  We present a generalization of the Hartree-Fock Bogoliubov (HFB) theory in
which the coupling between one and two quasi-particles is taken into
account.This is done by writing the excitation operators as linear combinations
of one and two HFB quasi-particles. The excitation energies and the
quasi-particle amplitudes are given by generalized Bogoliubov equations. The
excitation spectrum has two branches. The first one is a discrete branch which
is gapless and has a phonon character at large wave-length and, contrarily to
HFB, is always stable. This branch is detached from a continuum branch whose
threshold, at fixed total momentum, coincides with the two quasi-particle
threshold of the HFB theory. The gap between these two branches at P=0 is equal
to two times the HFB gap, which then provides for the relevant energy scale. We
also give numerical results for a specific case.
