Higher order decouplings of the dilated electron propagator with applications to ²PBe^-, ²PMg^- shape and ²SBe⁺ (1s^-1) auger resonances

Abstract

The full third order (Σ³), quasi-particle third order (Σ_q³) and Outer Valence Green's Function decouplings of the bi-orthogonal dilated electron propagator have been implemented for the first time and results from their application to ²PBe^-, ²PMg^- shape and ²SBe⁺ (1s^-1) Auger resonances are presented and compared with energies and widths obtained using the zeroth order (Σ⁰), quasi-particle second order (Σ_q²) and second order (Σ²) decouplings. The energies and widths from third order decoupling for shape resonances are close to those obtained using second order self-energy approximants. The energy and width calculated using the third order decoupling for Auger resonances provide better agreement with experimental results, with the much more economic quasi-particle third order decoupling being just as effective. The differences between FDAs from different decouplings are analyzed to elicit the role of correlation and relaxation in the formation and decay of shape and Auger resonances.