Approximated forms of the RII and RIII redistribution matrices are frequently applied to simplify the numerical solution of the radiative transfer problem for polarized radiation, taking partial frequency redistribution (PRD) effects into account. A widely used approximation for RIII is to consider its expression under the assumption of complete frequency redistribution (CRD) in the observer frame (RIII CRD). The adequacy of this approximation for modeling the intensity profiles has been firmly established. By contrast, its suitability for modeling scattering polarization signals has only been analyzed in a few studies, considering simplified settings. In this work, we aim at quantitatively assessing the impact and the range of validity of the RIII CRD approximation in the modeling of scattering polarization. Methods. We first present an analytic comparison between RIII and RIII CRD. We then compare the results of radiative transfer calculations, out of local thermodynamic equilibrium, performed with RIII and RIII CRD in realistic 1D atmospheric models. We focus on the chromospheric Ca i line at 4227 A and on the photospheric Sr i line at 4607 A.

翻译：RII和RIII重分布矩阵的近似形式常被用于简化含部分频率重分布（PRD）效应的偏振辐射传输问题的数值求解。其中，RIII的一种广泛使用的近似是在观测系中假设完全频率重分布（CRD）条件下的表达式（RIII CRD）。该近似对强度谱线轮廓建模的适用性已得到充分验证。相比之下，其在散射偏振信号建模中的适用性仅基于简化设置，在少数研究中得到分析。本研究旨在定量评估RIII CRD近似在散射偏振建模中的影响及有效范围。方法上，我们首先对RIII与RIII CRD进行解析比较，进而对比在真实一维大气模型中，基于非局部热动平衡条件下采用RIII与RIII CRD进行辐射传输计算的结果。重点分析色球层Ca i 4227埃谱线与光球层Sr i 4607埃谱线。