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Deep high spectral resolution spectroscopy and chemical composition of ionized nebulae

High spectral resolution spectroscopy has proved to be very useful for the advancement of chemical abundances studies in photoionized nebulae, such as H II regions and planetary nebulae (PNe). Classical analyses make use of the intensity of bright collisionally excited lines (CELs), which have a strong dependence on the electron temperature and density. By using high resolution spectrophotometric data, our group has led the determination of chemical abundances of some heavy element ions, mainly O++, O+ and C++ from faint recombination lines (RLs), allowing us to deblend them from other nearby emission lines or sky features. The importance of these lines is that their emissivity depends weakly on the temperature and density structure of the gas. The unresolved issue in this field is that recombination lines of heavy element ions give abundances that are about 2-3 times higher than those derived from CELs -in H II regions- for the same ion, and can even be a factor of 70 times higher in some PNe. This uncertainty puts into doubt the validity of face values of metallicity that we use as representative not only for ionized nebulae in the Local Universe, but also for star-forming dwarf and spiral galaxies at different redshifts. Additionally, high-resolution data can allow us to detect and deblend faint lines of neutron capture element ions in PNe. This information would introduce further restrictions to evolution models of AGBs and would help to quantify the chemical enrichment in s-elements produced by low and intermediate mass stars. The availability of an echelle spectrograph at the E-ELT will be of paramount interest to: (a) extend the studies of heavy element recombination lines to low metallicity objects, (b) to extend abundance determinations of s-elements to planetary nebulae in the extragalactic domain and to bright Galactic and extragalactic H II regions.