Symmetry and quantization of the two-skyrmion system: The case of the deuteron

In the Skyrme model for strong interactions we study two skyrmions at a fixed distance in the field configuration of minimum classical energy. The exact field configurations in three spatial dimensions are obtained by a numerical relaxation procedure. The hamiltonian is quantized semiclassically by introducing collective coordinates for the relative and rotational motion. It is found that the exact fields have more symmetry than those obtained from the "product ansatz" of minimum energy. This imposes restrictive selection rules on the quantum states. We obtain a nondegenerate ground state with the quantum numbers of the deuteron and a binding energy close to zero.