Pseudospin symmetry in nuclear physics

Probing the symmetries of the Dirac Hamiltonian with axially deformed scalar and vector potentials by similarity renormalization group

Symmetry is an important and basic topic in physics. The similarity renormalization group theory provides a novel view to study the symmetries hidden in the Dirac Hamiltonian, especially for the deformed system. Based on the similarity renormalization group theory, the contributions from the nonrelativistic term, the spin-orbit term, the dynamical term, the relativistic modification of kinetic energy, and the Darwin term are self-consistently extracted from a general Dirac Hamiltonian and, hence, we get an accurate description for their dependence on the deformation. Taking an axially deformed nucleus as an example, we find that the self-consistent description of the nonrelativistic term, spin-orbit term, and dynamical term is crucial for understanding the relativistic symmetries and their breaking in a deformed nuclear system.

Pseudospin symmetry in single particle resonant states

The pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the small component of the Dirac spinor. The origin of PSS in single particle bound states in atomic nuclei has been revealed and studied extensively. By examining the zeros of Jost functions corresponding to the small components of Dirac wave functions and phase shifts of continuum states, we show that the PSS in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. The exact conservation and the breaking of the PSS are illustrated for single particle resonances in spherical square-well and Woods-Saxon potentials.

Isospin asymmetry in the pseudospin dynamical symmetry

Pseudospin symmetry in nuclei is investigated considering the Dirac equation with a Lorentz structured Woods-Saxon potential. The isospin correlation of the energy splittings of pseudospin partners with the nuclear potential parameters is studied. We show that, in an isotopic chain, the pseudospin symmetry is better realized for neutrons than for protons. This behavior comes from balance effects among the central nuclear potential parameters. In general, we found an isospin asymmetry of the nuclear pseudospin interaction, opposed to the nuclear spin-orbit interaction which is quasi-isospin symmetric.