Treatment of Be<SUP>+</SUP> (1s<SUP>-1</SUP>)<SUP>2</SUP>S auger resonance with different decouplings of the dilated electron propagator

The diagonal 2ph-TDA and quasiparticle decouplings of the dilated electron propagator (based on an underlying bi-variational SCF) are utilized to calculate energy and width of the Be+(1s -1)2S Auger resonance for the first time. Comparison with experimental and other theoretical results reveals that the renormalized infinite order diagonal 2ph-TDA decoupling seems to offer a less balanced approach to the treatment of resonances than the second-order decoupling. The diagonal quasiparticle approximation to the self energy is seen to offer an effective and economic alternative to the non-diagonal propagator calculations

Treatment of molecular resonances using the bi-orthogonal dilated electron propagator with application to the <SUP>2</SUP>II<SUB>g</SUB> shape resonance in e-N<SUB>2</SUB> scattering

Preliminary results from the first application of the bi-orthogonal dilated electron propagator to the treatment of molecular resonances are presented for the energy and the width of the 2IIg shape resonance in e-N2 scattering. The corresponding resonant Feynman-Dyson amplitudes (FDAS) are plotted to get a quantitative affirmation of the topology of the lowest unoccupied molecular orbital (LUMO) for N2. It is shown that a plot of the resonant FDAS offer new insights into the role of correlation in the formation and decay of molecular shape resonances

Lowest unoccupied molecular orbital as the resonant orbital. An investigation using the bi-variational self-consistent field method

The bi-variational self-consistent field equations are solved to isolate the resonant orbitals for the CO and C2H4 molecules. These orbitals offer some correlation between the shape resonances in e-molecule scattering and the LUMO of the target molecule. The resonant orbital on the real line is shown to have the attributes of the LUMO for each system, and for the optimal complex scaling parameter, the resonant orbital displays the expected distortions due to meta-stable electron attachment. The results indicate that the bi-variational SCF may be employed in the unmasking and characterization of LUMOs and molecular shape resonances

Characterization of shape and auger resonances using the dilated one electron propagator method

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The two-particle one hole-Tamm-Dancoff approximation (2ph-TDA) decoupling of the dilated electron propagator with application to <SUP>2</SUP>P shape resonances in e-Be, e-Mg, and e-Ca scattering

Formulas for the renormalized full two-particle one hole-Tamm-Dancoff approximation (2ph-TDA) decoupling of the dilated biorthogonal electron propagator based on complex scaled bivariational self-consistent-field (SCF) procedure are derived and the diagonal 2ph-TDA approximation is implemented for the first time. The 2P shape resonances in e-Be, e-Mg, and e-Ca scattering are characterized using the diagonal 2ph-TDA, the second-order and the zeroth-order (bivariational SCF) approximations to the dilated electron propagator. A comparative investigation of these different decouplings reveals that although the resonance energies and widths depend on the level of correlation employed, greater correlation need not lead to sharper resonances