Pseudospin Symmetry In Resonant States Research Articles

Pseudospin symmetry in resonant states in deformed nucleus 154Dy

It is known that pseudospin symmetry plays a crucial role in formation of many physical phenomena. By combining the relativistic mean field theory with the complex momentum representation method, the pseudospin symmetry in the single particle resonant states in the deformed nucleus [Formula: see text]Dy is investigated through the energy and width splittings, the quadrupole deformation parameter, the radial density distributions and occupation probabilities of the pseudospin doublets. Near the continuum threshold, the pseudospin symmetry is well reserved in both bound and resonant states. The energy and width splittings of pseudospin doublets in resonant states exhibit correlations with the deformation and quantum numbers. The good pseudospin symmetry is expected with lower pseudo-orbital angular momentum projection [Formula: see text] and the main quantum number N. In general, an increase in deformation tends to weaken the quality of the pseudospin symmetry. The understanding of the evolution of the pseudospin doublets in the resonant states has been deepened by studying the pseudospin symmetry in the deformed nuclei.

Pseudospin symmetry in resonant states in deformed nuclei

Pseudospin symmetry (PSS) plays critical roles in the formation of many physical phenomena, and has been studied extensively from spherical nuclei to deformed nuclei. However, there remains an open question about the PSS in resonant states in deformed systems. For the first time, we investigate the PSS in resonant states in deformed nuclei by solving the Dirac equation in the complex-momentum representation for a potential with quadrupole deformation at the first order obtained from relativistic mean-field (RMF) calculations. Taking 170Yb as an example, we explore the PSS in the single-particle resonant states by examining the energies, widths and the density distribution. Compared with the bound states, the pseudospin splittings between the resonant pseudospin doublets are found to be small, and the radial density distributions of pseudospin doublets look very similar, which indicates that the PSS of resonant states is well reserved in deformed nuclei. Moreover, we have comprehensively studied the dependencies of the PSS on nuclear deformations and the shape of potential, which are helpful to recognize the evolution of resonant pseudospin doublets in weakly-bound deformed nuclei and understand their exotic properties.

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

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.

Isospin asymmetry of the pseudospin symmetry in nuclear resonant states

The role of Coulomb and $ \rho$ potentials in the asymmetry of the neutron and proton pseudospin splittings in nuclear resonant states are investigated. To this end, energies and widths of single-particle resonant states in the Sn isotopes are determined within the framework of relativistic mean-field theory combined with a method based on the analytic continuation of the coupling-constant method. We study the effect of these potentials on the energy splittings and widths splittings of the neutron and proton pseudospin partners in correlation with the mass number. Compared with the effect of the Coulomb potential, the $ \rho$ potential gives the main contribution to the isospin asymmetry of the pseudospin energy splittings and width splittings in the resonant states except for the proton rich nuclei. The pseudospin energy symmetry and width symmetry are not always better realized for neutrons than for protons in the resonant states. The Coulomb potential and the $ \rho$ potential always act in an opposite role in influencing the isospin asymmetry of the pseudospin symmetry in the resonant states.

Pseudospin symmetry in single-particle resonances in spherical square wells

The pseudospin symmetry (PSS) has been studied extensively for bound states. Recently we justified rigorously that the PSS in single particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [PRL 109, 072501 (2012)]. To understand more deeply the PSS, we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances. In particular, we are interested in how the energy and width splittings of PS partners depend on the depth of the scalar and vector potentials. We investigate the asymptotic behaviors of radial Dirac wave functions. Spherical square well potentials are employed in which the PSS breaking part in the Jost function can be well isolated. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PSS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single particle potential varies from zero to a finite value. The conservation and the breaking of the PSS in resonant states and bound states share some similar properties. The appearance of intruder states can be explained by examining the zeros of Jost functions. Origins of the threshold effect in the energy splitting and the anomaly in the width splitting of PS partners, together with many other problems, are still open and should be further investigated.