Comparison of approximation methods in one-dimensional many-body scattering theory

The Glauber approximation, the optical potential method, and the resonating group method are applied to McGuire's scattering problem for which the exact solution is known. This one-dimensional problem deals with N particles of the same mass, interacting via a two-body delta function potential. The parameters of the model are chosen so that it simulates nucleon–nucleus scattering. When the 'finite N correction' is included, the optical potential method is found to be remarkably accurate, even at low energies. The validity of the optical potential and resonating group methods for the bound state is also examined.