  In plasmas, electronic states can be well localized bound states or itinerant
free states, or something in between. In self-consistent treatments of plasma
electronic structure such as the average atom model, all states must be
accurately resolved in order to achieve a converged numerical solution. This is
a challenging numerical and algorithmic problem in large part due to the
continuum of free states which is relatively expensive and difficult to resolve
accurately. Siegert states are an appealing alternative. They form a complete
eigenbasis with a purely discrete spectrum while still being equivalent to a
representation in terms of the usual bound states and free states. However,
many of their properties are unintuitive, and it is not obvious that they are
suitable for self-consistent plasma electronic structure calculations. Here it
is demonstrated that Siegert states can be used to accurately solve an average
atom model and offer advantages over the traditional finite difference
approach, including a concrete physical picture of pressure ionization and
continuum resonances.
