Low energy nucleon-nucleon scattering with the Skyrme model in the geodetic approximation

We calculate nucleon-nucleon scattering at low energies and a large impact parameter in the Skyrme model within the framework for soliton scattering proposed by Manton. This corresponds to a truncation of the degrees of freedom of the 12 collective coordinates which essentially describe the rigid body motion of the pair of Skyrmions. We take to its logical conclusion the result that the induced kinetic energy for these collective coordinates in the product ansatz behaves as one over the separation and hence can dominate over the potential. This behavior implies to leading order that we can drop the potential, and the resulting motion reduces simply to geodesic motion on the manifold parametrized by the variables of the product ansatz. We formulate the semi-classical quantization of these variables to obtain the motion corresponding to the nucleonic states of the Skyrme model. This is the appropriate description for the nucleons in order to consider their scattering within Manton's framework in the semiclassical approximation. We investigate the implications for the scattering of nucleons with various initial polarizations using the approximation method of the ''variation of constants.''