  The scattering lengths and effective ranges that describe low-energy
nucleon-nucleon scattering are calculated in the limit of SU(3)-flavor symmetry
at the physical strange-quark mass with Lattice Quantum Chromodynamics. The
calculations are performed with an isotropic clover discretization of the quark
action in three volumes with spatial extents of L \sim 3.4 fm, 4.5fm and 6.7
fm, and with a lattice spacing of b \sim 0.145 fm. With determinations of the
energies of the two-nucleon systems (both of which contain bound states at
these up and down quark masses) at rest and moving in the lattice volume,
Luscher's method is used to determine the low-energy phase shifts in each
channel, from which the scattering length and effective range are obtained. The
scattering parameters, in the 1S0 channel are found to be m_pi a^(1S0) =
9.50^{+0.78}_{-0.69}^{+1.10}_{-0.80} and m_pi r^(1S0) =
{4.61^{+0.29}_{-0.31}^{+0.24}_{-0.26}, and in the 3S1 channel are m_pi a^(3S1)
= 7.45^{+0.57}_{-0.53}^{+0.71}_{-0.49} and m_pi r^(3S1) =
3.71^{+0.28}_{-0.31}^{+0.28}_{-0.35}. These values are consistent with the
two-nucleon system exhibiting Wigner's supermultiplet symmetry, which becomes
exact in the limit of large-N_c. In both spin channels, the phase shifts change
sign at higher momentum, near the start of the t-channel cut, indicating that
the nuclear interactions have a repulsive core even at the SU(3)-symmetric
point.
