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Particularly, in range of 0.5-3 MeV. I'm talking about situations, when a single atom encounters gamma photon.

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    $\begingroup$ Sounds impractical, since muons have a mean lifetime of 2.2 μs. $\endgroup$ Commented Apr 12 at 10:58
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    $\begingroup$ Well, obviously. I am still interested in theoretical answer, though. $\endgroup$ Commented Apr 12 at 11:01
  • $\begingroup$ What does “effectively” mean? Do you mean the muon atom will absorb the gamma better than the same atom with electrons. Or at all? $\endgroup$ Commented Apr 12 at 11:18
  • $\begingroup$ @kangermu I mean better. Atom will sometimes absorb gamma photons either way since nucleus could do it too, question is how likely will it do so. $\endgroup$ Commented Apr 12 at 11:57
  • $\begingroup$ @PM2Ring is that lifetime for free or bound muons? $\endgroup$ Commented Apr 18 at 21:50

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As a general rule the lighter a charged particle is the greater the scattering cross section for EM radiation. For example in Thomson scattering the cross section is proportional to $1/m$. That means muonic matter would be around $200$ times less effective at scattering x-rays than normal matter.

However scattering is strongest when the x-ray energy matches the K edge of the atom doing the scattering, and for normal matter ehe K edge energies are well below $1$ MeV. Muonic atoms are much more strongly bound so they can have K edges in the $1 - 3$ MeV range and for x-ray energies matching the muonic atom K edge the scattering would be enhanced. Whether this would make the scattering stronger than the scattering from normal matter I cannot say as I have never seen the calculation done.

So in general, no, muonic matter would not effectively scatter gamma rays or at least not compared to regular matter. But it's possible K edge scattering from muonic matter could be greater at energies above $1$ MeV.

Your question asks about scattering per atom but for completeness we should consider that muonic matter would be denser than normal matter so it would contain more scattering centres per unit volume. I would guess that the size of an atom scales approximately as the Bohr radius, and the Bohr radius is inversely proportional to the reduced mass. That means the atom number density would scale as $m^3$ so the scattering per unit volume would scale as $m^2$. This would make muonic matter around $40,000$ times more effective at scattering x-rays per unit volume.

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  • $\begingroup$ However, the muons should do little to the nuclear transitions that would lead to absorption. $\endgroup$ Commented Apr 12 at 12:42
  • $\begingroup$ I hadn't considered nuclear transitions as I'm pretty confident the scattering from electrons would be much greater. For nuclear transitions I guess the scattering per unit volume would be greater as you'd have more nuclei per unit volume for muonic matter. $\endgroup$ Commented Apr 12 at 12:47
  • $\begingroup$ Well, the question is about absorption… But yes, the scattering will be the dominant interaction. $\endgroup$ Commented Apr 12 at 12:49
  • $\begingroup$ For density, the radius of orbitals would be much smaller for muons. So bond lengths would be smaller. Each atom would be smaller, but space would still be filled with atoms. I would think that scattering from a layer of atoms in a crystal would be somewhat similar to normal matter, but there would be many more layers per meter. So my guess is muonic matter would scatter more. $\endgroup$ Commented Apr 12 at 12:55
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    $\begingroup$ I thought that difference in energy levels between muon orbitals would be high enough that gamma rays could be absorbed in similar ways visible light absorbed and re-emitted by normal atoms, no? $\endgroup$ Commented Apr 12 at 13:21

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