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   Abstract 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 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 (2 N ) 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. 

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