  The charged environment within a dense plasma leads to the phenomenon of
ionization potential depression (IPD) for ions embedded in the plasma. Accurate
predictions of the IPD effect are of crucial importance for modeling atomic
processes occurring within dense plasmas. Several theoretical models have been
developed to describe the IPD effect, with frequently discrepant predictions.
Only recently, first experiments on IPD in Al plasma have been performed with
an x-ray free-electron laser (XFEL), where their results were found to be in
disagreement with the widely-used IPD model by Stewart and Pyatt. Another
experiment on Al, at the Orion laser, showed disagreement with the model by
Ecker and Kr\"oll. This controversy shows a strong need for a rigorous and
consistent theoretical approach to calculate the IPD effect. Here we propose
such an approach: a two-step Hartree-Fock-Slater model. With this
parameter-free model we can accurately and efficiently describe the
experimental Al data and validate the accuracy of standard IPD models. Our
model can be a useful tool for calculating atomic properties within dense
plasmas with wide-ranging applications to studies on warm dense matter, shock
experiments, planetary science, inertial confinement fusion and studies of
non-equilibrium plasmas created with XFELs.
