Large-scale level-by-level calculations have been systematically performed to obtain the $L$-shell resonant electronic recombination cross sections of ${\mathrm{Fe}}^{15+}$ ions, using the relativistic configuration interaction method considering the complex electronic correlations, the Breit and QED corrections. The higher-order electron correlation effects between resonances associated with the double- and triple-excited channels are found to be very important, which reduced the recombination cross sections by nearly a factor of 2. The high-$n$ ($n\ge 6$) quasidegenerate Rydberg states contribute to the recombination spectra with resonant energies above 714.32 eV; the inclusion of core excitation ${\left(2s2p\right)}^{7}3l^2$ ($l$ = $s, p$, and $d$) autoionizing states is crucial to achieving accurate radiative branching ratios and cross sections, which are consequently reduced by nearly a factor of 1.5. The calculated results show excellent agreement with the available high-precision experimental measurements at heavy-ion test storage ring TSR. Based on this, the resonant transfer excitation (RTE) cross sections of Na-like ${\mathrm{Fe}}^{15+}$ ions incident on ${\mathrm{H}}_2$ molecules are obtained using the impulse approximation. It is found that the trielectronic excitation has a significant effect on the RTE cross sections, with the contribution being about $17.88\%$. It is expected that the present study will provide valuable insights into the spectral simulation of astrophysical and fusion plasmas.

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• Autoionization & Auger processes
• Electron correlation calculations for atoms & ions
• Electronic structure of atoms & molecules
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions
• Atomic systems