Shell-model description of collective deformation variables $\beta$ and $\gamma$ in ${}^{164-188}$Hf nuclei

Abstract

Symmetry-based models, such as the pseudo-SU(3) scheme, have proved to be highly useful tools for describing the low-energy structure of nuclei in the rare-earth region. This model is employed to study the evolution of the collective deformation variables beta and gamma in the ground state (0+) along the isotopic chain 164-188Hf. The truncation is carried out by considering the irreducible representations (irreps) with high spatial symmetry and pseudo-spin 0 and 1, so that both the most and less symmetric relevant irreps are included, the latter being of particular importance for the description of low-energy properties, especially the shape transition. The Hamiltonian includes spherical Nilsson single-particle energies, the quadrupole-quadrupole interaction, and pairing correlations. It is parameterised in a systematic manner, so that the description is obtained without free parameters. In agreement with experimental data, the maximum deformation beta occurs at N = 100, although the model predicts values that are about 20% smaller. As in other theoretical studies, a prolate deformation (gamma = 8o) is predicted for almost all nuclei in the shell, with a clear transition towards triaxial shapes for N > 110. An analysis of the effects of the pairing and Nilsson terms on the values of $\beta$ and gamma indicates that it is the latter that determine the prolate-oblate transition, with the pairing term playing only a marginal role. The absence of nucleons in the intruder sector is the most significant limitation of the model.

arXiv comment4 figures, 5 tables

References in corpus (21)

• Nuclear Ground-State Masses and Deformations
• Pseudo-spin as a Relativistic Symmetry
• Tables of E2 Transition Probabilities from the first $2^{+}$ States in Even-Even Nuclei
• The realistic collective nuclear Hamiltonian
• Spherical Shell Model description of rotational motion
• Role of triaxiality in the ground state shape of neutron rich Yb, Hf, W, Os, and Pt isotopes
• Analytic predictions for nuclear shapes, the prolate dominance and the prolate-oblate shape transition in the proxy-SU(3) model
• Collective structural evolution in neutron-rich Yb, Hf, W, Os and Pt isotopes
• The proxy-SU(3) symmetry in atomic nuclei
• Shell model description of normal parity bands in odd-mass heavy deformed nuclei
• Parameter-free predictions for the collective deformation variables beta and gamma within the pseudo-SU(3) scheme
• Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
• Pseudo SU(3) shell model: Normal parity bands in odd-mass nuclei
• Effects of Pairing in the Pseudo-SU(3) Model
• Microscopic study of neutron-rich Dysprosium isotopes
• Broken axial symmetry as essential feature to predict radiative capture in heavy nuclei
• Excited bands in odd-mass rare-earth nuclei
• Giant dipole resonance in Sm isotopes within TDHF method
• Electromagnetic properties in ${}^{160-170}$Dy nuclei: A microscopic description by the pseudo-SU(3) shell model
• Microscopic study of low-lying energy levels and electromagnetic properties in even-even ${}^{168-178}$Yb nuclei
• Theoretical study of normal deformed rotational bands of odd-mass ${}^{167,169,171}$Lu nuclei