Role of the Coulomb and the vector-isovector $\rho$ potentials in the isospin asymmetry of nuclear pseudospin

Abstract

We investigate the role of the Coulomb and the vector-isovector $\rho$ potentials in the asymmetry of the neutron and proton pseudospin splittings in nuclei. To this end, we solve the Dirac equation for the nucleons using central vector and scalar potentials with Woods-Saxon shape and $Z$ and $N-Z$ dependent Coulomb and $\rho$ potentials added to the vector potential. We study the effect of these potentials on the energy splittings of proton and neutron pseudospin partners along a Sn isotopic chain. We use an energy decomposition proposed in a previous work to assess the effect of a pseudospin-orbit potential on those splittings. We conclude that the effect of the Coulomb potential is quite small and the $\rho$ potential gives the main contribution to the observed isospin asymmetry of the pseudospin splittings. This isospin asymmetry results from a cancellation of the various energy terms and cannot be attributed only to the pseudospin-orbit term, confirming the dynamical character of this symmetry pointed out in previous works.

arXiv comment9 pages, 11 figures, uses revtex4; title was changed and several small corrections were made throughout the text

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• Pseudospin symmetry and the relativistic harmonic oscillator
• Tensor coupling and pseudospin symmetry in nuclei
• Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator
• Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations
• Isospin dependence of pseudospin symmetry in nuclear resonant states
• Temperature effects on nuclear pseudospin symmetry in the Dirac-Hartree-Bogoliubov formalism
• Pseudospin symmetry in nuclear structure and its supersymmetric representation
• New insight on pseudospin doublets in nuclei