Context : Barium is a key element in constraining the evolution of the ( not well understood ) r-process in the first galactic stars and currently the Ba abundances in these very metal-poor stars were mostly measured under the Local Thermodynamical Equilibrium ( LTE ) assumption , which may lead in general to an underestimation of Ba .

Aims : We present here determinations of the barium abundance taking into account the non-LTE ( NLTE ) effects in a sample of extremely metal-poor stars ( EMP stars ) : 6 turnoff stars and 35 giants .

Methods : The NLTE profiles of the three unblended Ba ii lines ( 4554 Ã , 5853 Ã , 6496 Ã ) have been computed .
The computations were made with a modified version of the MULTI code , applied to an atomic model of the Ba atom with 31 levels of Ba i , 101 levels of Ba ii , and compared to the observations .

Results : The ratios of the NLTE abundances of barium relative to Fe are slightly shifted towards the solar ratio .
In the plot of [ Ba/Fe ] versus [ Fe/H ] , the slope of the regression line is slightly reduced as is the scatter .
In the interval -3.3 < [ Fe / H ] < -2.6 , [ Ba/Fe ] decreases with a slope of about 1.4 and a scatter close to 0.44 .
For [ Fe / H ] < -3.3 the number of stars is not sufficient to decide whether [ Ba/Fe ] keeps decreasing ( and then CD-38:245 should be considered as a peculiar ” barium-rich star ” ) or if a plateau is reached as soon as [ Ba / Fe ] \approx - 1 .
In both cases the scatter remains quite large , larger than what can be accounted for by the measurement and determination errors , suggesting the influence of a complex process of Ba production , and/or inefficient mixing in the early Galaxy .

Conclusions :