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

Cheuk-Yin Wong, Andrzej Staszczak

Published 2019-02-18Version 1

The $^{12}$C nucleus with $N$=6 and $Z$=6 is a doubly-magic closed-shell nucleus in a toroidal potential and Wheeler's triangular resonating group model of $^{12}$C as three clusters of alpha particles will naturally generate a toroidal density if the nucleons interchanging between the clusters are allowed to circulate continuously from one cluster to another. Experimentally, many excited states of $^{12}$C decay predominantly into three alpha particles, and the triangular clusters of three alpha particles have a high degree of overlap with a torus. We explore a toroidal description for some excited states of $^{12}$C and search for the signature that will reveal a possible toroidal configuration of the nucleus. We find that the $^{12}$C nucleus in a toroidal configuration distinguishes itself by toroidal multiplets of particle-hole excitations between one toroidal shell to another. Subject to further confirmation, the Hoyle state and many of its higher excited states may be tentatively attributed to those of a $^{12}$C nucleus in a toroidal configuration.