Quasiparticle random phase approximation with the Pauli Exclusion Principle fully fulfilled

The violation of the Pauli Exclusion Principle (PEP) in the framework of th e Quasiparticle Random Phase Approximation is examined within the proton-ne utron monopole Lipkin model. For the first time, the solution of the QRPA e quation including an exact description of the PEP is presented. Restoring t he PEP, the QRPA solution is considerably stabilized and a better agreement with the exact solution is achieved for the energy of the first excited st ate, the ground state expectation value of the quasiparticle number operato r and beta transition amplitudes.