Nucleon-nucleon interactions in a three-dimensional momentum helicity representation

Partial wave (PW) decomposition approaches have been widely used in the few-body calculation. After truncation, a PW representation leads to coupled equations on angular momentum quantum numbers. The complexity of modern few-nucleon interactions with a different spin, isospin, and angular momentum combinations, demands avoiding a partial wave representation completely and working directly with vector variables by replacing the discrete angular momentum quantum numbers with continuous angle variables. Such a non-PW method is called a three-dimensional (3D) approach. To this aim, the nucleon-nucleon (NN) interactions are formulated in momentum-helicity basis states and obtained by adding the corresponding partial wave components to a desired total NN angular momentum. In our numerical study, the matrix elements of CD-Bonn potential are calculated in a 3D scheme and tested for deuteron binding energy and neutron-proton scattering. The 3D form of CD-Bonn interaction reproduces the PW results with very high accuracy and are in excellent agreement with experimental data.