Pseudospin symmetry in resonant states and its dependence on the shape of potential

Abstract

The complex momentum representation method is used to explore the single particle resonances in nuclei. The energies, widths, and wavefunctions are obtained by solving the Dirac equation with a Woods-Saxon potential, in which the parameters are determined from the RMF calculations for 132Sn. The pseudospin symmetry is investigated for the resonant states in comparison with bound states. Approximate degeneracy is shown in the energies, widths, and wavefunctions between the pseudospin doublets including the resonant and bound states. The influence of the potential shape on the pseudospin symmetry is checked. The quality of pseudospin symmetry is shown to be dependent of the parameters, which is explained in terms of the change of potential with these parameters. The energy and width splittings between the pseudospin doublets are sensitive to the potential parameters, which is clarified by the change of the derivative of potential with r. Moreover, the pseudospin splitting in the wavefunctions and its dependence on potential shape are analyzed. The wave function splitting between the pseudospin doublets is quantitatively obtained in the momentum space for the resonant states because they are local and square integrable. Considering that a real nuclear field is similar to a Woods-Saxon potential, the change of the parameters in Woods-Saxon potential can reflect the change of nuclear field from stable nuclei to drop-line nuclei. Therefore, the present researches are helpful to understand the level structure of the weakly bound nuclei and their exotic properties.