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 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.

Automated summary

The matrix elements of relativistic nucleon-nucleon (NN) potentials are calculated directly from nonrelativistic potentials without partial wave decomposition. An iterative method is used to solve the integral equations for two-nucleon (2N) spin-singlet and spin-triplet states. Numerical analysis shows high accuracy in reproducing deuteron binding energy and neutron-proton elastic scattering using the relativistic NN potential obtained with CD-Bonn potential.