Neutrons and anti-neutrons repel each other with a Yukawa force mediated by pion exchange. The range of the force is determined by the mass of the pion, and is up to around 3 femtometres. This is only a few times the diameter of a neutron, so this is a very short range force. Luboš Motl gives a characteristically excellent description of the physics involved in his ansser to Is the long range neutron-antineutron interaction repulsive or attractive?Is the long range neutron-antineutron interaction repulsive or attractive?.
The Yukawa force is unrelated to the annihilation mechanism. For annihilation the neutron and antineutron wavefunctions need to overlap, which basically means their centres need to get within a femtometre of each other.
As a general rule the wavefunctions describing quantum objects decay exponentially with distance at long range. This means they decay rapidly and beyond a few particle radii have essentially decreased to nothing. Although in principle annihilation is possible at many times the particle radius the timescales for this are unrealistically long, so long range annihilation can be ignored.