Eur. Phys. J. Special Topics 229, 2367–2387 (2020)
https://doi.org/10.1140/epjst/e2020-000034-3

Regular Article

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

¹ Institute of Nuclear and Particle Physics, National Centre for Scientific Research “Demokritos”, GR-15310 Aghia Paraskevi, Attiki, Greece
² Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, 1784 Sofia, Bulgaria

^a e-mail: bonat@inp.demokritos.gr

Received: 10 March 2020
Accepted: 28 August 2020
Published online: 23 October 2020

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 β and γ 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.