Quasiparticle Random Phase Approximation with inclusion of the Pauli Exclusion Principle

Limitations of the Quasiparticle Random Phase Approximation (QRPA) are studied within an exactly solvable model, with a two body interaction of Fermi type. A special attention is paid to the violation of the Pauli exclusion principle (PEP) in solving the QRPA equation. A comparison of the exact solution, obtained by the diagonalization of a schematic nuclear Hamiltonian and those obtained within the standard QRPA, the renormalized QRPA, the QRPA with pertubative treatment of the PEP and the QRPA with exact consideration of the PEP, is presented. The agreement quality is judged in terms of the quasiparticle number operator matrix elements in the ground state and in the first excited states, of the beta transition amplitudes, of the Ikeda sum rule and of the nuclear matrix element for the double beta decay. We have found that restoring the PEP, the QRPA solutions are considerably stabilized and a better agreement with the exact solution is obtained.