Calculation of relativistic nucleon-nucleon potentials in three dimensions

In this paper, we have applied a three-dimensional approach for the calculation of the relativistic nucleon-nucleon potential. The quadratic operator relation between the non-relativistic and the relativistic nucleon-nucleon interactions is formulated as a function of relative two-nucleon momentum vectors, which leads to a three-dimensional integral equation. The integral equation is solved by the iteration method, and the matrix elements of the relativistic potential are calculated from non-relativistic ones. The spin-independent Malfliet-Tjon potential is employed in the numerical calculations, and the numerical tests indicate that the two-nucleon observables calculated by the relativistic potential are preserved with high accuracy.