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

Abstract

This study investigates the tetrahedral structure in ${}^{80}$Zr and Lambda ($\Lambda$) impurity effect in ${}_{\Lambda }^{81}$Zr using the multidimensionally constrained relativistic Hartree-Bogoliubov model. The ground states of both ${}^{80}$Zr and ${}_{\Lambda }^{81}$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.

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