An Alpha Particle Model for Carbon-12

TL;DR

This paper presents a novel deformable body model for Carbon-12 based on Skyrme theory, incorporating quantum graph methods to compute its energy states and explore new nuclear configurations.

Contribution

Introduces a deformable Skyrmion model for Carbon-12 using quantum graph theory, advancing beyond rigid body approximations.

Findings

Computed new energy levels for Carbon-12

Identified several novel nuclear states

Demonstrated the applicability of quantum graph methods

Abstract

We introduce a new model for the Carbon-12 nucleus and compute its lowest energy levels. Our model is inspired by previous work on the rigid body approximation in the $B=12$ sector of the Skyrme model. We go beyond this approximation and treat the nucleus as a deformable body, finding several new states. A restricted set of deformations is considered, leading to a configuration space $\mathcal{C}$ which has a graph-like structure. We use ideas from quantum graph theory in order to make sense of quantum mechanics on $\mathcal{C}$ even though it is not a manifold. This is a new approach to Skyrmion quantisation and the method presented in this paper could be applied to a variety of other problems.