An Alpha Particle Model for Carbon-12

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.

New figures added. Revised version to appear in Nuclear Physics A

References in corpus (4)

• Structure and rotations of the Hoyle state
• Evidence for Triangular D_3h Symmetry in 12C
• A dynamical $\alpha$-cluster model of ${}^{16}$O
• States of Carbon-12 in the Skyrme Model

Cited by in corpus (16)

• Vibrational modes of Skyrmions
• Exploring the generalized loosely bound Skyrme model
• Oxygen-16 Spectrum from Tetrahedral Vibrations and their Rotational Excitations
• Realistic classical binding energies in the $\omega$-Skyrme model
• Coriolis terms in Skyrmion Quantization
• Rolling Skyrmions and the Nuclear Spin-Orbit Force
• ADHM skyrmions
• Dielectric Skyrmions
• A consistent two-skyrmion configuration space from instantons
• The Inevitability of Sphalerons in Field Theory
• Electromagnetic transition rates of Carbon-12 and Oxygen-16 in rotational-vibrational models
• Finkelstein-Rubinstein constraints from ADHM data and rational maps
• Nudged Elastic Bands and Lightly Bound Skyrmions
• Compressibility of dense nuclear matter in the $\rho$-meson variant of the Skyrme model
• Quantization of skyrmions using instantons
• A dynamical Interpretation of Sequential Decay in Reactive Scattering