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Title: Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles

Abstract

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. The conclusions do not depend on the particular shapes of the potentials and can be important in different fields of physics. When both scalar and vector potentials are spherical, these conditions for isospectrality imply that the spin-orbit and Darwin terms of either the upper component or the lower component of the Dirac spinor vanish, making it equivalent, as far as energy is concerned, to a spin-0 state. In this case, besides energy, a scalar particle will also have the same orbital angular momentum as the (conserved) orbital angular momentum of either the upper or lower component of the corresponding spin-1/2 particle. We point out a few possible applications of this result.

Authors:
; ;  [1];  [2];  [2]
  1. Department of Physics and Centre for Computational Physics, University of Coimbra, P-3004-516 Coimbra (Portugal)
  2. (Brazil)
Publication Date:
OSTI Identifier:
20995245
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevC.75.047303; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIRAC EQUATION; ENERGY SPECTRA; ORBITAL ANGULAR MOMENTUM; PARTICLES; POTENTIALS; RELATIVISTIC RANGE; SCALARS; SPHERICAL CONFIGURATION; SPIN; SYMMETRY; VECTORS

Citation Formats

Alberto, P., Castro, A. S. de, Malheiro, M., Departamento de Fisica e Quimica, Universidade Estadual Paulista, 12516-410 Guaratingueta, SP, and Departamento de Fisica, Instituto Tecnologico de Aeronautica, CTA, 12228-900 Sao Jose dos Campos, SP, Brazil and Instituto de Fisica, Universidade Federal Fluminense, 24210-340 Niteroi. Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.047303.
Alberto, P., Castro, A. S. de, Malheiro, M., Departamento de Fisica e Quimica, Universidade Estadual Paulista, 12516-410 Guaratingueta, SP, & Departamento de Fisica, Instituto Tecnologico de Aeronautica, CTA, 12228-900 Sao Jose dos Campos, SP, Brazil and Instituto de Fisica, Universidade Federal Fluminense, 24210-340 Niteroi. Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles. United States. doi:10.1103/PHYSREVC.75.047303.
Alberto, P., Castro, A. S. de, Malheiro, M., Departamento de Fisica e Quimica, Universidade Estadual Paulista, 12516-410 Guaratingueta, SP, and Departamento de Fisica, Instituto Tecnologico de Aeronautica, CTA, 12228-900 Sao Jose dos Campos, SP, Brazil and Instituto de Fisica, Universidade Federal Fluminense, 24210-340 Niteroi. Sun . "Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles". United States. doi:10.1103/PHYSREVC.75.047303.
@article{osti_20995245,
title = {Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles},
author = {Alberto, P. and Castro, A. S. de and Malheiro, M. and Departamento de Fisica e Quimica, Universidade Estadual Paulista, 12516-410 Guaratingueta, SP and Departamento de Fisica, Instituto Tecnologico de Aeronautica, CTA, 12228-900 Sao Jose dos Campos, SP, Brazil and Instituto de Fisica, Universidade Federal Fluminense, 24210-340 Niteroi},
abstractNote = {We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. The conclusions do not depend on the particular shapes of the potentials and can be important in different fields of physics. When both scalar and vector potentials are spherical, these conditions for isospectrality imply that the spin-orbit and Darwin terms of either the upper component or the lower component of the Dirac spinor vanish, making it equivalent, as far as energy is concerned, to a spin-0 state. In this case, besides energy, a scalar particle will also have the same orbital angular momentum as the (conserved) orbital angular momentum of either the upper or lower component of the corresponding spin-1/2 particle. We point out a few possible applications of this result.},
doi = {10.1103/PHYSREVC.75.047303},
journal = {Physical Review. C, Nuclear Physics},
number = 4,
volume = 75,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • The Cornell potential consists of Coulomb and linear potentials, i.e. −a/x+bx, that has received a great deal of attention in particle and nuclear physics. In this paper, we present exact solutions of the Dirac equation with the mixed scalar–vector–pseudoscalar Cornell potential under spin and pseudospin symmetry limits. The corresponding eigenfunctions are given in the form of the biconfluent Heun polynomials. -- Highlights: •We investigate the Dirac equation with the scalar–vector–pseudoscalar Cornell potential. •The solutions are discussed in view of spin and pseudospin symmetry limits. •The energy levels and the wave function are presented in Heun biconfluent equations.
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