D. Van Neck

Microscopic calculations of Compton scattering on the free proton and light nuclei are presented. For the description of Compton scattering on the proton the conventional K-matrix approach and the ``Dressed K-Matrix'' model are introduced. The latter approach can be used to calculate polarizabilities as well as Compton scattering for photon energies upto 1 GeV since it obeys the symmetry properties which are appropriate in the different energy regions. In particular, crossing symmetry, gauge invariance and unitarity are satisfied. The extent of violation of analyticity (causality) is used as an expansion parameter. Coherent Compton scattering on light nuclei at 200--300 MeV is studied in the impulse approximation and is shown to be a sensitive probe of the in-medium properties of the \Delta -resonance. Modifications of the properties of the \Delta-resonance due to the nuclear medium are accounted for through the self-energy operator of the \Delta. The dominant medium effects such as the Pauli blocking effects in the decay width, effective nucleon mass and particle--hole excitations in the pion propagator are consistently included in nuclear matter.

Green’s function techniques are powerful tools for studying interacting many-fermion systems in a structural and diagrammatical way. The central equation in this method is the Dyson equation which determines, through an approximation for the self-energy, the Green’s function of the system. In a previous paper [J. Chem. Phys. 115, 15 (2001)] a self-consistent solution scheme of the Dyson equation up to second order in the interaction, the Dyson(2) scheme, has been presented for closed-shell atoms. In this context, self-consistency means that the electron propagators appearing in a conserving approximation for the self-energy are the same as the solutions of the Dyson equation, i.e., they are fully dressed. In the present paper this scheme is extended to open-shell atoms. The extension is not trivial, due to the loss of spherical symmetry as a result of the partially occupied shells, but can be simplified by applying an appropriate angular averaging procedure. The scheme is validated by studying the second-row atomic systems B, C, N, O, and F. Results for the total binding energy, ionization energy and single-particle levels are discussed in detail and compared with other computational tools and with experiment. In open-valence-shell atoms a new quantity—the electron affinity—appears which was not relevant in closed-shell atoms. The electron affinities are very sensitive to the treatment of electron correlations, and their theoretical estimate is a stringent test for the adequacy of the applied scheme. The theoretical predictions are in good agreement with experiment. Also, the Dyson(2) scheme confirms the nonexistence of a stable negative ion of N. The overall effect of the self-consistent Dyson(2) scheme with regard to the Dyson(1) (i.e., Hartree–Fock) concept, is a systematic shift of all quantities, bringing them closer to the experimental values. The second-order effects turn out to be indispensable for a reasonable reproduction of the electron affinity. © 2002 American Institute of Physics.