NN scattering formulations without partial-wave decomposition

Recently a new three-dimensional (3D) formulation for scattering of two spin-half particles, either identical or unidentical, is presented. In the formulation the free linear-momentum states are not expanded into the angular-momentum states and the system's spin and isospin states, respectively, are described by the product of the spin and isospin states of the two particles. We apply this technique to calculate nucleon-nucleon (NN) scattering. But as NN interaction models are usually being parametrized regarding to the NN total isospin, we take the total isospin state, instead of the product of the isospin states of the two nucleons, as part of the 3D basis state. We evaluate the Lippmann-Schwinger equations for NN T-matrix elements in these 3D basis states and end up with a set of coupled integral equations for the NN T-matrix elements in two variables, namely the magnitude of the relative momentum and the scattering angle. We show as an example the spinaveraged differential cross section, which can be calculated directly from the solution of the set of the integral equations. The recently developed 3D formulation also introduces a set of six spin operators to express any interaction of two spin-half particles. We show the Bonn NN potential in terms of these six spin operators.