Magnetic monopole bound state Magnetic monopole (mm) bound states  
Background: I'm an experimentalist, simple equations are appreciated. 
(Complicated equations are fine, as long as I can ask questions.) 
This is one of many nice question on mm's.
When I heard years ago that magnetic monopoles had never (maybe once) been detected, I thought the answer might be magnetic atoms.  If mm's exists then they should come in both poles, and then get themselves bound into magnetic atoms.
First question:  What are magnetic monopole bound states called?  Certainly someone has figured this out.  
Second question:  What's the size of the magnetic pole, or what is the energy of the magnetic bound state.  Is the energy the same as the Rydberg?  (With a different mass.)  
A mm bound state seems like it might be a dark mater candidate.   Is anyone looking for them?
(something like the x-ray absorption spectra through areas with mostly dark mater.) 
Additional information.  I found this on the web.
http://www-spires.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-2497.pdf
Which does answer many of my question.  
The coupling for magnet monopoles would be very strong!
Not alpha (the fine structure constant), but as 1/alpha!  
Does anyone know of other similar papers?    
OK and now I'm getting confused.  If the magnetic atom has 
such a big binding energy, then the mass of the "atom" could be much less than the sum of the masses of the two magnetic monopoles.  (I'm assuming that the monopole mass has to be bigger than the maximum energy of CERN, else they would have seen monopoles already.)  
Are there any limits on the dark matter WIMP masses?   
Edit: More questions generated by answers. (to Timaeus)
I'm afraid that I only know enough to ask rather naive questions.
Of course a monopole is going to have other properties.
Beside mass, can it be a lepton or baryon?  Perhaps it has an electric dipole moment to go along with it's magnetic "charge".  Does it also have to have an electric charge?  All that seems fine.  Now I'm picturing this "magnetic atom" being like the hydrogen atom.  So that even if each magnetic monopole does have to have an electric charge, the composite atom can be neutral.  (each of it's pieces has equal but opposite charge) 
The magnetic binding energy also seems to be very large.  (Did you read the Slac article?)  To me that means that to create a monopole pair in a beam smasher, one is going to need not only twice the mass energy, but also the binding energy of the monopole - anti monopole pair.  (which could be huge?  Can the binding energy be bigger that than the mass energy?)  Mind you I'm not talking about a magnetic atom here, but something similar to an electron - positron pair.   
Finally I was reading about gamma rays from dark matter areas.  Could these be due to emissions from "magnetic" atoms?  There is no law that says dark matter has to be totally dark.. it could just be shinning at some wavelength/ energy that we haven't looked at yet.          
 A: The magnetic atom you are talking about is called monopolium. (that's the answer to your first question).
It is correct that the monopolium binding energy might be very large. People have attempted to compute it, but such calculations are inherently unreliable because the Dirac magnetic charge is so large (equivalent to 68.5e), which makes the coupling of the monopole to the photon too large to allow for a perturbative expansion to converge. This makes it very difficult to provide a definitive answer: this is a matter which would need to be settled by experiment (if monopoles exist and there are possibilities to study them in a laboratory). 
A: A magnetic monopole isn't a particle any more than an electric monopole is a particle.
Some particles have a net electric charge and so are monopole source terms.
If the electron had a magnet charge then since it also has an electric charge you could do a duality rotation between electric fields and magnetic fields and have it instead be purely electric charge.
So if you actually want to have a particle with a nonzero magnetic charge you need a particle with a different ratio of magnetic charge to electric charge. Different than the known existing particles.
As for this being dark matter, its not going to be dark if it has an electromagnetic charge.

An electric monopole is an electron or positron, No? Are you saying an electron is not a particle?

Electrons have an electric charge, so do positrons, muons, antimuons, tauons, antitauons; up, down, strange, charm, top, and bottom quarks and their antiparticles (and each one of the three colors). As do the W+ and W- bosons. And each of those particles also has a mass and other types of charge. They aren't just an electric monopole sitting there with no other properties.
So one can't run around asking what the electric monopole ground states are, since positronium has different bound states than a bound muon-antimuon pair and so forth.
The main thrust of my answer is that the key to being forced to have magnetic monopole source terms in our theory is to have objects with different ratios of electric charge over magnetic charge. So by electromagnetic duality between electric and magnetic fields which particles have magnetic charge will depend on having ones with different ratios and then a choice within the duality.
So it very much does not point to a specific particle being the lone object with magnetic charge. Once you have both electric and magnetic charge there is some inherent ambiguity in what you call electric fields and what you call magnetic fields.
Right now we call the field with monopole source terms an electric field. If there are monopoles of different ratios we won't be able to force one of the fields to have no sources and hence we just have to randomly call something magnetic or something electric.
Much like calling an electron matter and the positron antimatter. That word and name is arbitrary. And so would the word electric in a world with different ratios of charge.

(I'm assuming that the monopole mass has to be bigger than the maximum energy of CERN, else they would have seen monopoles already.)

Maybe we have seen them already. That was my whole point. So if duality wasn't enough then what if, say, some known particles have magnetic charge but the value of the charge was super tiny. How are you going to know if it was in a very very unstable particle and had a very very very tiny charge.

Of course a monopole is going to have other properties.
  Beside mass, can it be a lepton or baryon?

Or even a whole new type. Which can affect the binding energy if it has a new charge (color for the strong interaction is a different kind of charge). So how could you just compute a binding energy without knowing all these other properties?
Just like you can't compute the binding energy of an "electric monopole" since hydrogen and positronium and muonium and muonic hydrogen and so on all have different binding energies.

Now I'm picturing this "magnetic atom" being like the hydrogen atom. So that even if each magnetic monopole does have to have an electric charge, the composite atom can be neutral. (each of it's pieces has equal but opposite charge)

But since the particles with the charge can have other charge and can have various mass, the binding energy could have a range of values.

The magnetic binding energy also seems to be very large. (Did you read the Slac article?)
To me that means that to create a monopole pair in a beam smasher, one is going to need not only twice the mass energy, but also the binding energy of the monopole - anti monopole pair. (which could be huge? Can the binding energy be bigger that than the mass energy?)

You have it backwards. A hydrogen atom has less energy than the sum of the energies of the electron and the proton. So producing a bound state requires less energy than producing the parts.

Mind you I'm not talking about a magnetic atom here, but something similar to an electron - positron pair.

That's why I brought up positronium.

Finally I was reading about gamma rays from dark matter areas. Could these be due to emissions from "magnetic" atoms? There is no law that says dark matter has to be totally dark.. it could just be shinning at some wavelength/ energy that we haven't looked at yet.

If dark matter can radiate, then it can lose orbital angular momentum and then why does it stay in the arrangements of diffuse haloes instead of contracting into compact objects and clumping the way regular matter does.
Sure there might be room for a small amount of not really dark matter (you could call it faint matter) but wouldn't we still need dark matter? And indeed if it turns out that dark matter is made out of thousands of new particles with thousands of new charges and different properties it might be hard to learn about them.
Even worse. If they have different properties and new charges and could be streaming through earth they could be affecting our particle accelerator experiments in a way to prevent pairs (say if a strongly charged river flows through earth with one of these new charges, then it might prevent particle antiparticle pairs with this new charge from forming) and so they could even have a low mass.
This is wildly speculative at this point unless you have a reason to say there should be a specific particle with specific properties or else if the actual concern is dark matter you should be looking at what the evidence says the particle should have as properties. So focus on the observational results or the theoretical principles.
But if you are interested in faint matter there are many possibilities but you need to start with a reason. For instance at Lawrence Livermore National Lab they started with the idea of explaining the equality of matter and dark matter abundance along with a quark confinement type interaction in  Direct Detection of Stealth Dark Matter through Electromagnetic Polarizability if it had a very small magnetic charge too that probably wouldn't change things very much, but it wouldn't be the reason it acts the way it does.
A: I would think tightly bound monopolism would have a huge wave function at the origin and quickly decay in a blaze of glory.
What would stabilize it?
Also would it residual interactions be small enough not be seen in dark matter searches. And if it decayed to two photons (but not too fast) there'd be a nice line we could see with Fermi Gamma-ray Space Telescope.
