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

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.