Comparison of density-matrix theory and pairing theory

The ground states and the first 2(+) states of O-20 and O-22 are derived using two schemes, one consisting of the Hartree-Fock-Bogoliubov theory (HFB) plus the quasi-paxticle random phase approximation (QRPA) and the other consisting of the stationary solution and the small amplitude limit of the time-dependent density-matrix theory (TDDM). It is found that although the two schemes give similar results for the ground state of O-20, there axe differences between the results obtained with the two methods for the first 2(+) state of O-20 and the ground state of O-22: The first 2(+) state of O-20 derived with TDDM has a larger collectivity, and TDDM induces a long-range correlation in the ground state of O-22, which cannot be obtained with the HFB calculation. The origins of the differences are discussed.