Level shifts, continuum lowering, and the mobility edge in dense plasmas

The many-body problem in a hot dense plasma is treated using the ‘‘effective one-particle’’ description of density-functional theory. Three key ideas emerge, viz., (i) the neutral-pseudoatom (NPA) concept to describe a nucleus plus its electron distribution in the plasma, (ii) the concept of hopping electrons describing the effect of the ion-distribution on the electrons, which are shown to exist as bound, hopping, and free electrons, and (iii) the concept of the mobility edge replacing that of the continuum edge as we go to denser plasmas. The NPA concept shows that the electron-density profile around an ion in a plasma is very similar to that of the isolated neutral atom in a relevant configuration, and explains the absence of large polarization shifts predicted by simple plasma-screening theories. Several models of the ion distribution are used to study level shifts as a function of temperature and density. The change of continuum phase shifts with density is shown to give information about level formation. The appearance of hopping electrons signals the breakdown of Saha theory and the need to evaluate the effective charge ${\mathit{Z}}^{\mathrm{*}}$ of an ion in a dense plasma as a function of the ion distribution. The ion-correlation sphere is shown to be the ‘‘optimal volume’’ that maximizes the number of hopping states in the plasma. The mobility edge for the plasma percolation cluster is calculated and shown to depend on exchange-plus-correlation effects of electrons and ions, a Friedel-sum contribution, and a percolation contribution.