The stability of Hartree-Fock solutions and of collective motion

Abstract It is proved that the stability of the Hartree-Fock ground state against any small deformation, preserving the single particle nature of the wave function, ensures the stability of collective motions in the random phase approximation and vice versa. Therefore, if a collective motion has a finite life time, the H.F. ground state is necessarily unstable against the deformation generated by the corresponding collective mode. As an illustration, an infinite system of particles interacting by means of a δ-function potential is considered and it is shown that the stability condition for the H.F. ground state is in fact identical to that for the collective motion.