Context :

Aims : We discuss the importance of pure hydrogen white dwarf atmosphere models with Ly- \alpha far red wing opacity in the analysis of the white dwarf cooling sequence of the globular cluster NGC 6397 .

Methods : Our recently improved atmosphere models account for the previously missing opacity from the Ly- \alpha hydrogen line broadened by collisions of the absorbing hydrogen atoms with molecular and atomic hydrogen .
These models are the first that well reproduce the UV colors and spectral energy distributions of cool white dwarfs with T _ { eff } < 6000 K observed in the Galactic Disk .

Results : Fitting the observed F 814 W magnitude and F 606 W - F 814 W color we obtained a value for the true distance modulus , \mu = 12.00 \pm 0.02 , that is in agreement with recent analyses .
We show that the stars at the end of the cooling sequence appear to be \sim 160 K cooler when models that account for Ly- \alpha opacity are used .
This indicates that the age of NGC 6397 derived from the white dwarf cooling sequence using atmosphere models that do not include the correct Ly- \alpha opacity is underestimated by \sim 0.5 Gyr .

Conclusions : Our analysis shows that it is essential to use white dwarf atmosphere models with Ly- \alpha opacity for precise dating of old stellar populations from white dwarf cooling sequences .