Reactions of captured muons with nuclei

[shelanachium]

I read many years ago that muons captured by nuclei with Z>10 react with these nuclei faster than their simple decay. In other words, such reactions as muon + Fe-56 --> Mn-56 + muon-neutrino are faster than the simple decay of the muon to electron, muon-neutrino and electron-antineutrino.

I expected this reaction, which is analagous to EC as in Be-7, because the muon orbits much closer to the nucleus than an electron (and in high-Z nuclei the muon orbital is largely within the nucleus); also the energy available to drive this reaction is of the order of 100 Mev, not the few Mev available to drive EC reactions.

Yet my internet search on muonic atoms has turned up no mention of such reactions. Am I mistaken?

I am interested because if muons do react with heavy nuclei, traces of noble gases should appear through muon interaction with the lightest stable isotopes of Sr and Ba in minerals of these; if these isotopes capture muons the resulting Rb and Cs nuclides largely decay to Kr and Xe:

Sr-84 + muon ---> Rb-84 + muon-neutrino; then most of Rb-84 decays by beta+ or EC to Kr-84.

Analagous reactions with Ba-130 and Ba-132 should generate Xe-130 and Xe-132.

 

[eys_physics]

I think you are correct in your reasoning.
You can find some information about decays of muonic atoms in the following article (if you have access to it)

Eur. Phys. J. C47, p. 336 (W. Bertl et al.)

The muon-capture rate (MC) according to that reference grows as Z^4.

Muonic atoms are often used to study different properties of nuclei (for example radii) and hyperfine structure. But I don't see why you are interesting in creating noble gases this way. You know that muonic atoms decay by for example with muon-capture so in some way I don't understand your question for these type of experiments.

 

[shelanachium]

Muon Capture by heavy nuclei

Many thanks for reference, should be able to find in University Library.

I am not interested in making noble gases from Sr and Ba minerals but in seeing if Nature does so through muons in secondary cosmic rays. The amount of Kr and Xe accumulated could give a crude estimate of the age of the minerals, or if this is already known, whether or not there has been any notable change in cosmic-ray flux since they formed - though obviously the muon flux will depend on the depth of the mineral; low capture at shallow depths (muons too energetic for capture) and at great depths most will already have been captured or decayed.

Because of the geological activity of the Earth, the depth of the mineral could have changed radically over time; lunar and martian samples from known depths might be more informative.

Ru-containing minerals should also contain traces of long-lived Tc-98 and 99 from muon capture.

Just curiosity I'm afraid! Not a physicist but an amateur scientific polymath strongest on chemistry and biology!