Toroidal States of the $^{12}$C Nucleus

TL;DR

This paper investigates toroidal intrinsic states in the $^{12}$C nucleus, exploring their properties through cluster and shell models, and numerical solutions to understand their structure and potential for future research.

Contribution

It introduces a detailed analysis of toroidal states in $^{12}$C using generator-coordinate methods in cluster and shell models, supported by mean field calculations.

Findings

Identification of toroidal density distributions in $^{12}$C states

Comparison of cluster and shell model descriptions

Numerical solutions supporting the existence of toroidal configurations

Abstract

Among the states of $^{12}$C, there is an important subset of $K$=0 and $K$=$I$ planar intrinsic states in which the intrinsic motion of the nucleons are confined in the planar region defined by the three-alpha cluster or by their generated toroid. The intrinsic nuclear densities of these states are toroidal in nature. We study these $^{12}$C toroidal states from the generator-coordinate viewpoints in both the alpha cluster model and the toroidal shell model. Numerical solutions in the toroidal mean field approximation are examined to pave the way for future extensions and refinements.