Ionization balance for optically thin plasmas: Rate coefficients for all atoms and ions of the elements H to Ni

We present in this paper new and updated calculations of the ionization equilibrium for all the elements from H to Ni. We collected for these elements all the data available in the literature for the ionization and radiative plus dielectronic recombination rates. In particular, the dielectronic rates have been fitted with a single formula and the related coefficients are tabulated. Our results are compared with previous works.