An extension of the RPA approach to include both 1p1h x phonon configu
rations and the single-particle continuum in a unified framework has b
een done using the consistent Green-function formalism. The microscopi
c calculations of the giant E1 resonance in Ca-40, 48Ca and Pb-208 hav
e been performed in the 1p1h + 2p2h + continuum approximation develope
d here. A reasonable agreement with experiment, including a descriptio
n of the widths, has been obtained. We underestimate the experimental
width values by 14% for Ca-40, 11% for 48Ca and 4% for Pb-208.