CII] and [$^{13}$CII] lines to the
predictions of a homogeneous model for the C$^{+}$/C interface in the envelope
of a molecular cloud and from this comparison we determined the electron
density, temperature and C$^{+}$ column density of the gas. We detect the CRRLs
toward four positions, where their velocity and widths (FWHM 2.3 km s$^{-1}$)
confirms that they trace the envelope of the ISF. Toward two positions we
detect the CRRLs, and the [CII] and [$^{13}$CII] lines with a signal-to-noise
ratio >5, and we find $n_{e^{-}}=0.65\pm0.12$ cm$^{-3}$ and $0.95\pm0.02$
cm$^{-3}$, which corresponds to a gas density $n_{H}\approx5\times10^{3}$
cm$^{-3}$ and a thermal pressure of $p_{th}\approx4\times10^{5}$ K cm$^{-3}$.
We also constrained the ionization fraction in the denser portions of the
molecular cloud using the HCN(1-0) and C$_{2}$H(1-0) lines to
$x(e^{-})<3\times10^{-6}$. The derived electron densities and ionization
fraction imply that $x(e^{-})$ drops by a factor >100 between the C$^{+}$ layer
and the regions probed by HCN(1-0).
