Resonance energies, strengths, cross sections and linear polarization of x-ray dielectronic satellite lines for resonant recombination processes of Au69+ - Au65+ ions

Energy levels, radiative transition rates, autoionization rates, resonance strengths, and state resolved cross sections associated with the $\Delta n=1$ ($2s$, $2p$ $\to 3l$) resonant electronic recombination processes in Ne- to Si-like gold ions (Au${}^{69+}$ - Au${}^{65+}$) have been systematically calculated in the isolated resonance approximation using the Flexible Atomic Code based on the relativistic configuration interaction method. The calculations include not only the dominant dielectronic recombination but also higher-order trielectronic and quadruelectronic recombination processes. The calculated energies show excellent agreement with available experimental and theoretical values, with deviation within 0.32%. Additionally, the resonance energies and resonance strengths for prominent resonances align well with existing theoretical data. Using density matrix formalism, we have also calculated the degree of linear polarization for x-ray dielectronic satellite lines produced by the dominant LMM and LMN resonant electronic recombination processes. Further, the differential cross section for Au${}^{69+}$ - Au${}^{65+}$ ions are discussed and employed to simulate and identify EBIT experimental spectra. These results are expected to be used in the diagnosing high-temperature L-shell gold plasmas and of fusion plasmas in particular.