Multiple $SU(3)$ algebras in interacting boson model and shell model: Results for $(\beta ,\gamma$) bands and scissors $1^{+}$ band

Abstract

Shell model and interacting boson model spaces admit multiple $S{U}^{(\alpha )}(3)$ algebras generating the same rotational spectra but different $E2$ decay properties, depending on the phases $\alpha$ in the quadrupole generator. In the ground ($g$) $K=0^{+}$ bands in nuclei this is demonstrated recently using systems with nucleons in a single oscillator shell [Kota, Sahu and Srivastava, Bulg. J. Phys. {\bf 46}, 313 (2019); Eur. Phys. J. Special Topics {\bf 229}, 2389 (2020)]. Going beyond these preliminary studies, results are presented here for $E2$ decay properties of $\beta$ and $\gamma$ bands members, as generated by multiple $SU(3)$ algebras, using $sdg$IBM and $sdgi$IBM examples. In addition, results are presented for the $E2$ and $M1$ decay properties of the levels of the $1^{+}$ scissors band in heavy nuclei using $sdg$IBM-2 and $sdgi$IBM-2. The scissors $1^{+}$ band properties are also studied using a shell model example with six protons in $(pf)$ shell and twelve neutrons in $(sdg)$ shell. These results establish that: (i) with multiple $SU(3)$ algebras, it is possible to have rotational bands with very weak $E2$ strengths among the levels where normally one expects strong strengths; (ii) $E2$ decay of the levels of $\beta$ and $\gamma$ bands to the ground band are quite different for some of the $S{U}^{(\alpha )}(3)$ algebras with strong dependence on $\alpha$; (iii) it is possible to have the scissors $1^{+}$ band with the $E2$ and $M1$ decay of the low-lying levels of this band to the $g$ band are strong or weak depending on $\alpha$.

arXiv comment6 tables, 4 figures

References in corpus (16)

• Magnetic dipole excitations in nuclei: elementary modes of nucleonic motion
• Collective Modes in Light Nuclei from First Principles
• Nilsson-SU3 selfconsistency in heavy N=Z nuclei
• Analytic predictions for nuclear shapes, the prolate dominance and the prolate-oblate shape transition in the proxy-SU(3) model
• Emergent symplectic symmetry in atomic nuclei: Ab initio symmetry-adapted no-core shell model
• Parameter Symmetry of the Interacting Boson Model
• Incompleteness of Representation Theory: Hidden symmetries and Quantum Non-Integrability
• Broken SU(3) symmetry in deformed even-even nuclei
• Multichannel dynamical symmetry and cluster-coexistence
• Ground-$\gamma$ band coupling in heavy deformed nuclei and SU(3) contraction limit
• Effects of Pairing in the Pseudo-SU(3) Model
• Description of deformed nuclei in the sdg boson model
• Studies of the electric dipole transitions of deformed rare-earth nuclei
• Sum Rules for B(M1,0+ -> 1+) Strength in IBM-3 and IBM-4
• Quadrupole properties of the eight $SU(3)$ algebras in $(sdgi)$ space
• Multiple multi-orbit pairing algebras in shell model and interacting boson models

Cited by in corpus (1)

• Proxy-$SU(4)$ symmetry in A=60-90 region