Spin polarization effect on linear polarization of photon emission following resonant electron capture of lithiumlike ions

Dielectronic recombination (DR) of highly charged ions with spin-polarized electrons is studied within the framework of density-matrix theory. Special attention is paid to the question of how spin polarization of the recombined electron affects the polarization behavior of the subsequent photon emission. To address this question, while a general density-matrix formalism applicable to any DR process of arbitrary ions is presented, here, it is applied to a particular DR process (i.e., $1{s}^{2}2s\phantom{\rule{0.16em}{0ex}}{J}_{i}=1/2+\ensuremath{\varepsilon}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}1s2{s}^{2}2{p}_{1/2}\phantom{\rule{0.16em}{0ex}}{J}_{d}=1\ensuremath{\rightarrow}1{s}^{2}2{s}^{2}\phantom{\rule{0.16em}{0ex}}{J}_{f}=0+\ensuremath{\gamma}$) of lithiumlike ${\mathrm{I}}^{50+}$ ions as an example. For this particular process, detailed calculations are carried out for different spin polarization states of the recombined electron by utilizing the multiconfigurational Dirac-Hartree-Fock method. It is found that the spin polarization of the recombined electron hardly affects the linear polarization ${P}_{1}$ (i.e., the first Stokes parameter) of the photon emission, whereas the polarization ${P}_{2}$ (i.e., the second Stokes parameter) depends strongly on the spin polarization. In addition, owing to big differences in the magnitudes of ${P}_{1}$ and ${P}_{2}$, a large polarization tilt angle $\ensuremath{\chi}$ is obtained that is remarkably affected by the spin polarization, especially for the forward and backward photon emission. These polarization behaviors are found to be rather similar to the results obtained in radiative recombination of highly charged ions with polarized electrons [Maiorova et al., Phys. Rev. A 107, 042814 (2023)] and can be readily observed using modern x-ray polarimeters. Based on the strong dependences obtained, we suggest that accurate measurements of the polarization behaviors can be applied to diagnosing the spin polarization state of electron beams, which is more feasible and promising than the case of radiative recombination [Maiorova et al., Phys. Rev. A 107, 042814 (2023)] owing to the resonance nature of DR processes.