Pseudospin, supersymmetry and the shell structure of atomic nuclei

Abstract

The evolution of single-particle energies with varying isospin asymmetry in the shell model is an important issue when predicting changes in the shell structure for exotic nuclei. In many cases pseudospin partner levels, that are almost degenerate in energy for stable nuclei, are relevant in extracting the size of the shell gaps. A breaking of the pseudospin symmetry can affect the size of these gaps and change the magic numbers accordingly. The strength of the pseudospin splitting is expected to depend in particular on isovector-dependent and tensor contributions to the effective nuclear interaction. A description employing supersymmetric quantum mechanics allows to derive a pseudospin symmetry breaking potential that is regular in contrast to the pseudospin-orbit potential in the conventional relativistic treatment. The derived perturbation potential provides a measure to quantify the symmetry breaking and it can be employed to improve mean-field calculations in order to better reproduce the experimentally observed shell evolution. General potentials with exact pseudospin symmetry are obtained that can be used in relativistic mean-field Hamiltonians.

33 pages, 1 table, 6 figures, additional references, minor corrections, note added in proof, accepted for publication in Nuclear Physics A

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Cited by in corpus (12)

• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• Pseudospin symmetry in single particle resonant states
• Pseudospin symmetry in single particle resonances in spherical square wells
• Perturbative interpretation of relativistic symmetries in nuclei
• Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations
• Pseudospin symmetry in supersymmetric quantum mechanics: II. Spin-orbit effects
• Generalized Spin and Pseudo-Spin Symmetry: Relativistic Extension of Supersymmetric Quantum Mechanics
• Effects of tensor interaction on pseudospin energy splitting and shell correction
• Further investigation of the relativistic symmetry by similarity renormalization group
• Pseudospin symmetry in nuclear structure and its supersymmetric representation
• New insight on pseudospin doublets in nuclei
• Pseudospin symmetry: Recent progress with supersymmetric quantum mechanics