  Reliably interpreting spectra from electron-ionized cosmic plasmas requires
accurate ionization balance calculations for the plasma in question. However,
much of the atomic data needed for these calculations have not been generated
using modern theoretical methods and are often highly suspect. This translates
directly into the reliability of the collisional ionization equilibrium (CIE)
calculations. We make use of state-of-the-art calculations of dielectronic
recombination (DR) rate coefficients for the hydrogenic through Na-like ions of
all elements from He up to and including Zn. We also make use of
state-of-the-art radiative recombination (RR) rate coefficient calculations for
the bare through Na-like ions of all elements from H through to Zn. Here we
present improved CIE calculations for temperatures from $10^4$ to $10^9$ K
using our data and the recommended electron impact ionization data of
\citet{Mazz98a} for elements up to and including Ni and Mazzotta (private
communication) for Cu and Zn. DR and RR data for ionization stages that have
not been updated are also taken from these two additional sources. We compare
our calculated fractional ionic abundances using these data with those
presented by Mazzotta et al. for all elements from H to Ni. The differences in
peak fractional abundance are up to 60%. We also compare with the fractional
ionic abundances for Mg, Si, S, Ar, Ca, Fe, and Ni derived from the modern DR
calculations of \citet{Gu03a,Gu04a} for the H-like through Na-like ions, and
the RR calculations of \citet{Gu03b} for the bare through F-like ions. These
results are in better agreement with our work, with differences in peak
fractional abundance of less than 10%.
