Generalized pseudo-SU(3) model and pairing

Abstract

The pseudo-SU(3) model is extended to explicitly include the spin and protonneutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU (3), is expressed in terms of pseudo-space tensors and a general result is given for calculating its matrix elements. The importance of pairing correlations in pseudo-SU(3) model calculations is demonstrated by examining the dependence of wavefunctions, low-energy collective excitation spectra, and moments of inertia on the strength of the pairing interaction.

Consequences of a relativistic pseudospin symmetry for radial nodes and intruder levels in nuclei

“…For example, (n r s 1/2 , (n r −1)d 3/2 ) will havel = 1, (n r p 3/2 , (n r −1)f 5/2 ) will havel = 2, etc. This pseudospin symmetry has been used to explain features of deformed nuclei [3], including superdeformation [4] and identical bands [5,6] and to establish an effective shell-model coupling scheme [7]. In view of its central role in both spherical and deformed nuclei, there has been an intense effort to understand the origin of this symmetry.…”

Pseudospin symmetry in nuclear structure and its supersymmetric representation

“…The SUSY can be either exact (also called unbroken) or broken [126]. The SUSY is exact when the eigenvalue equation (19) has a zero energy eigenstate E S (0) = 0. In this case, as a usual convention, the Hamiltonian H 1 has an additional eigenstate at zero energy that does not appear in its partner Hamiltonian H 2 , because B − ψ 1 (0) = 0 means ψ 2 (0) = 0, i.e., the trivial eigenfunction of H 2 identically equals zero.…”

“…Based on this concept, a simple but useful pseudo-SU(3) model was proposed, and it was generalized to be the pseudo-symplectic model [16,17,18,19]. The concept of pseudospin symmetry has been also widely used in the odd-mass nuclei in the interacting Boson-Fermion model [20].…”

The fundamental role of symmetry in nuclear models

“…Recall that spin-orbit interactions also brings about a significant re-arrangment of the single-particle energy levels of the spherical harmonic oscillator and that pseudo-SU(3) [34] and pseudo-symplectic models [35] have been proposed to take this into account. The above considerations suggest that the re-ordering of the relevant shell-model configurations due to deformation is an even larger concern in strongly-deformed nuclei.…”