Can an orbiting electron/positron ensemble be in an excited spin-2 state? Is orbital AM still quantized in units of [math]\hbar[/math]? It seems the latter answer is yes, as you could say the particles orbit about a common center, so the problem is not so different from a massive atomic center.

You can't get spin-2 form two spin 1/2 particles. Orbital AM is quantized as you suspect.

 

The energy states are basically half the value of hydrogen, as you'd expect from a classical system orbiting their common center of mass.

Thanks, I shall ponder... OK, can't this state be excited by absorbing a photon, say, to level spin-2? I am imagining the particle spins parallel and an orbital vector parallel also. Don't we go up in angular momentum quantum numbers with excited energy levels? [Tell me current notations.]

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Sometimes the terms 'ortho' and 'para' are used to refer to relative spins. I am asking about a parallel particle spin state with unit orbital AM also.

Edited March 23, 200916 yr by Norman Albers
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Spin, no. Angular momentum, yes. The normal notation is J = L + S and F = J + I (in atomic systems I is the nuclear spin), and I'm not sure id any special notation would be used in positronium, so I'll assume the total angular momentum is F. So you should be able to end up with an F = 2 system, just as in normal Hydrogen (though AFAIK in positronium this angular angular momentum would not be associated with just the electron, as it is in Hydrogen)

Ah yes, after cleaning up my terminology this makes sense.