Pair excitations in fermi fluids

We present a theory of multi-pair excitations in strongly interacting Fermi systems. Based on an equations-of-motion approach for time-dependent pair correlations it leads to a qualitatively new structure of the density-density response function. Our theory reduces to both, i) the "correlated" random-phase approximation (RPA) for fermions if the two-pair excitations are ignored, and ii) the correlated Brillouin-Wigner perturbation theory for bosons in the appropriate limit. The theory preserves the two first energy-weighted sum rules. A familiar problem of the standard RPA is that its zero-sound mode is energetically much higher than found in experiments. The popular cure of introducing an average effective mass in the Lindhard function violates sum rules and describes the physics incorrectly. We demonstrate that the inclusion of correlated pair excitations gives the correct dispersion. As in ⁴He, a modification of the effective mass is unnecessary also in ³He.