On the basis of the multi-configuration Dirac–Fock method and the density matrix theory treatment of photoionization (PI) dynamics, a systematic investigation for 4d inner-shell PI of exemplary Ba atom and Ba-like Nd⁴⁺, Gd⁸⁺ and Yb¹⁴⁺ ions is performed. Starting from the general framework of the relativistic, the relaxation effects are considered by using a set of relaxed one-electron orbitals in solving the coupled Dirac equations. Our results uncover for the first time that the relaxation effects, arising from the overlap integrals between orbitals of the initial state and the relaxed final state, may play a paramount role in determining the magnetic sublevel cross sections, the photoelectron angular-distribution asymmetry parameters, and the fluorescence polarizations of the subsequent x-ray radiation, particularly for neutral atoms close to the threshold regime. Yet the importance of inclusion of the orbital relaxation weakens as the incoming photon energy and/or the degree of atom ionization increases. The nature of these influences is explored, which allows us to get more insight on the physical process and mechanism involved. Our results are consistent with those obtained by the experiments and other theoretical predictions.

基于多构狄拉克-福克方法和密度矩阵理论处理光电离（PI）动力学，系统地研究了示例性Ba原子和Ba样Nd ⁴⁺，Gd ^8+的4 d内壳PI和Yb ¹⁴⁺离子被执行。从相对论的一般框架开始，在求解耦合狄拉克方程时，通过使用一组松弛的单电子轨道来考虑松弛效应。我们的结果首次发现，由初始状态和松弛最终状态的轨道之间的重叠积分引起的弛豫效应可能在确定磁子能级横截面，光电子角分布不对称参数，以及随后的X射线辐射的荧光偏振，特别是对于接近阈值范围的中性原子。然而，随着入射光子能量和/或原子电离度的增加，包含轨道弛豫的重要性减弱。探索了这些影响的性质，这使我们可以更深入地了解所涉及的物理过程和机制。我们的结果与通过实验和其他理论预测获得的结果一致。