Are Neutrons and anti-Neutrons attracted to each other over distance?

Question

Lets create a scenario where you have a total vacuum and you're shooting into this vacuum two streams, one, a Neutron stream and the other an anti-Neutron stream and because you're curious what will happen, you cross the streams, so they touch (well, at least according to our the neutron/anti-neutron gun sites, but on a quantum level, they rarely get close, lets say, 10 nano-meters is the average distance between particle and anti-particle, a very small distance in most cases but a large distance between 2 particles.

Now, I know that some of the Neutrons would decay into protons and positrons, and this would at least happen to some of the Neutrons very quickly, but lets ignore that, or, lets pretend this is done inside a huge magnet that pulls any charged particles far away, so all we have to worry about is Neutrons and Anti-Neutrons passing each other.

I read in this question that the wave functions of the Neutron and anti-Neutron could interact and this could in theory happen at any distance though in practice, it's much more likely to happen when close.

My question is, any Neutron-antiNeutron interaction would probably need to happen via the strong force, which is very short range, but in theory, the up and down quarks and an anti-quark's in the Neutron have wave functions which creates some uncertainty on their precise location so interaction could happen at greater distance.

My question is, in general, how close would a Neutron and anti-Neutron have to get to each other to show some kind of attractive force to each other. Would the two streams in this hypothetical example fly past each other with minimal interaction or would there be a nice explosion of gamma-rays as the streams cross, a kind of inverse Pauli exclusion principal that would draw them together and how close would they need to be for that to happen a fair percentage of the time, like say, about 50% conversion per second (A second being a long time for a sub-atomic particle)? I realize precise calculations might get long, I'm just looking for a kind of roughly correct simply explained answer.

Related, but what about hydrogen and anti hydrogen streams. I imagine, because of the Electrons and Positrons those particle/antiparticle streams would interact with each other at significantly greater distance.

This question which got closed got me thinking about this. I don't think there's any attraction but reading the other question there seems to be some wave function interaction which once started, creates a charged attraction.

What this implies to me is, if you have a piece of Iron and anti-Iron, several feet apart and separated by a vacuum, as the electrons and positrons might begin to evaporate with each other at a distance, the matter and anti-matter would grow opposite charges and the attraction would then draw them together. Initially they would only be attracted to each other by gravity but at a certain distance (not sure how close) an electromagnetic attraction would form between them together faster and that could look a lot like an attractive force between matter and anti-matter when it's really just electromagnetic attraction.

Answer 1

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?.

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.