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

Journal Article · Mon May 15 00:00:00 EDT 2006 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.73.054309· OSTI ID:20771530

Castro, A.S. de; Alberto, P; Lisboa, R; Malheiro, M ^[1]

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1. Departamento de Fisica e Quimica, Universidade Estadual Paulista, 12516-410 Guaratingueta, SP, Brazil and Departamento de Fisica and Centro de Fisica Computacional, Universidade de Coimbra, P-3004-516 Coimbra (Portugal)

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}{sup 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.

• OSTI ID: 20771530
• Journal Information: Physical Review. C, Nuclear Physics, Vol. 73, Issue 5; Other Information: DOI: 10.1103/PhysRevC.73.054309; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUND STATE
CHIRAL SYMMETRY
CHIRALITY
DIRAC EQUATION
HARMONIC OSCILLATORS
MASSLESS PARTICLES
MATHEMATICAL SOLUTIONS
MEAN-FIELD THEORY
NUCLEONS
POTENTIALS
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
SCALARS
SPIN
THREE-DIMENSIONAL CALCULATIONS
TRANSFORMATIONS
VECTORS