Pauli resonance states in light nuclei: How they appear and how they can be eliminated

A systematic analysis of parameters and properties of the Pauli resonance states is performed for light nuclei ^6Li, ^7Li, ^8Be, ^9Be, and ^10B, which are treated as two-cluster systems. The Pauli resonance states are redundant solutions of the resonating group method. They appear when one tries to use a more advanced description of the internal structure of interacting clusters. Our calculations are performed in the standard and advanced versions of the resonating group method. The standard version employs wave functions of the many-particle oscillator shell model to describe the internal motion of nucleons within each cluster. The advanced version is based on a three-cluster resonating group method. As in the standard version, the internal wave functions of three clusters are approximated by wave functions of the many-particle oscillator shell model. However, in the advanced version, a pair of clusters can form a bound state and then the third cluster is considered to interact with such two clusters, being in such the bound state. It is found that the Pauli resonance states in nuclei under consideration are observed at energies between 11 and 46 MeV, and their widths vary from 8 keV to 6. 7 MeV. The analysis of the wave functions of Pauli resonance states and matrix elements of the norm kernel allowed us to formulate an effective method for eliminating Pauli resonance states. It is demonstrated that this method effectively eliminates all determined the Pauli resonance states.