X-ray Thomson scattering for partially ionized plasmas including the effect of bound levels

X-ray Thomson scattering is being developed as a method to measure the temperature, electron density, and ionization state of high energy density plasmas such as those used in inertial confinement fusion. Most experiments are currently done at large laser facilities that can create bright X-ray sources, however the advent of the X-ray free electron laser (X-FEL) provides a new bright source to use in these experiments. One challenge with X-ray Thomson scattering experiments is understanding how to model the scattering for partially ionized plasmas in order to include the contributions of the bound electrons in the scattered intensity. In this work we take the existing models of Thomson scattering that include elastic ion-ion scattering and the electron-electron plasmon scattering and add the contribution of the bound electrons in the partially ionized plasmas. We validated our model by analyzing existing beryllium experimental data. We then consider several higher Z materials such as Cr and predict the existence of additional peaks in the scattering spectrum that requires new computational tools to understand. We also show examples of experiments in CH and Al that have bound contributions that change the shape of the scattered spectra.