Fully renormalized quasi-particle random phase approximation, spurious states and ground state correlations

An approach, called fully renormalized QRPA (FR-QRPA), which takes into account the Pauli principle for the ground state correlations (GSC) and fulfills the Ikeda sum rule has recently been developed. Here a new rotational invariant model of the V states is formulated within the FR-QRPA and deformed nuclei Nd-150, (SM)-S-154 and Er-168 are studied. Two different Hamiltonians are used to describe the low-lying excited states (the famous scissors mode). One Hamiltonian is constructed to be rotational invariant and the spurious rotational state is separated by moving its energy to zero. The second Hamiltonian mixes the spurious rotational state with different vibrational states having the same quantum numbers. The GSC measured by the number of quasiparticles in the ground state are studied for the Hamiltonians within the QRPA, R-QRPA and FR-QRPA approaches. The present investigation demonstrates an advantage of the FR-QRPA over the other approaches. Within the rotational invariant FR-QRPA the GSC are stronger than within the R-QRPA by about 20%. The spurious rotational state in the rotational invariant case contributes within the FR-QRPA more than 50% to the total number of quasiparticles in the ground state of the nuclei in question.