Random Phase Approximation without Bogoliubov Quasi-particles

A new version of random phase approximation is proposed for low-energy harmonic vibrations in nuclei. The theory is not based on the quasi-particle vacuum of the BCS/HFB ground state, but on the pair condensate determined in Ref. [4]. The current treatment conserves the exact particle number all the time. As a first test the theory is considered in two special cases: the degenerate model (large pairing limit) and the vanished-pairing limit.