Accuracy issues in spectroscopic modeling of K$_{\alpha}$ emission from M-shell ions in dense plasmas

Although K$_{\alpha}$ emission originates from simple $1s-2p$ transitions, the many-electron ions of mid-$Z$ materials in warm, dense matter conditions introduce significant computational complexity to K$_{\alpha}$ spectroscopic modeling. First, complete models of M-shell ions in dense plasmas are inherently complex since they must include a large number of states with open $3p$ and $3d$ shells. Next, single-temperature models for collisional-radiative kinetics are inadequate since the thermal electrons that control the distribution of charge states in the M shell have insufficient energy to participate in inner-shell processes. Finally, near-solid densities introduce physical effects such as pressure ionization, the formation of quasi-bound states, and line broadening, which are not intrinsically included in the isolated-ion structure calculations used in most spectroscopic models. These issues are explored for K$_{\alpha}$ emission from M-shell Cu using several independent models.