Attractive Channel Skyrmions and the Deuteron

The deuteron is described as a quantum state on a ten-dimensional manifold M 10 of Skyrme fields of degree two, which are obtained by calculating the holonomy of SU (2) instantons. The manifold M 10 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 −∆ + V , where ∆ is the covariant Laplace operator on M 10 and V is the potential which M 10 inherits from the Skyrme potential energy functional. Quantum states are complex-valued functions on the double cover of M 10 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 deuteron's electrostatic and magnetostatic properties are also calculated and compared with experiment.