Relativistic nucleon-nucleon potentials in a spin-dependent three-dimensional approach

The matrix elements of relativistic nucleon-nucleon $(NN)$ potentials are calculated directly from the nonrelativistic potentials as a function of relative $NN$ momentum vectors, without using a partial wave decomposition. To this aim, the quadratic operator relation between the relativistic and nonrelativistic $NN$ potentials is formulated in momentum-helicity basis states. It leads to a single integral equation for the two-nucleon $(2N)$ spin-singlet state and four coupled integral equations for two-nucleon spin-triplet states, which are solved by an iterative method. Our numerical analysis indicates that the relativistic $NN$ potential obtained using CD-Bonn potential reproduces the deuteron binding energy and neutron-proton elastic scattering differential and total cross-sections with high accuracy.