Linear polarization of x rays emitted in radiative recombination into the $K$ and $L$ shells of Kr, Xe, Bi, and U ions

Recently, the polarization measurement of $L$-shell radiative recombination $\left(L\text{−}\mathrm{RR}\right)$ x rays was performed on the Tokyo-EBIT [N. Numadate et al., Phys. Rev. A 105, 023109 (2022)], and the reported theoretical result performed by the flexible atomic code (FAC) was higher than the experimental value. We present joint theoretical investigations on the linear polarization of x rays emitted from the RR into Kr, Xe, Bi, and U ions by two distinct theoretical approaches, i.e., the present relativistic calculations and the revised FAC using the density matrix formalism, in which the relativistic and multipole effects are fully considered. In addition, the energy and atomic number $Z$ dependences of $L$-RR x-ray polarization are further investigated. Our results are in good agreement with experimental values for $K$ shells and are closer to those for $L$ shells than previous calculations. However, deviations still exist between the theoretical calculations and experimental results for $L$ shells. It is found that the effect of the configuration interaction and the finite nuclear size on the polarization of $L$-RR x rays is not substantial. More theories and experiments are required to explain these deviations.