  The Hitomi results on the Perseus cluster lead to improvements in our
knowledge of atomic physics which are crucial for the precise diagnostic of hot
astrophysical plasma observed with high-resolution X-ray spectrometers.
However, modeling uncertainties remain, both within but especially beyond
Hitomi's spectral window. A major challenge in spectral modeling is the Fe-L
spectrum, which is basically a complex assembly of n>2 to n=2 transitions of Fe
ions in different ionization states, affected by a range of atomic processes
such as collisional excitation, resonant excitation, radiative recombination,
dielectronic recombination, and innershell ionization. In this paper we perform
a large-scale theoretical calculation on each of the processes with the
flexible atomic code (FAC), focusing on ions of Fe XVII to Fe XXIV that form
the main body of the Fe-L complex. The new data are found to be consistent
within 20% with the recent individual R-matrix calculations for the main Fe-L
lines. By further testing the new FAC calculations with the high-quality RGS
data from 15 elliptical galaxies and galaxy clusters, we note that the new
model gives systematically better fits than the current SPEX v3.04 code, and
the mean Fe abundance decreases by 12%, while the O/Fe ratio increases by 16%
compared with the results from the current code. Comparing the FAC fit results
to those with the R-matrix calculations, we find a temperature-dependent
discrepancy of up to ~10% on the Fe abundance between the two theoretical
models. Further dedicated tests with both observed spectra and targeted
laboratory measurements are needed to resolve the discrepancies, and
ultimately, to get the atomic data ready for the next high-resolution X-ray
spectroscopy mission.
