  The extended quasiparticle picture is adapted to non-Fermi systems by
suggesting a Pad\'e approximation which interpolates between the known small
scattering-rate expansion and the deviation from the Fermi energy. The first
two energy-weighted sum rules are shown to be fulfilled independent of the
interpolating function for any selfenergy. For various models of
one-dimensional Fermions scattering with impurities the quality of the Pad\'e
approximation for the spectral function is demonstrated and the reduced density
matrix or momentum distribution is reproduced not possessing a jump at the
Fermi energy. Though the two-fold expansion is necessary to realize the
spectral function and reduced density, the extended quasiparticle approximation
itself is sufficient for the description of transport properties due to
cancellation of divergent terms under integration. The T-matrix approximation
leads to the delay time as the time two particles spend in a correlated state.
This contributes to the reduced density matrix and to an additional part in the
conductivity which is presented at zero and finite temperatures. Besides a
localization at certain impurity concentrations, the conductivity shows a
maximum at small temperatures interpreted as onset of superconducting behaviour
triggered by impurities. The Tan contact reveals the same universal behaviour
as known from electron-electron scattering.
