Description of heavy deformed nuclei within the pseudo-SU(3) shell model

Abstract

Abstract. We present a review of the pseudo-SU(3) shell model and its application to heavy deformed nuclei. The model have been applied to describe the low energy spectra, B(E2) and B(M1) values. A systematic study of each part of the interaction within the Hamiltonian was carried out. The study leads us to a consistent method of choosing the parameters in the model. A systematic application of the model for a sequence of rare earth nuclei demonstrates that an overarching symmetry can be used to predict the onset of deformation as manifested through low-lying collective bands.The scheme utilizes an overarching sp(4,R) algebraic framework. IntroductionOver the past years many calculations were carried out by using the SU(3) shell model and the pseudo-SU(3) symmetry. Ongoing improvements and innovations in experimental techniques (4π detectors, radioactive beams, etc.) anticipate the identification of additional new phenomena in the near future, and more information about the existing ones. However, it is commonly accepted that the nuclear shell model should be able to address most of these issues and provide answers. The problem is that most shell-model theories are limited by the large dimensions of the required model spaces, which increases unmanageably with the number of nucleons A. Furthermore, more microscopic calculations are needed exactly in the region of heavy nuclei, in the mass range A ≥ 100.Having this problem, it is essential to take full advantage of symmetries, those that are exact, as well as those which are only partially fulfilled.The selection rules that are associated with such symmetries generate, respectively, weakly coupled and disconnected subspaces of the full space and this allows for a significant reduction in the dimensionality of the model space. The symmetry used here is the pseudo-spin symmetry.A shell model theory for heavy nuclei requires a severe truncation of the model space. To reproduce the essential physics found in the low-energy states of a large space in a smaller one, we have to select the basis states relative to those parts of the interaction that dominate the low-energy structure. Nuclear physics supports the view that the nuclear effective interaction appropriate to low-energy excitations must have a strong correlation with the pairing and quadrupole-quadrupole interactions. The Q · Q interaction, which dominates for near midshell nuclei, is known to introduce deformation and led to the introduction of the SU(3) shell model. This led also to a very natural way to truncate large model spaces, namely to consider few basis states in correspondence with the eigenvalue of Q · Q operator.

Shape Coexistence in Even–Even Nuclei: A Theoretical Overview

“…The first example found experimentally in 2002 was 158 Gd, in which 13 excited 0 + states have been found below 3.1 MeV [492][493][494][495]. Many theoretical interpretations have been suggested for these 0 + states, including two-phonon octupole character [496], the pseudo-SU(3) model [497][498][499], the quasiparticle-phonon model [500], and the pairing plus quadrupole model [501].…”

“…The large number of excited 0 + states appearing in 156,158 Gd 92,94 has been interpreted in terms of the geometric collective model [496], the IBM [496], the quasiparticlephonon model [500], the pairing plus quadrupole model [501], and the pseudo-SU(3) symmetry [497][498][499]508,509].…”