Attractive channel Skyrmions and the deuteron Original Research Article

The deuteron is described as a quantum state on a ten-dimensional manifold M10 of Skyrme fields of degree two, which are obtained by calculating the holonomy of SU(2) instantons. The manifold M10 includes both toroidal configurations of minimal energy and configurations which are approximately the product of two Skyrmions in the most attractive relative orientation. The quantum Hamiltonian is of the form −Δ + V, where Δ is the covariant Laplace operator on M10 and V is the potential which M10 inherits from the Skyrme potential energy functional. Quantum states are complex-valued functions on the double cover of M10 satisfying certain constraints. There is a unique bound state with the quantum numbers of the deuteron, and its binding energy is approximately 6 MeV. Some of the deuteronʹs electrostatic and magnetostatic properties are also calculated and compared with experiment.