https://doi.org/10.1140/epja/i2005-10177-0
Original Article
The spin and pseudospin symmetries in the relativistic formalism: Similarities and differences
1
Departamento de Física Moderna, Universidad de Cantabria, E-39005, Santander, Spain
2
Department of Mathematics, St. Petersburg Institute for Railway Engineering, 190031, St. Petersburg, Russia
3
Departamento de Física Aplicada, Universidad de Cantabria, E-39005, Santander, Spain
4
Department of Physics, St. Petersburg University for Telecommunications, 191065, St. Petersburg, Russia
* e-mail: marcoss@unican.es
Received:
18
August
2005
Accepted:
25
November
2005
Published online:
15
December
2005
The effects of the symmetry breaking terms, spin-orbit potential (SOP) and pseudospin-orbit potential (PSOP), in the spin and pseudospin symmetries, respectively, are studied in a comparative way. The analytical properties of the small component F of the Dirac spinor for pseudospin doublets (PSDs) are investigated around the singularity point of the PSOP. We show that the PSOP and the pseudocentrifugal barrier must be appropriately related to each other to describe adequately the wave functions in the nuclear surface, whereas it is not the case for the centrifugal barrier and the SOP. We also determine a modified PSOP smaller than the PSOP when the parameter ¯, appearing in it, is left to vary in the domain of real numbers. The inclusion of this modified PSOP allows us to define a continuous way that connects the two states of a PSD as ¯ varies continuously between the physical (integer) values of ¯ corresponding to these states. Our results indicate that whereas the SOP can be considered as a small spin symmetry breaking term that allows a simple explanation of the spin symmetry, the consideration of the PSOP as the pseudospin symmetry breaking term presents serious difficulties. Thus, we propose a new strategy to explain, in a simple way, the quasi-degeneracy of the PSDs.
PACS: 24.10.Jv Relativistic models – / 21.60.Cs Shell model – / 21.10.Pc Single-particle levels and strength functions – / 24.80.+y Nuclear tests of fundamental interactions and symmetries –
© Società Italiana di Fisica and Springer-Verlag, 2005