# Toroidal states in $^{28}$Si with covariant density functional theory in 3D lattice space

## TL;DR

This study uses covariant density functional theory in 3D lattice space to explore high-spin toroidal states in silicon-28, revealing multiple stable toroidal configurations and their relation to observed resonances and alpha clustering.

## Contribution

It provides the first detailed theoretical analysis of high-spin toroidal states in $^{28}$Si using a 3D lattice covariant density functional approach.

## Key findings

- Thirteen toroidal states with spins from 0 to 56ħ identified.
- Excitation energies match observed resonances at specific spins.
- Evidence of alpha clustering in high-spin toroidal states.

## Abstract

The toroidal states in $^{28}$Si with spin extending to extremely high are investigated with the cranking covariant density functional theory on a 3D lattice. Thirteen toroidal states with spin $I$ ranging from 0 to 56$\hbar$ are obtained, and their stabilities against particle emissions are studied by analyzing the density distributions and potentials. The excitation energies of the toroidal states at $I=28$, 36, 44$\hbar$ reasonably reproduce the observed three resonances extracted from the 7-$\alpha$ de-excitation of $^{28}$Si. The $\alpha$ clustering of these toroidal states is supported by the $\alpha$-localization function.