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I was reading this wikipedia article on positronium (a type of exotic atom) and noticed it mentioned that positronium has a spectra (of course).

So naturally this makes me wonder, have we looked at stars or other glowing objects to try to detect spectra of exotic atoms? It seems plausible to me that there would be extremely faint but non-0 spectra of these exotic atoms within the stars, or maybe in the center of the galaxy.

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    $\begingroup$ Cool question! Potentially interesting in Chemistry SE is this answer to What is a "hydrogen-like" or "hydrogenic" atom? One certainly sees annihilation photons from e+/e- pairs, certainly some come from decay of positronium, but I think that you are asking about electromagnetic transitions between bound states only (final state is still an exotic atom of some sort)? $\endgroup$
    – uhoh
    Commented Sep 3, 2022 at 2:05

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Yes, we look into stellar spectra searching for whatever exotics. This way new elements were discovered (helium, in solar chromosphere), exotic states of other elements not studied well in terrestrial conditions (e.g. coronium, https://en.wikipedia.org/wiki/Coronium).

Regarding positronium, it is short-lived, and is not accumulated in sufficient amounts to yield readily observable spectral features. The positronium decay $\gamma$-quanta (511 keV line) $are$ observed (near the galactic center in particular; in pulsar spectra, etc.) Estimates for observing lines corresponding to transitions between different bound states of positronium are not very promising; e.g. https://ui.adsabs.harvard.edu/abs/1996A%26AS..120C.365B/abstract

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