# Effect of tetrahedral shapes in heavy and superheavy nuclei

## TL;DR

This study investigates the potential for tetrahedral deformation in heavy and superheavy nuclei using a microscopic-macroscopic model, finding no stable tetrahedral shapes but identifying minor energy effects from combined octupole deformations in some superheavy nuclei.

## Contribution

First comprehensive search for tetrahedral shapes in heavy nuclei using a well-tested microscopic-macroscopic model, with detailed analysis of deformation parameters and stability.

## Key findings

- No stable tetrahedral shapes found in studied nuclei.
- Minor energy lowering (~0.7 MeV) due to combined octupole deformations in superheavy nuclei.
- Conditional minima are mostly excited states without barriers.

## Abstract

We search for effects of tetrahedral deformation $\beta_{32}$ over a range of $\sim 3000$ heavy and superheavy nuclei, $82\leq Z \leq 126$, using a microscopic-macroscopic model based on the deformed Woods-Saxon potential, well tested in the region. We look for the energy minima with a non-zero tetrahedral distortion, both absolute and conditional - with the quadrupole distortion constrained to zero. In order to assure reliability of our results we include 10 most important deformation parameters in the energy minimization. We could not find any cases of stable tetrahedral shapes. The only sizable - up to 0.7 MeV - lowering of the ground state occurs in superheavy nuclei $Z\geq 120$ for $N=173-188$, as a result of a {\it combined} action of two octupole deformations: $\beta_{32}$ and $\beta_{30}$, in the ratio $\beta_{32}/\beta_{30}\approx \sqrt{3/5}$. The resulting shapes are moderately oblate, with the superimposed distortion $\beta_{33}$ {\it with respect to the oblate axis}, which makes the equator of the oblate spheroid slightly triangular. Almost all found conditional minima are excited and not protected by any barrier, a handful of them are degenerate with the axial minima.