  By the quenched lattice QCD simulation for two nucleons with finite
scattering energy, validity of the delivative expansion of the general
nucleon-nucleon potential U(r,r') = V(r, {\nabla}_r) \delta^3(r-r') is studied.
The relative kinetic energy between two nucleons is introduced through the
anti-periodic boundary condition in the spatial directions. On a hypercubic
lattice with the lattice spacing a ~ 0.137 fm and the spatial extent L_s ~ 4.4
fm with the pion mass m_{\pi} ~ 530 MeV, the local potentials for two different
energies (E ~ 0 MeV and 45 MeV) are compared and found to be identical within
statistical errors, which validates the local approximation of U(r,r') up to
E=45 MeV for the central and tensor potentials. Central potentials in the
spin-singlet channel for different orbital angular momentums (l=0 and l=2) at E
~ 45 MeV are also found to be the same within the errors, which also supports
the local approximation.
