  The mean ionization state (MIS) is a critical property in dense plasma and
warm dense matter research, for example as an input to hydrodynamics
simulations and Monte-Carlo simulations. Unfortunately, however, the best way
to compute the MIS remains an open question. Average-atom (AA) models are
widely-used in this context due to their computational efficiency, but as we
show here, the canonical approach for calculating the MIS in AA models is
typically insufficient. We therefore explore three alternative approaches to
compute the MIS. Firstly, we modify the canonical approach to change the way
electrons are partitioned into bound and free states; secondly, we develop a
novel approach using the electron localization function; finally, we extend a
method which uses the Kubo-Greenwood conductivity to our average-atom model.
Through comparisons with higher-fidelity simulations and experimental data, we
find that any of the three new methods usually out-performs the canonical
approach, with the electron localization function and Kubo-Greenwood methods
showing particular promise.
