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After reading this article regarding Positronium BEC formation (for lasing purposes), there is a mention in there regarding Ps "up" atoms not annihilating with "down" atoms, the article is pretty vague about it and does not give much details, but i presume it is referring to the +1 and -1 polarizations of orthopositronium (J=1) excitation in a magnetic field.

Is there a known reference for the exact annihilation rates/cross sections/etc for Ps of the same type? certainly if one could put a condensate of positroniums of the same type and not having them annihilate each other at all or a very low rate, it would be a big deal for the future of space propulsion

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Not an answer, just a hint, but this is a bose-to-bose system, namely positronium effective field to photon field, so it is just a classical problem with effective parameters. I don't know an estimate for the parameters, hence not an answer. – Ron Maimon Sep 14 '12 at 2:44
    
This presentation discusses lifetimes neutrino.ethz.ch/Positron/talks/PhDsem2002c.pdf . The electron and positron of the positronium annihilated very fast with the electromagnetic interaction, so forget future space propulsions. – anna v Jun 22 at 7:54

Positronium is an exotic species composed of positron and electron. Depending on the allignment of the spins of postron and electron, the total spin of the positron can be zero or 1 (for the ground state for which l=0) and are designated as: ^1S (para-positronium) and ^3S (orto-positronium)

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i hope it is refering to ortho and para- components of positronium. When ortho -positronium collides with a para-positronium, they annihilate to give gamma photons. – Ishfaq Hassan Jun 21 at 11:58

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