Since the invention of quantum mechanics, even the simplest example of the collisional breakup of a system of charged particles, e(-) + H --> H(+) + e(-) + e(-) (where e(-) is an electron and H is hydrogen), has resisted solution and is now one of the last unsolved fundamental problems in atomic physics. A complete solution requires calculation of the energies and directions for a final state in which all three particles are moving away from each other. Even with supercomputers, the correct mathematical description of this state has proved difficult to apply. A framework for solving ionization problems in many areas of chemistry and physics is finally provided by a mathematical transformation of the Schrodinger equation that makes the final state tractable, providing the key to a numerical solution of this problem that reveals its full dynamics.

An overview of PURGATORIO, a new implementation of the INFERNO 1 equation of state model, is presented. The new algorithm emphasizes a novel decimation scheme for automatically resolving the structure of the continuum density of states, circumventing limitations of the pseudo-R matrix algorithm previously utilized.

We have carried out a comprehensive theoretical and experimental study of electron scattering from molecular nitrogen at energies below 10.0 eV. In the theoretical component of this project we have generated differential and integral cross sections for elastic scattering and vibrational excitation in converged vibrational close-coupling calculations. In the experiments, we have measured dift'erential cross sections for these processes at scattering angles from 20' to 130 in a crossed-beam experiment at a large number of energies between 0.55 and 10 eV and, in a complementary time-of-Right experiment, total cross sections at energies between 0.08 and 10.0 eV. The measured angular distributions have been extrapolated to 0 and 180 using a procedure based on a nonlinear least-squares fit constrained by known physical properties of the e-Nz scattering matrix; numerical integration of the resulting extrapolated distributions yields integrated cross sections with almost no error beyond that inherent in the measured angular data. We find generally good agreement between the present experimental and theoretical cross section, particularly at energies near the H~r esonance near 2.39 eV. In previous studies of scattering in this region, such comparisons have been made problematical by the difhculty of ascertaining the appropriate theoretical scattering energy. We recommend here a protocol for resolving this problem for both elastic scattering and vibrational excitation.PACS number(s): 34.80.6s

We report on recent developments with the Purgatorio code, a new implementation of Liberman's Inferno model. This fully relativistic average atom code uses phase shift tracking and an efficient refinement scheme to provide an accurate description of continuum states. The resulting equations of state accurately represent the atomic shell-related features which are absent in Thomas-Fermi-based approaches. We discuss various representations of the exchange potential and some of the ambiguities in the choice of the effective charge Z * in average atom models, both of which affect predictions of electrical conductivities and radiative properties.