Eur. Phys. J. A (2007) 34: 429-441
https://doi.org/10.1140/epja/i2007-10515-2

Regular Article - Theoretical Physics

Pseudospin symmetry in the Dirac phenomenology

¹ Departamento de Fısica Moderna, Universidad de Cantabria, E-39005, Santander, Spain
² Departamento de Fısica Aplicada, Universidad de Cantabria, E-39005, Santander, Spain
³ Department of Physics, St. Petersburg University for Telecommunications, 191065, St. Petersburg, Russia

^* e-mail: marcoss@unican.es

Received: 28 June 2007
Accepted: 7 January 2008
Published online: 24 January 2008

Abstract

In the phenomenological relativistic framework of the Dirac equation for spherical nuclei, we use different kinds of single-particle central potentials ( Σ_S + Σ₀ to investigate certain aspects of the spin and pseudospin (PS) symmetries. Neither the splitting of PS doublets (PSDs) nor the similarity of the radial parts of the small components (F/r of the corresponding Dirac spinors have been found related with the magnitude of Σ_S + Σ₀ , in the sense predicted by several authors in the last decade. This conclusion is shown to be valid, in particular, for a potential of Coulomb type. We give a simple explanation for the strong correlation established in the relativistic calculations between the similarity of the radial parts of the big (small) components of the Dirac spinors of two spin (pseudospin) partners and the number of their nodes. The direct effects of the so-called PS symmetry-breaking term (and its singularity point) on the F functions of the PSDs are also analysed.