PARTICLE NUMBER FLUCTUATIONS IN THE QUASI-PARTICLE RANDOM-PHASE-APPROXIMATION AND RENORMALIZED QUASI-PARTICLE RANDOM-PHASE-APPROXIMATION

Particle number fluctuations in the quasiparticle random-phase approxi mation (QRPA) and the renormalized quasiparticle random-phase approxim ation are investigated. A closed expression for the ground state wave function is used, which allows an exact evaluation of the ground state phonon number and correlation function, being valid to any order in t he backward amplitudes. in realistic calculations a sudden increase in the par-tide number fluctuations is found in both approximations when the particle-particle interaction approaches the value at which the Q RPA collapses. This behavior is strongly correlated with the ground st ate quasiparticle content and can be understood as a signature of the phase transition previously found in simpler exactly solvable models.