UVES observations of QSO 0000-2620: molecular hydrogen abundance in the damped Ly alpha system at z(abs)=3.3901

We have discovered molecular hydrogen in a fourth quasar damped Ly alpha sy stem thereafter DLA). The UVES spectrograph on the 8.2m ESO Kueyen telescop e has allowed the detection of H-2 in gas with low metallicity, Z/Z. simila r or equal to 10(-2) and high neutral hydrogen column density, N(HI) simila r or equal to 2.6 x 10(21) cm(-2), at redshift z(abs) = 3.3901 toward QSO 0 000-2620. The measured Hz fractional abundance of f(H-2) similar or equal t o 4 x 10(-8) is lower than a typical value for Galactic interstellar clouds of high IV(H I) column density by a factor of (2 - 3) x 10(6). Since H-2 m olecules are formed efficiently on dust grains, it implies that the dust co ndensation in this DLA is negligible, and hence the abundances derived from metal absorption lines are the actual ones. The obtained f(H-2) value lead s to an estimate of the dust number density of [n(d)](DLA) similar to 10(-3 ) [n(d)](ISM), which is consistent with the dust-to-gas ratio (k) over tild e less than or equal to 1.6 x 10(-3) derived independently from the [Cr/Zn] and [Fe/Zn] ratios.