  Neutral sodium is a minority species in the atmospheres of late-type stars,
and line formation in local thermodynamic equilibrium (LTE) is often a poor
assumption, in particular for strong lines. We present an extensive grid of
non-LTE calculations for several NaI lines in cool stellar atmospheres,
including metal-rich and metal-poor dwarfs and giants. For the first time, we
constructed a Na model atom that incorporates accurate quantum mechanical
calculations for collisional excitation and ionisation by electrons as well as
collisional excitation and charge exchange reactions with neutral hydrogen.
Similar to LiI, the new rates for hydrogen impact excitation do not affect the
statistical equilibrium calculations, while charge exchange reactions have a
small but non-negligible influence. The presented LTE and non-LTE
curves-of-growth can be interpolated to obtain non-LTE abundances and abundance
corrections for arbitrary stellar parameter combinations and line strengths.
The typical corrections for weak lines are -0.1...-0.2dex, whereas saturated
lines may overestimate the abundance in LTE by more than 0.5dex. The non-LTE Na
abundances appear very robust with respect to uncertainties in the input
collisional data.
