Abstract
Context. Rigorous modeling of the $\ion{Ba}{ii}$ ${\lambda}4554$ formation is potentially interesting since this strongly polarized line forms in the solar chromosphere where the magnetic field is not very well known. Aims. We investigate the role of isotropic collisions with neutral hydrogen in the formation of the polarized $\ion{Ba}{ii}$ ${\lambda}4554$ line and, thus, in the determination of the magnetic field. Methods. Multipole relaxation and transfer rates of the d- and p-states of $\ion{Ba}{ii}$ by isotropic collisions with neutral hydrogen are calculated. We consider a plane-parallel layer of $\ion{Ba}{ii}$ that is situated at the low chromosphere and that is anisotropically illuminated from below, which produces linear polarization in the ${\lambda}4554$ line by scattering processes. To compute that polarization, we solve the statistical equilibrium equations for $\ion{Ba}{ii}$ levels including collisions, radiation, and magnetic-field effects. Results. Variation laws of the relaxation and transfer rates with hydrogen number density nH and temperature were deduced. The polarization of the ${\lambda}4554$ line is clearly affected by isotropic collisions with neutral hydrogen, although the collisional depolarization of its upper level $^2{\rm P}_{3/2}$ is negligible. This is because the alignment of the metastable levels $^2{\rm D}_{3/2}$ and $^2{\rm D}_{5/2}$ of the $\ion{Ba}{ii}$ are vulnerable to collisions. At the height of formation of the ${\lambda}4554$ line where $n_{\rm H} \sim 2 \times 10^{14}$ cm-3, we find that neglecting the collisions induces ~25% inaccuracy in the calculation of the polarization and ~35% inaccuracy on microturbulent magnetic field determination. Conclusions. The polarization of the ${\lambda}4554$ line decreases due to collisions with hydrogen atoms. In addition, during scattering processes collisions could change the frequency of the $\ion{Ba}{ii}$ photons. To quantitatively study this line, one should deal with the problem of development of general theory treating partial redistribution of frequencies and including transfer and relaxation rates by collisions for a multilevel atom with hyperfine structure.