In this first paper of a series, we report on the use of quasar spectra obtained with the UVES high resolution spectrograph and available through the ESO VLT archive to build the first sample of sub-DLA systems, absorbers with HI column densities > 10^{19} cm^{-2} but lower than the classical definition of damped Ly-alpha systems (DLAs) 2x10^{20} cm^{-2}. A systematic investigation of the properties of these systems and a comparison with those of the DLAs (Paper II of this series; Peroux et al. 2003b) is expected to provide new clues on the association of high column density absorbers with galaxies and on the overall evolution of the neutral hydrogen gas mass and metal content in the Universe. In the spectra of 22 quasars which were found suitable for a sub-DLA search, we identified 12 sub-DLAs and 1 borderline case between the DLA and sub-DLA systems in the redshift interval z = 1.8-4.3. We measured the column densities of HI and up to 16 ions of low-, intermediate- and high-ionization. We further investigated the significance of the ionization corrections in the determination of the chemical abundances from the low-ionization ions in the sub-DLA HI column density range. Using the predictions of different ion ratios as a function of the ionization parameter computed with the CLOUDY software package, we have estimated that with the exception of one case, the ionization corrections to the abundances of 9 systems for which we were able to constrain the ionization parameter, are lower than 0.2 dex for all of the elements except AlII and ZnII down to HI column densities of log N(HI) = 19.3 cm^{-2}. We finally present the first sub-DLA chemical abundance database which contains the abundance measurements of 11 different elements (O, C, Si, N, S, Mg, Al, Fe, Ni, Zn, and Cr).
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