Partial 4d photoionization cross sections have been calculated for atomic barium including a polarization potential to evaluate the effects of core polarization. Results of three theoretical models are compared: (i) the relativistic random-phase approximation, (ii) the relativistic random-phase approximation modified to include relaxation, and (iii) the relativistic random-phase approximation modified to include relaxation and core polarization. Theory is also compared with photoelectron spectroscopy measurements. The inclusion of both relaxation and polarization effects in the calculations greatly improves agreement with experiment. © 2005 The American Physical Society.