Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

Abstract

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and ${\gamma }^5$ chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry related problems have the same spectrum, but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

arXiv comment33 pages, 10 figures, uses revtex macros

References in corpus (19)

• Pseudo-spin as a Relativistic Symmetry
• 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
• Pseudospin symmetry and the relativistic harmonic oscillator
• A Relativistic Symmetry in Nuclei
• Relativistic Harmonic Oscillator with Spin Symmetry
• Pseudospin symmetry and its approximation in real nuclei
• One-dimensional Dirac oscillator in a thermal bath
• Tensor coupling and pseudospin symmetry in nuclei
• The Isospin Asymmetry in the Pseudo-spin Dynamical Symmetry
• Pseudospin symmetry as a relativistic dynamical symmetry in the nucleus
• U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator
• Bound States of the Dirac Equation for a Class of Effective Quadratic Plus Inversely Quadratic Potentials
• Bound states by a pseudoscalar Coulomb potential in 1+1 dimensions
• Role of the Coulomb and the vector-isovector $\rho$ potentials in the isospin asymmetry of nuclear pseudospin
• Bounded solutions of neutral fermions with a screened Coulomb potential
• Perturbative breaking of the pseudospin symmetry in the relativistic harmonic oscillator
• Bounded solutions of fermions in the background of mixed vector-scalar inversely linear potentials
• The nuclear pseudospin symmetry along an isotopic chain

Cited by in corpus (42)

• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• First experimental realization of the Dirac oscillator
• On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds
• Rotating effects on the Dirac oscillator in the cosmic string spacetime
• Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry
• Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term
• Noninertial effects on the quantum dynamics of scalar bosons
• Pseudospin symmetry in single particle resonances in spherical square wells
• Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations
• Quantum dynamics of scalar bosons in a cosmic string background
• Spin and pseudospin symmetries in the antinucleon spectrum of nuclei
• Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction
• Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles
• On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries
• Spin and pseudospin symmetries of the Dirac equation with confining central potentials
• Playing relativistic billiards beyond graphene
• Spin and Pseudospin symmetries in the Dirac equation with central Coulomb potentials
• Relating pseudospin and spin symmetries through chiral transformation with tensor interaction
• Exact Solution of Dirac Equation with Charged Harmonic Oscillator in Electric Field: Bound States
• Pseudospin, supersymmetry and the shell structure of atomic nuclei
• Relativistic Effects of Mixed Vector-Scalar-Pseudoscalar Potentials for Fermions in 1+1 Dimensions
• Approximate bound states of the Dirac equation with some physical quantum potentials
• Solutions of the Dirac equation with the shifted Deng-Fan potential including Yukawa-like tensor interaction
• Relativistic confinement of neutral fermions with a trigonometric tangent potential
• Generalized relativistic harmonic oscillator in minimal length quantum mechanics
• κ state solutions for the fermionic massive spin-1/2 particles interacting with double ring-shaped Kratzer and oscillator potentials
• General spin and pseudospin symmetries of the Dirac equation
• Confinement of spin-0 and spin-1/2 particles in a mixed vector-scalar coupling with unequal shapes for the potentials
• Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential
• Missing solution in a Cornell potential
• Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials
• Comparison theorems for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions
• 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
• Effective Mass Schrodinger Equation via Point Canonical Transformation
• Kappa-deformed Dirac oscillator in an external magnetic field
• Approximate Analytical Solutions of the Pseudospin Symmetric Dirac Equation for Exponential-type Potentials
• Pseudospin symmetry in nuclear structure and its supersymmetric representation
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential
• Fermions embedded in a scalar-vector kink-like smooth potential
• Generalized Dirac oscillator in cosmic string space-time
• Analytical solutions of the Dirac equation using the Tridiagonal Representation Approach: General study, limitations, and possible applications