Nuclear tetrahedral configurations at spin zero

The possibility of the existence of stable tetrahedral deformations at spin zero is investigated using the Skyrme-HFBCS approach and the generator coordinate method (GCM). The study is limited to nuclei in which the tetrahedral mode has been predicted to be favored on the basis of non-self-consistent models. Our results indicate that a clear identification of tetrahedral deformations is unlikely because they are strongly mixed with the axial octupole mode. However, the excitation energies related to the tetrahedral mode are systematically lower than those of the axial octupole mode in all the nuclei included in this study.

Figure 1

Variation of the total mean-field energy as a function of the quadrupole $Q_{20}$ moment (in ${\mathrm{fm}}^2$). Triangles, squares, and circles denote results obtained using the SIII, ${\mathrm{SkM}}^{*}$, and SLy4 parametrizations of the Skyrme force, respectively.

Figure 2

Total mean-field energy obtained with the HF (squares) and HFBCS (circles) methods as a function of the dimensionless ${\beta }_{30}$ (solid symbols) and ${\beta }_{32}$ (open symbols) deformation parameters.

Figure 3

Single-particle energies as a function of octupole deformation ${\beta }_{30}$ and ${\beta }_{32}$ for ${}^{110}\mathrm{Zr}$ calculated for SLy4 force. The positive and negative parity levels are denoted by solid and dashed lines, respectively.

Figure 4

Parity and particle number projected energies as a function of the octupole deformations ${\beta }_{30}$ and ${\beta }_{32}$. In the two top subfigures (a and b) corresponding to ${}^{110}\mathrm{Zr}$, the results obtained with the SLy4 (circles) and SIII (squares) are compared. In the other subfigures, only calculations performed with SLy4 are shown. The circles and squares denote then the energies as a function of ${\beta }_{30}$ and ${\beta }_{32}$, respectively. In all subfigures solid and open symbols refer to positive and negative parity, respectively.