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We compare three methods to calculate the nucleon-nucleon t-matrix based onthe three-dimensional formulation of J. Golak et al., Phys. Rev. C 81, 034006,(2010). In the first place we solve a system of complex linear inhomogeneousequations directly for the t-matrix. Our second method is based on iterationsand a variant of the Lanczos algorithm. In the third case we obtain thet-matrix in two steps, solving a system of real linear equations for thek-matrix expansion coefficients and then solving an on-shell equation, whichconnects the scalar coefficients of the k- and t-matrices. A very goodagreement among the three methods is demonstrated for selected nucleon-nucleonscattering observables using a chiral next-to-next-to-leading-orderneutron-proton potential. We also apply our three-dimensional framework to thedemanding problem of proton-proton scattering, using a corresponding version ofthe nucleon-nucleon potential and supplementing it with the (screened) Coulombforce, taken also in the three-dimensional form. We show converged results fortwo different screening functions and find a very good agreement with othermethods dealing with proton-proton scattering.

Different Methods for the Two-Nucleon T-Matrix in the Operator Form