Parameter-free predictions for the collective deformation variables beta and gamma within the pseudo-SU(3) scheme

TL;DR

This paper investigates how the short-range nucleon-nucleon interaction influences nuclear shape predictions within the pseudo-SU(3) model, providing parameter-free predictions for deformation variables beta and gamma in rare earth nuclei.

Contribution

It introduces a method to select the appropriate SU(3) irreducible representation based on the nuclear shell region, improving shape transition predictions without adjustable parameters.

Findings

Predicts prolate to oblate shape transition near N=114-116 in rare earth isotopes.

Shows the highest weight irrep aligns with experimental shape transition data.

Reproduces the prolate dominance in ground states of even-even nuclei.

Abstract

The consequences of the short range nature of the nucleon-nucleon interaction, which forces the spatial part of the nuclear wave function to be as symmetric as possible, on the pseudo-SU(3) scheme are examined through a study of the collective deformation parameters beta and gamma in the rare earth region. It turns out that beyond the middle of each harmonic oscillator shell possessing an SU(3) subalgebra, the highest weight irreducible representation (the hw irrep) of SU(3) has to be used, instead of the irrep with the highest eigenvalue of the second order Casimir operator of SU(3) (the hC irrep), while in the first half of each shell the two choices are identical. The choice of the hw irrep predicts a transition from prolate to oblate shapes just below the upper end of the rare earth region, between the neutron numbers N=114 and 116 in the W, Os, and Pt series of isotopes, in agreement with available experimental information, while the choice of the hC irrep leads to a prolate to oblate transition in the middle of the shell, which is not seen experimentally. The prolate over oblate dominance in the ground states of even-even nuclei is obtained as a by-product.