  Charge state distributions in hot, dense plasmas are a key ingredient in the
calculation of spectral quantities like the opacity. However, they are
challenging to calculate, as models like Saha-Boltzmann become unreliable for
dense, quantum plasmas. Here we present a new variational model for the charge
state distribution, along with a simple model for the energy of the
configurations that includes the orbital relaxation effect. Comparison with
other methods reveals generally good agreement with average atom based
calculations, the breakdown of the Saha-Boltzmann method, and mixed agreement
with a chemical model. We conclude that the new model gives a relatively
inexpensive, but reasonably high fidelity method of calculating the charge
state distribution in hot dense plasmas, in local thermodynamic equilibrium.
