Influence of Collisions with Hydrogen on Titanium Abundance Determinations in Cool Stars

The possibility of solving the problem of a discrepancy in the non-LTE abundances from Ti I and Ti II lines in metal-poor stars is investigated by applying accurate data to take into account the collisions with hydrogen atoms. For this purpose, 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 following charge-exchange processes: Ti I \(+\) H \(\leftrightarrow\) Ti II \(+\) H\({}^{-}\) and Ti II \(+\) H \(\leftrightarrow\) 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 what is obtained using approximate formulas to calculate the rate coefficients. In metal-poor stars we have failed to reconcile the non-LTE abundances from lines of two ionization stages. The problem known in the literature cannot be solved only based on an improvement of the rates of collisions with hydrogen atoms in non-LTE calculations with classical model atmospheres.