A Griffin-Hill-Wheeler version of the Hartree-Fock (GHW-HF) equations is presented and applied to the He and Be atoms using both Slater and Gaussian orbitals. The kernels are evaluated analytically and the GHW-HF equations are solved by iteration. The integration for the generator coordinate is obtained by discretisation emphasizing the continuous character of the GHW formulation. The results with the Slater Is orbital for He reach the H F limit. When Gaussians are employed the results are better than published H F calculations with these orbitals.
A recently developed [Phys. Rev. A 79, 042707 (2009)] impact parameter coupled pseudostate approximation (CP) is applied to calculate triple differential cross sections for single ionization of He by C 6+ , Au 24+ , and Au 53+ projectiles at impact energies of 100 and 2 MeV/amu for C 6+ and 3.6 MeV/amu for Au 24+ and Au 53+ . For C 6+ , satisfactory, but not perfect, agreement is found with experimental measurements in coplanar geometry, but there is substantial disagreement with data taken in a perpendicular plane geometry. The CP calculations firmly contradict a projectile-nucleus interaction model which has been used to support the perpendicular plane measurements. For Au 24+ and Au 53+ , there is a complete lack of accord with the available experiments. However, for Au 24+ the theoretical position appears to be quite firm with clear indications of convergence in the CP approximation and very good agreement between CP and the completely different three-distorted-waves eikonal-initial-state (3DW-EIS) approximation. The situation for Au 53+ is different. At the momentum transfers at which the measurements were made, there are doubts about the convergence of the CP approximation and a factor of 2 difference between the CP and 3DW-EIS predictions. The discord between theory and experiment is even greater with the experiment giving cross sections a factor of 10 larger than the theory. A study of the convergence of the CP approximation shows that it improves rapidly with reducing momentum transfer. As a consequence, lower-order cross sections than the triple are quite well converged and present an opportunity for a more reliable test of the experiment.
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