A realistic three-dimensional calculation of relativistic nucleon-nucleon interactions

The matrix elements of relativistic nucleon-nucleon interaction are calculated directly in terms of momentum vectors, without using a partial wave decomposition. The quadratic operator relation between the relativistic and non-relativistic nucleon-nucleon ($NN$) interactions is formulated in momentum-helicity basis states. The non-linear relation leads to a single integral equation for total $NN$ spin $s=0$ and two coupled integral equations for $s=1$, which are solved by the iteration method. The input for the calculations are non-relativistic nucleon-nucleon interactions and two different models of realistic $NN$ interactions, i.e. Bonn-B and AV18, are used. The numerical tests indicate that the $NN$ observables calculated by the relativistic $NN$ interactions are preserved with high accuracy.