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.

arXiv comment21 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 (74)

• Supersymmetry and Quantum Mechanics
• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Nuclear magic numbers: new features far from stability
• Pseudo-spin as a Relativistic Symmetry
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• From low-momentum interactions to nuclear structure
• New effective interactions in RMF theory with non-linear terms and density-dependent meson-nucleon coupling
• Three-body forces: From cold atoms to nuclei
• A Giant Halo at the Neutron Drip Line
• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• Collapse of the N=28 shell closure in ${}^{42}$Si
• The pseudo-spin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line
• Neutron halo in deformed nuclei
• Spin symmetry in the anti-nucleon spectrum
• Density-Dependent Relativistic Hartree-Fock Approach
• Pseudospin symmetry and the relativistic harmonic oscillator
• Spherical Relativistic Hartree theory in a Woods-Saxon basis
• Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation
• Halos in medium-heavy and heavy nuclei with covariant density functional theory in continuum
• Shell Structure and $\rho$-Tensor Correlations in Density-Dependent Relativistic Hartree-Fock theory
• On the Relativistic Foundations of Pseudospin Symmetry in Nuclei
• Generalized Pseudo-SU(3) Model and Pairing
• Relativistic Harmonic Oscillator with Spin Symmetry
• Spin-isospin resonances: A self-consistent covariant description
• $\beta$-decay half-lives of neutron-rich nuclei and matter flow in the $r$-process
• Pseudospin symmetry and its approximation in real nuclei
• Pseudo-spin Symmetry and Relativistic Single-nucleon Wave Functions
• Relativistic Hartree-Fock-Bogoliubov theory with Density Dependent Meson-Nucleon Couplings
• Tensor coupling and pseudospin symmetry in nuclei
• Pseudospin symmetry in single particle resonant states
• The Isospin Asymmetry in the Pseudo-spin Dynamical Symmetry
• Pseudospin symmetry as a relativistic dynamical symmetry in the nucleus
• Test of Pseudospin Symmetry in Deformed Nuclei
• 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
• U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator
• Intertwining technique for the one-dimensional stationary Dirac equation
• Superheavy magic structures in the relativistic Hartree-Fock-Bogoliubov approach
• Analytic continuation of single-particle resonance energy and wave function in relativistic mean field theory
• Relativistic Mean Field Approach and the 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
• Antibaryons bound in nuclei
• Pseudospin symmetry in single particle resonances in spherical square wells
• Perturbative interpretation of relativistic symmetries in nuclei
• Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations
• Consequences of a Relativistic Pseudospin Symmetry for Radial Nodes and Intruder Levels in Nuclei
• Exploration of relativistic symmetry by the similarity renormalization group
• Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory
• Spin and pseudospin symmetries in the antinucleon spectrum of nuclei
• Density-dependent deformed relativistic Hartree-Bogoliubov theory in continuum
• Isospin dependence of pseudospin symmetry in nuclear resonant states
• Pseudospin symmetry in supersymmetric quantum mechanics: II. Spin-orbit effects
• The Resurrection of a Symmetry in Nucleon - Nucleus Scattering
• 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
• Superdeformed bands in 32S and neighboring nuclei predicted within the Hartree-Fock method
• Three-dimensional mesh calculations for covariant density functional theory
• Implications of Pseudospin Symmetry on Relativistic Magnetic Properties and Gamow - Teller Transitions in Nuclei
• Resonant states of deformed nuclei in complex scaling method
• Avoid the Tsunami of the Dirac sea in the Imaginary Time Step method
• Symmetries and Supersymmetries of the Dirac Hamiltonian with Axially-Deformed Scalar and Vector Potentials
• Pseudospin, supersymmetry and the shell structure of atomic nuclei
• Violation of pseudospin symmetry in nucleon-nucleus scattering: exact relations
• Role of the Coulomb and the vector-isovector $\rho$ potentials in the isospin asymmetry of nuclear pseudospin
• Structure of positive energy states in a deformed mean-field potential
• Relevance of pseudospin symmetry in proton-nucleus scattering
• Further investigation of the relativistic symmetry by similarity renormalization group
• Resonant states and pseudospin symmetry in the Dirac Morse potential
• Hamiltonian Flow Equations for a Dirac Particle in an External Potential
• 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 (3)

• 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
• Fermion inter-particle potentials in 5D and a dimensional restriction prescription to 4D