Energy dependence of nucleon-nucleon potentials

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We investigate the energy dependence of potentials defined through the Bethe-Salpeter wave functions. We analytically evaluate such a potential in the Ising field theory in 2 dimensions and show that its energy dependence is weak at low energy. We then numerically calculate the nucleon-nucleon potential at non-zero energy using quenched QCD with anti-periodic boundary condition. In this case we also observe that the potentials are almost identical at E≃ 0 and E≃ 50 MeV, where E is the center of mass kinetic energy.