Context :

Aims : We aim at deriving the physical conditions in the neutral gas associated with damped Lyman- \alpha systems using observation and analysis of H _ { 2 } and C i absorptions .

Methods : We obtained a high-resolution VLT-UVES spectrum of the quasar Q 2348 - 011 over a wavelength range covering the metal and molecular absorptions from the log N ( H i ) = 20.50 \pm 0.10 damped Lyman- \alpha system at z _ { abs } = 2.4263 .
We detect H _ { 2 } in this system and measure column densities of H _ { 2 } , C i , C i ^ { * } , C i ^ { ** } , P ii , S ii , Fe ii , Si ii and Ni ii .
From the column density ratios and in particular the relative populations of the H _ { 2 } rotational and C i fine-structure levels , we derive the physical conditions in the gas ( abundances , dust-depletion , particle density , kinetic temperature and ionizing flux ) .

Results : Molecular hydrogen is detected in seven components in the first four rotational levels ( J = 0-3 ) .
Absorption lines of H _ { 2 } J = 4 and 5 rotational levels are detected in four of these components .
This leads to a total molecular fraction of \log f \simeq - 1.69 ^ { +0.37 } _ { -0.58 } .
Fourteen components are needed to reproduce the metal-line profiles .
The overall metallicity is found to be - 0.80 , - 0.60 , - 1.17 , -0.89 , -0.45 \pm 0.10 for , respectively , [ Si/H ] , [ S/H ] , [ Fe/H ] , [ Ni/H ] and [ P/H ] .
We confirm the findings by others that there is a clear correlation between \log N ( Fe ii ) / N ( S ii ) and \log N ( Si ii ) / N ( S ii ) from different components indicative of a dust-depletion pattern .
The dust depletion in the H _ { 2 } components is not large and ranges from \log N ( Fe ii ) / N ( S ii ) = - 0.8 to -0.2 when the most important depletion ( up to \log N ( Fe ii ) / N ( S ii ) = - 1.2 ) occurs in components where H _ { 2 } is not detected .
The gas in H _ { 2 } bearing components is found to be cold but still hotter than similar gas of our Galaxy ( T \sim 140 K instead of typically 70 K ) , dense ( n \sim 50 - 200 cm ^ { -2 } ) , and embedded into a moderate to high UV field , about one to two orders of magnitude higher than in the solar vicinity .
This suggests the gas in H _ { 2 } -bearing DLAs is clumpy , and star-formation probably occurs in the associated object .

Conclusions :