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