We performed the non-local thermodynamic equilibrium ( non-LTE , NLTE ) calculations for Ca i-ii with the updated model atom that includes new quantum-mechanical rate coefficients for Ca i + H i collisions from two recent studies and investigated the accuracy of calcium abundance determinations using the Sun , Procyon , and five metal-poor ( MP , -2.6 \leq [ Fe/H ] \leq - 1.3 ) stars with well-determined stellar parameters .
Including H i collisions substantially reduces over-ionisation of Ca i in the line formation layers compared with the case of pure electronic collisions and thus the NLTE effects on abundances derived from Ca i lines .
We show that both collisional recipes lead to very similar NLTE results .
As for Ca ii , the classical Drawinian rates scaled by S _ { H } = 0.1 are still applied .
When using the subordinate lines of Ca i and the high-excitation lines of Ca ii , NLTE provides the smaller line-to-line scatter compared with the LTE case for each star .
For Procyon , NLTE removes a steep trend with line strength among strong Ca i lines seen in LTE and leads to consistent [ Ca/H ] abundances from the two ionisation stages .
In the MP stars , the NLTE abundance from Ca ii 8498 Å agrees well with the abundance from the Ca i subordinate lines , in contrast to LTE , where the abundance difference grows towards lower metallicity and reaches 0.46 dex in BD -13 ^ { \circ } 3442 ( [ Fe/H ] = -2.62 ) .
NLTE largely removes abundance discrepancies between the high-excitation lines of Ca ii and Ca ii 8498 Å obtained for our four [ Fe/H ] < -2 stars under the LTE assumption .
We investigated the formation of the Ca i resonance line in the [ Fe/H ] < -2 stars .
When the calcium abundance varies between [ Ca/H ] \simeq - 1.8 and -2.3 , photon loss in the resonance line itself in the uppermost atmospheric layers drives the strengthening of the line core compared with the LTE case , and this effect prevails over the weakening of the line wings , resulting in negative NLTE abundance correction and underestimation of the abundance derived from Ca i 4226 Å compared with that from the subordinate lines , by 0.08 to 0.32 dex .
This problem may be related to the use of classical homogeneous ( 1D ) model atmospheres .
The situation is improved when the calcium abundance decreases and the Ca i 4226 Å line formation depths are shifted into deep atmospheric layers that are dominated by over-ionisation of Ca i .
However , the departures from LTE are still underestimated for Ca i 4226 Å at [ Ca/H ] \simeq - 4.4 ( HE 0557-4840 ) .
Consistent NLTE abundances from the Ca i resonance line and the Ca ii lines are found for HE 0107-5240 and HE 1327-2326 with [ Ca/H ] \leq - 5 .
Thus , the Ca i /Ca ii ionisation equilibrium method can successfully be applied to determine surface gravities of [ Ca/H ] \precsim - 5 stars .
We provide the NLTE abundance corrections for 28 lines of Ca i in a grid of model atmospheres with 5000 K \leq T _ { eff } \leq 6500 K , 2.5 \leq log g \leq 4.5 , –4 \leq [ Fe/H ] \leq 0 , which is suitable for abundance analysis of FGK-type dwarfs and subgiants .