ON THE ORBITAL PICTURE OF SHAPE RESONANCES USING FEYNMAN-DYSON AMPLITUDES FROM DIFFERENT DECOUPLINGS OF THE DILATED ELECTRON PROPAGATOR

The orbital picture of shape resonances is investigated by examining t he radial charge density distributions calculated from resonant Feynma n-Dyson amplitudes for the P-2 Shape resonances in e-Be, e-Mg, and e-C a scattering using the zeroth (bivariational self-consistent field), s econd order and the diagonal two particle one hole-Tamm-Dancoff approx imation decouplings of the dilated electron, propagator. A comparison between the radial density distributions from the highest occupied and the resonant orbital/Feynman-Dyson amplitude(s) reveals an accumulati on of the electron density near the target for optimal value of the co mplex scaling parameter. The nodal pattern of the radial distributions differs from that expected for the lowest unoccupied p orbitals but t heir dominant contribution to the charge density distribution is clear ly seen. A study of the difference between the radial densities obtain ed from various decoupling schemes highlights the role of correlation and relaxation in the characterization of these resonances. The role o f coordinate space span of the primitive Gaussian-type orbital basis i n characterization of these resonances is discussed.