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Context. 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. Aims. 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. Methods. We observed the C102 α (6109.901 MHz) and C109 α (5011.420 MHz) carbon radio recombination lines (CRRLs) using the Effelsberg 100 m 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 μm-[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. Results. We detect the CRRLs toward four positions, where their velocity ( v LSR  ≈ 11 km s −1 ) and widths ( σ v  ≈ 1 km s −1 ) confirms that they trace the envelope of the ISF. Toward two positions we detect the CRRLs, and the 158 μm-[CII] and [ 13 CII] lines with a signal-to-noise ratio ≥5, and we find n e −  = 0.65 ± 0.12 cm −3 and 0.95 ± 0.02 cm −3 , which corresponds to a gas density n H  ≈ 5 × 10 3 cm −3 and a thermal pressure of p th  ≈ 4 × 10 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 × 10 −6 . Conclusions. 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). This suggests that electron collisional excitation does not play a significant role in setting the excitation of HCN(1–0) toward the region studied, as it is responsible for only ≈10% of the observed emission.