Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations

Abstract

The origin of pseudospin symmetry (PSS) and its breaking mechanism are explored by combining supersymmetry (SUSY) quantum mechanics, perturbation theory, and the similarity renormalization group (SRG) method. The Schrödinger equation is taken as an example, corresponding to the lowest-order approximation in transforming a Dirac equation into a diagonal form by using the SRG. It is shown that while the spin-symmetry-conserving term appears in the single-particle Hamiltonian $H$, the PSS-conserving term appears naturally in its SUSY partner Hamiltonian $\tilde{H}$. The eigenstates of Hamiltonians $H$ and $\tilde{H}$ are exactly one-to-one identical except for the so-called intruder states. In such a way, the origin of PSS deeply hidden in $H$ can be traced in its SUSY partner Hamiltonian $\tilde{H}$. The perturbative nature of PSS in the present potential without spin-orbit term is demonstrated by the perturbation calculations, and the PSS-breaking term can be regarded as a very small perturbation on the exact PSS limits. A general tendency that the pseudospin-orbit splittings become smaller with increasing single-particle energies can also be interpreted in an explicit way.

arXiv comment31 pages, 11 figures, 2 tables

References in corpus (64)

• 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
• Dirac and Klein-Gordon equations with equal scalar and vector potentials
• 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
• Spin symmetry in the anti-nucleon spectrum
• Density-Dependent Relativistic Hartree-Fock Approach
• Pseudospin symmetry and the relativistic harmonic oscillator
• Shell Structure and $\rho$-Tensor Correlations in Density-Dependent Relativistic Hartree-Fock theory
• Magic numbers for superheavy nuclei in relativistic continuum Hartree-Bogoliubov theory
• On the Relativistic Foundations of Pseudospin Symmetry in Nuclei
• A Relativistic Symmetry in Nuclei
• Relativistic Harmonic Oscillator with Spin Symmetry
• Pseudospin symmetry and its approximation in real nuclei
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Relativistic Hartree-Fock-Bogoliubov theory with Density Dependent Meson-Nucleon Couplings
• Pseudo-spin Symmetry and Relativistic Single-nucleon Wave Functions
• Tensor coupling and pseudospin symmetry in nuclei
• Pseudospin symmetry in single particle resonant states
• Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics
• 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
• An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry
• Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry
• Relativistic Mean Field Approach and the Pseudo-Spin Symmetry
• Pseudo-spin symmetry in density-dependent relativistic Hartree-Fock theory
• Non-local mean field effect on nuclei near Z=64 sub-shell
• Perturbative interpretation of relativistic symmetries in nuclei
• Consequences of a Relativistic Pseudospin Symmetry for Radial Nodes and Intruder Levels in Nuclei
• Exploration of relativistic symmetry by the similarity renormalization group
• Test of Nuclear Wave Functions for Pseudospin Symmetry
• Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory
• Spin and pseudospin symmetries in the antinucleon spectrum of nuclei
• Isospin dependence of pseudospin symmetry in nuclear resonant states
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles
• New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case
• 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
• Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthen problem
• Spin and Pseudospin symmetries in the Dirac equation with central Coulomb potentials
• Implications of Pseudospin Symmetry on Relativistic Magnetic Properties and Gamow - Teller Transitions in Nuclei
• Spin Symmetry for Anti-Lambda Spectrum in atomic nucleus
• Relativistic effect of spin and pseudospin symmetries
• 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
• Generalized Spin and Pseudo-Spin Symmetry: Relativistic Extension of Supersymmetric Quantum Mechanics
• Relevance of pseudospin symmetry in proton-nucleus scattering
• Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio's oscillator
• Tensor coupling effects on spin symmetry in anti-Lambda spectrum of hypernuclei
• Hamiltonian Flow Equations for a Dirac Particle in an External Potential
• Nuclear Wave Functions for Spin and Pseudospin Partners
• Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian
• Pseudospin symmetry and structure of nuclei with $Z\ge$ 100
• Supersymmetric analysis for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions
• New insight on pseudospin doublets in nuclei

Cited by in corpus (29)

• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• Towards an ab initio covariant density functional for nuclear structure
• Pseudospin symmetry in single particle resonances in spherical square wells
• Pseudospin symmetry in supersymmetric quantum mechanics: II. Spin-orbit effects
• Proton radioactivity described by covariant density functional theory with Similarity Renormalization Group method
• Relativistic Brueckner-Hartree-Fock theory for neutron drops
• Relativistic Killingbeck Energy States Under an External Magnetic Fields
• Relativistic interpretation on the nature of nuclear tensor force
• Green's function method for the spin and pseudospin symmetries in the single-particle resonant states
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Solutions of the Dirac equation with the shifted Deng-Fan potential including Yukawa-like tensor interaction
• Further investigation of the relativistic symmetry by similarity renormalization group
• Spin symmetry in the Dirac sea derived from the bare nucleon-nucleon interaction
• Resonant states and pseudospin symmetry in the Dirac Morse potential
• Dirac bound states of anharmonic oscillator in external fields
• An Investigation of the Bound State Solutions of the Klein-Gordon Equation for the Generalized Woods-Saxon Potential in Spin Symmetry and Pseudo-spin Symmetry Limits
• Non-relativistic expansion of Dirac equation with spherical scalar and vector potentials by similarity renormalization group
• κ state solutions for the fermionic massive spin-1/2 particles interacting with double ring-shaped Kratzer and oscillator potentials
• The bound state solutions of the $D$-dimensional Schrödinger equation for the Woods-Saxon potential
• Non-relativistic expansion of Dirac equation with spherical scalar and vector potentials by reconstituted Foldy-Wouthuysen transformation
• Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential
• Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
• Stationary states of fermions in a sign potential with a mixed vector-scalar coupling
• Probing spin and pseudospin symmetries in deformed nuclei by the Green's function method
• Relativistic symmetry breaking in light kaonic nuclei
• Pseudospin symmetry in nuclear structure and its supersymmetric representation
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential
• Recent progresses on the pseudospin symmetry in single particle resonant states
• Pseudospin symmetry: Recent progress with supersymmetric quantum mechanics