Ionization Correction Factors for Planetary Nebulae: I- Using optical
  spectra
  We compute a large grid of photoionization models that covers a wide range of
physical parameters and is representative of most of the observed PNe. Using
this grid, we derive new formulae for the ionization correction factors (ICFs)
of He, O, N, Ne, S, Ar, Cl, and C. Analytical expressions to estimate the
uncertainties arising from our ICFs are also provided. This should be useful
since these uncertainties are usually not considered when estimating the error
bars in element abundances. Our ICFs are valid over a variety of assumptions
such as the input metallicities, the spectral energy distribution of the
ionizing source, the gas distribution, or the presence of dust grains. Besides,
the ICFs are adequate both for large aperture observations and for pencil-beam
observations in the central zones of the nebulae. We test our ICFs on a large
sample of observed PNe that extends as far as possible in ionization, central
star temperature, and metallicity, by checking that the Ne/O, S/O, Ar/O, and
Cl/O ratios show no trend with the degree of ionization. Our ICFs lead to
significant differences in the derived abundance ratios as compared with
previous determinations, especially for N/O, Ne/O, and Ar/O.
