Tetrahedral and Triangular Deformations of $Z=N$ Nuclei in Mass Region $A\sim 60-80$

Abstract

We study static non-axial octupole deformations in proton-rich $Z=N$ nuclei, ${}^{64}$Ge, ${}^{68}$Se, ${}^{72}$Kr, ${}^{76}$Sr, ${}^{80}$Zr and ${}^{84}$Mo, by using the Skyrme Hartree-Fock plus BCS calculation with no restrictions on the nuclear shape. The calculation predicts that the oblate ground state in ${}^{68}$Se is extremely soft for the $Y_{33}$ triangular deformation, and that in ${}^{80}$Zr the low-lying local minimum state coexisting with the prolate ground state has the $Y_{32}$ tetrahedral deformation.

Comments: 8 pages, 4 Postscript figures, REVTEX