Pseudospin symmetry in nuclear structure and its supersymmetric representation

Abstract

The quasi-degeneracy between the single-particle states $(n,l,j=l+1/2)$ and $(n-1,l+2,j=l+3/2)$ indicates a special and hidden symmetry in atomic nuclei---the so-called pseudospin symmetry (PSS)---which is an important concept in both spherical and deformed nuclei. A number of phenomena in nuclear structure have been successfully interpreted directly or implicitly by this symmetry, including nuclear superdeformed configurations, identical bands, quantized alignment, pseudospin partner bands, and so on. Since the PSS was recognized as a relativistic symmetry in 1990s, there have been comprehensive efforts to understand its properties in various systems and potentials. In this Review, we mainly focus on the latest progress on the supersymmetric (SUSY) representation of PSS, and one of the key targets is to understand its symmetry-breaking mechanism in realistic nuclei in a quantitative and perturbative way. The SUSY quantum mechanics and its applications to the SU(2) and U(3) symmetries of the Dirac Hamiltonian are discussed in detail. It is shown that the origin of PSS and its symmetry-breaking mechanism, which are deeply hidden in the origin Hamiltonian, can be traced by its SUSY partner Hamiltonian. Essential open questions, such as the SUSY representation of PSS in the deformed system, are pointed out.

21 pages, 16 figures; Focus issue to celebrate the 40 year anniversary of the 1975 Nobel Prize to Aage Niels Bohr, Ben Roy Mottelson and Leo James Rainwater in Physica Scripta

References in corpus (27)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Nuclear magic numbers: new features far from stability
• Three-body forces: From cold atoms to nuclei
• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• Collapse of the N=28 shell closure in ${}^{42}$Si
• Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation
• Shell Structure and $\rho$-Tensor Correlations in Density-Dependent Relativistic Hartree-Fock theory
• Spin-isospin resonances: A self-consistent covariant description
• Pseudospin symmetry in single particle resonant states
• Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator
• Nuclear halo structure and pseudo-spin symmetry
• Pseudo-spin symmetry in density-dependent relativistic Hartree-Fock theory
• Real stabilization method for nuclear single particle resonances
• Non-local mean field effect on nuclei near Z=64 sub-shell
• Perturbative interpretation of relativistic symmetries in nuclei
• Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations
• Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory
• Density-dependent deformed relativistic Hartree-Bogoliubov theory in continuum
• Isospin dependence of pseudospin symmetry in nuclear resonant states
• A mean field study of single-particle spectra evolution in Z=14 and N=28 chains
• Localized form of Fock terms in nuclear covariant density functional theory
• Three-dimensional mesh calculations for covariant density functional theory
• Symmetries and Supersymmetries of the Dirac Hamiltonian with Axially-Deformed Scalar and Vector Potentials
• Pseudospin, supersymmetry and the shell structure of atomic nuclei
• Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models
• Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian
• Pseudospin symmetry and structure of nuclei with $Z\ge$ 100

Cited by in corpus (2)

• Non-relativistic expansion of Dirac equation with spherical scalar and vector potentials by similarity renormalization group
• Temperature effects on nuclear pseudospin symmetry in the Dirac-Hartree-Bogoliubov formalism