We performed the non-local thermodynamic equilibrium (non-LTE) calculations for Ti I-II with the updated model atom that includes quantum-mechanical rate coefficients for inelastic collisions with hydrogen atoms. We have calculated for the first time the rate coefficients for bound-bound transitions in inelastic collisions of titanium atoms and ions with hydrogen atoms and for the charge-exchange processes: Ti I + H <-> Ti II + H- and Ti II + H <-> Ti III + H-. The influence of these data on non-LTE abundance determinations has been tested for the Sun and four metal-poor stars. For Ti I and Ti II, the application of the derived rate coefficients has led to an increase in the departures from LTE and an increase in the titanium abundance compared to that, obtained with approximate formulas for the rate coefficients. In metal-poor stars, we have failed to achieve consistent non-LTE abundances from lines of two ionization stages. The known in the literature discrepancy in the non-LTE abundances from Ti I and Ti II lines in metal-poor stars cannot be solved by improvement of the rates of inelastic processes in collisions with hydrogen atoms in non-LTE calculations with classical model atmospheres.
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