Can neutronium, (as in the exotic -onium atom composed of $n\bar n$ and not the degenerate matter kind) exist?

Question

First off I'd like to say yeas I know what neutron-degenerate matter aka neutronium is and how it's likely what's inside neutron starts, this isn't what the wuestion is abount. I am referring to an -onium atom made of a neutron and anti-neutron, or neutr-onium.

We have produced positronium ($e^+e^-$) and pionium ($\pi^+\pi^-$) both of which are exotic atoms composed of a particle and its antiparticle and have predicted true muonium ($\mu^+\mu^-$) and protonium ($p\bar p$). But what about $n\bar n$ or using IUPAC nomenclature neutronium (or perhaps true neutronium considered how the namespace collision between muonium and true muonium was dealt). Is it a possible bound state? Initially it seems no since you need some force to bind them and both the neutron and anti-neutron are neutral so unless one is willing to accept an incredibly slow binary orbit mediated by gravity as abound state the answer seems no. But neutrons are not truly neutral particles but composite particles which gives us some options. So going by forces

1. Gravity, already noted and probably negligible at this scale,

2. Electromagnetism

   2a. Magnetic fields. neutrons have a magnetic moment meaning is both the neutron and antineutron spin the same way they should generate opposing dipole moments which should generate an attractive force as each pole sees an opposite pole whose pull is only mostly cancelled out by the slightly farther same pole.

   2b. Electric fields. Not sure, maybe there might be polarization of the nearby vacuum and of the positions of the three quarks inside each neutron but I'm not completely sure.

3. Weak force. Yukawa interactions involving W and Z bosons might generate some force but unless the distance between the two is very small it's probably negligible.

4. Strong force. The big one and the one I don't have much of a clue about. Protonium is already expected to interact mainly though the strong force so it makes sense to assume it would be the same for neutronium. It shouldn't even differ that much from normal neutron-neutron interaction except that if one neutron sends a charged carrier meson the other neutron would receive its charge conjugate instead, because the other neutron is actually an antineutron.

All of the above leads me to think that neutronium($n\bar n$) might be possible but no idea if it actually is, hence why I'm asking this question. So is neutronium possible and if so is it possible for us to predict any of its properties even approximately? In addition I'd be appreciative of any links to papers that properly focus on neutronium, my own research only found it being mentioned as something that might possibly mix states with protonium, always a sidenote at best but I might've missed something.

Answer 1

From wikipedia:

Protonium (symbol: Pn), also known as antiprotonic hydrogen

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Protonium has a mean lifetime of approximately 1.0 μs

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Unlike the hydrogen atom, in which the dominant interactions are due to the Coulomb attraction of the electron and the proton, the constituents of protonium interact predominantly through the strong interaction. Thus multiparticle interactions involving mesons in intermediate states may be important. Hence the production and study of protonium would be of interest also for the understanding of internucleon forces.

To start with the hydrogen atom is the best studied quantum mechanically solution of the coulomb potential, i.e. the electromagnetic interaction. Substituting a heavier negatively charged particle in the potential, gives solutions for the orbitals that have a small radius, due to the excess mass. In the case of the muonium the orbitals are still far away from the proton. In the case of the protonium its orbitals overlap with the orbitals of the proton, hence the " predominantly through the strong interaction".

Now a bound state of neutron antineutron, should not be called with an "onium" ending , because it does not have a hydrogen type solution for the orbitals, as there is no 1/r coulomb potential. The elecromagnetic effects you are discussing are already very weak as they are second order effects, and the coupling constant of 1/137 would make any effect a fine structure to the structure that the strong interaction will impose on antineutron-neutron.

I found this paper ( link to Arxiv version ) discussing antineutron-neutron scattering that might interest you. If a good experiment of antineutrons on protons at low energy could be designed your "neutronium" would appear as a resonance at a very low energy in the scattering crossection.