On the orbital picture of shape resonances using Feynman–Dyson amplitudes from different decouplings of the dilated electron propagator

Abstract

The orbital picture of shape resonances is investigated by examining the radial charge density distributions calculated from resonant Feynman–Dyson amplitudes for the 2P shape resonances in e-Be, e-Mg, and e-Ca scattering using the zeroth (bivariational self-consistent field), second order and the diagonal two particle one hole-Tamm–Dancoff approximation 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 accumulation of the electron density near the target for optimal value of the complex scaling parameter. The nodal pattern of the radial distributions differs from that expected for the lowest unoccupied p orbitals but their dominant contribution to the charge density distribution is clearly seen. A study of the difference between the radial densities obtained from various decoupling schemes highlights the role of correlation and relaxation in the characterization of these resonances. The role of coordinate space span of the primitive Gaussian-type orbital basis in characterization of these resonances is discussed.