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For calculation of the single-channel nucleon-nucleon scattering a phase-functions method has been proposed. Using a phase-functions method the following phase shifts of a np- scattering numerically for 1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-, 1F3-, 3F3-, 1G4-, 3G4- states are calculated. The calculations has been performed using realistic nucleon-nucleon potentials Argonne group (Av18, Av14sscc, Av8’, Av8’sscc, Av6’, Av4’, Av2’). Obtained phase shifts are in good agreement with the results obtained in the framework of other methods. Using the obtained phase shifts we have calculated the full cross-section np- scattering.

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