Investigation of the intershell higher order resonant recombination and polarization of X-ray emission of B-like silicon ions

K-shell dielectronic, trielectronic, and quadruelectronic recombination and polarization of X-ray emission have been studied for the highly charged Si⁹⁺ ions in the initial ground state ²P_1/2 and the metastable state ²P_3/2 using the Flexible Atomic Code. It is found that the resonant recombination cross section from the long-lived metastable state is comparable in magnitude with that of the ground state, so it is important for plasma diagnostics. For Si⁹⁺(²P_1/2), trielectronic recombination contributions of nearly 25% to the total resonant recombination strength are predicted, which is less than previous calculations. We compare the degree of linear polarization for the eleven dominant resonant recombination satellite lines from the initial parent Si⁹⁺(²P_1/2) and Si⁹⁺(²P_3/2) ions. For the same X-ray lines, large variations of polarization are found between ²P_1/2 and ²P_3/2, which can be employed to diagnose formation mechanisms of intermediate resonance states and corresponding X-ray lines.