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.

5 pages, uses revtex macros

References in corpus (1)

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

Cited by in corpus (14)

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• Approximate Dirac solutions of complex -symmetric Pöschl-Teller potential in view of spin and pseudospin symmetries
• Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials
• New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential
• Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
• Relativistic Coulomb scattering of spinless bosons
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential
• Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions
• Solutions of the spatially-dependent mass Dirac equation with the spin and pseudo-spin symmetry for the Coulomb-like potential