Tetrahedral shape and Lambda impurity effect in $^{80}$Zr with a multidimensionally constrained relativistic Hartree-Bogoliubov model

TL;DR

This paper explores the tetrahedral nuclear shape in Zr-80 and the effects of a Lambda impurity in Zr-81, revealing shape changes, binding energy variations, and complex density distribution relationships using a multidimensional relativistic model.

Contribution

It introduces a detailed relativistic model to study tetrahedral shapes and Lambda impurity effects in Zr isotopes, highlighting shape deformation changes and binding energy behaviors.

Findings

Tetrahedral configurations found in ground states of Zr-80 and Zr-81.

Lambda impurity affects deformation parameters and binding energies.

Weak correlation between Lambda separation energy and density overlap.

Abstract

This study investigates the tetrahedral structure in $^{80}$Zr and Lambda ($\Lambda$) impurity effect in $^{81}_{~\Lambda}$Zr using the multidimensionally constrained relativistic Hartree-Bogoliubov model. The ground states of both $^{80}$Zr and $^{81}_{~\Lambda}$Zr exhibit a tetrahedral configuration, accompanied by prolate and axial-octupole shape isomers. Our calculations reveal there are changes in the deformation parameters $\beta_{20}$, $\beta_{30}$, and $\beta_{32}$ upon $\Lambda$ binding to $^{80}$Zr, except for $\beta_{32}$ when $\Lambda$ occupies $p$-orbits. Compared to the two shape isomers, the $\Lambda$ particle exhibits weaker binding energy in the tetrahedral state when occupying the $1/2^+[000](\Lambda_s)$ or $1/2^-[110]$ single-particle states. In contrast, the strongest binding occurs for the $\Lambda$ particle in the $1/2^-[101]$ state with tetrahedral shape. Besides, a large $\Lambda$ separation energy may not necessarily correlate with a significant overlap between the density distributions of the $\Lambda$ particle and the nuclear core, particularly for tetrahedral hypernuclei.