Context :

Aims : If NGC 6397 contains a large fraction of “ second generation ” stars ( > 70 % according to recent analysis ) , the helium abundance of its stars might also be affected , show some star-to-star variation , and be larger than the standard Big Bang abundance Y \sim 0.24 .
Can we derive constraints on this issue from the analysis of the main sequence width and from its luminosity function ?

Methods : We build up new models for the turnoff masses and the main sequence down to the hydrogen burning minimum mass , adopting two versions of an updated equation of state ( EOS ) including the OPAL EOS .
Models consider different initial helium and CNO abundances to cover the range of possible variations between the first and second generation stars .
We compare the models with the observational main sequence .
We also make simulations of the theoretical luminosity functions , for different choices of the mass function and of the mixture of first and second generation stars , and compare them with the observed luminosity function , by means of the Kolmogorov Smirnov –KS– test .

Results : The study of the widht of the main sequence at different interval of magnitude is consistent with the hypothesis that both generations are present in the cluster .
If the CNO increase suggested by spectroscopic observation is taken into account the small helium spread of the main sequence in NGC 6397 implies a substantial helium uniformity ( \Delta Y \sim 0.02 ) between first and second generation stars .
The possible spread in helium doubles if an even larger increase of CNO is considered .
The luminosity function is in any case well consistent with the observed data .

Conclusions :