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