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

TL;DR

This paper explores how multiple $SU(3)$ algebra structures in shell and interacting boson models influence the decay properties of various nuclear bands, revealing that decay strengths can vary significantly with algebra phase choices.

Contribution

It demonstrates the impact of multiple $SU(3)$ algebras on nuclear band decay properties, extending previous studies to include $eta$, $ ext{gamma}$, and scissors bands using boson and shell models.

Findings

Weak $E2$ strengths can occur in rotational bands due to multiple $SU(3)$ algebras.

Decay properties of $eta$ and $ ext{gamma}$ bands depend strongly on algebra phase $ ext{alpha}$.

Scissors $1^+$ band decay strengths vary with $ ext{alpha}$, being either strong or weak.

Abstract

Shell model and interacting boson model spaces admit multiple $SU^{(\alpha)}(3)$ 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 $SU^{(\alpha)}(3)$ 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 $\alpha$.