We have performed calculations by abandoning the assumption of local thermodynamic equilibrium (within the so-called non-LTE approach) for Al I and Si I with model atmospheres corresponding to stars of spectral types F–G–Kwith differentmetal abundances. To take into account inelastic collisions with hydrogen atoms, for the first time we have applied the cross sections calculated by Belyaev et al. using model approaches within the formalism of the Born–Oppenheimer quantum theory. We show that for Al I non-LTE leads to higher ionization (overionization) than in LTE in the spectral line formation region and to a weakening of spectral lines, which is consistent with earlier non-LTE studies. However, our results, especially for the subordinate lines, differ quantitatively from the results of predecessors. Owing to their large cross sections, the ion-pair production and mutual neutralization processes Al I(nl) + HI(1s) ↔ Al II(3s2) + H− provide a close coupling of highly excited Al I levels with the Al II ground state, which causes the deviations from the equilibrium level population to decrease compared to the calculations where the collisions only with electrons are taken into account. For three moderately metal-deficient dwarf stars, the aluminum abundance has been determined from seven Al I lines in different models of their formation. Under the assumption of LTE and in non-LTE calculations including the collisions only with electrons, the Al I 3961 ˚A resonance line gives a systematically lower abundance than the mean abundance from the subordinate lines, by 0.25–0.45 dex. The difference for each star is removed by taking into account the collisions with hydrogen atoms, and the rms error of the abundance derived from all seven Al I lines decreases by a factor of 1.5–3 compared to the LTE analysis. We have calculated the non- LTE corrections to the abundance for six subordinate Al I lines as a function of the effective temperature (4500 K ≤ Teff ≤ 6500 K), surface gravity (3.0 ≤ log g ≤ 4.5), and metal abundance ([M/H] = 0, −1, −2, and −3). For Si I including the collisions with HI leads to the establishment of equilibrium populations in the spectral line formation region even in hot metal-deficient models and to vanishingly small departures from LTE in spectral lines.
