Do bound, unstable particles decay more slowly?

[nickyrtr]

Take some unstable particle species, and put two of them into an exotic atom or exotic molecule, such that the two bound particles fully occupy a 1s orbital. For example, two negative muons orbiting an alpha particle, or two mesons orbiting a massive baryon. Decay of either orbiting particle disrupts the nice symmetry of the filled 1s state, so does this bound state extend the lifetime of these unstable particles? If so, would it be a tiny effect or a significant effect?

 

[mfb]

In general, additional particles nearby open additional decay channels and make decays more likely (and therefore shorten the lifetime).
In particular, negative muons get bound to nuclei and can react with a proton to form a neutron and a neutrino, similar to inverse beta decay. The muon reaction is much faster as the orbital is very close to and inside the nucleus and as the reaction has ~100 MeV available.

Neutrons in stable nuclei are an example where unstable particles become stable.

There is at least one isotope that is stable with electrons, but can beta decay if the innermost shell is empty. The energy is not sufficient to release a free electron, but a bound electron is possible.