Attractive Channel Skyrmions and the Deuteron

Abstract

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 $-Δ+V$, where $Δ$ 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.