Context : Iron plays a crucial role in studies of late-type stars .
In their atmospheres , neutral iron is the minority species and lines of Fe i are subject to the departures from LTE .
In contrast , one believes that LTE is a realistic approximation for Fe ii lines .
The main source of the uncertainties in the non-local thermodynamic equilibrium ( non-LTE = NLTE ) calculations for cool atmospheres is a treatment of inelastic collisions with hydrogen atoms .

Aims : We investigate the effect of Fe i + H i and Fe ii + H i collisions and their different treatment on the Fe i /Fe ii ionisation equilibrium and iron abundance determinations for Galactic halo benchmark stars HD 84937 , HD 122563 , and HD 140283 and a sample of 38 very metal-poor ( VMP ) giants in the dwarf galaxies with well known distances .

Methods : We perform the NLTE calculations for Fe i - Fe ii with applying quantum-mechanical rate coefficients for collisions with H i from Barklem ( 2018 , B18 ) , Yakovleva , Belyaev , and Kraemer ( 2018 , YBK18 ) , and Yakovleva , Belyaev , and Kraemer ( 2019 , YBK19 ) .

Results : We find that collisions with H i serve as efficient thermalisation processes for Fe ii , such that the NLTE abundance corrections for Fe ii lines do not exceed 0.02 dex , in absolute value , at [ Fe/H ] \gtrsim - 3 and reach +0.06 dex at [ Fe/H ] \sim - 4 .
For a given star , different treatments of Fe i + H i collisions by B18 and YBK18 lead to similar average NLTE abundances from the Fe i lines , although there exist discrepancies in the NLTE abundance corrections for individual lines .
With using quantum-mechanical collisional data and the Gaia based surface gravity , we obtain consistent abundances from the two ionisation stages , Fe i and Fe ii , for a red giant HD 122563 .
For a turn-off star HD 84937 and a subgiant HD 140283 , we analyse the iron lines in the visible and the ultra-violet ( UV , 1968 to 2990 Å ) range .
For either Fe i or Fe ii , abundances from the visible and UV lines are found to be consistent in each star .
The NLTE abundances from the two ionisation stages agree within 0.10 dex , when using the YBK18 data , and 0.13 dex in case of B18 .
The Fe i /Fe ii ionisation equilibrium is achieved for each star of our stellar sample in the dwarf galaxies , with the exception of stars at [ Fe/H ] \lesssim - 3.7 .

Conclusions :