An alpha particle model for Carbon-12

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 C which has a graph-like structure. We use ideas from quantum graph theory in order to make sense of quantum mechanics on 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.