Extraction of phase shifts from ensemble densities for composite system scattering

Abstract

A simple approach for low energy electron scattering by a composite target is presented in which the compound system is described by the ensemble densities and the scattering phase deduced from the quantum defects (QDT). Full calculation of the scattering wave functions is not needed. The ensemble density functional describes the interacting many-fermion bound system, in terms of the first-order densities which represent the ground and several excited state configurations, provided an accurate correlation energy is available. In particular, each configuration is composed of the common set of base core orbitals and single valence orbitals. The valence orbital energies can then be used to deduce the QDT, which are then extrapolated above the scattering threshold energy to obtain the phase shift. Alternatively, the slowly varying single particle potential that generates the orbitals can directly be adopted in the extrapolation; this can lead to a genuine ensemble density approach for scattering states. The inelastic scattering is also studied, which requires the density with one hole orbital in the core set. The importance of the dynamic correlations, including the long-range polarization, is stressed.