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• HeavyWater
In summary, the conversation discusses the lifetimes of unstable particles such as Tritium and positronium. The speaker requests information on how to calculate the lifetime of these particles and provides a resource for further reading. They also mention the decay modes of muonium and positronium and speculate on the cause of their decay. Other participants in the conversation offer helpful comments and suggest possible methods for calculating the lifetime of positronium.

#### HeavyWater

The lifetime of Tritium is about 13 years. The lifetime of positronium is about one-tenth of a nanosecond. Can you point me to some papers or tell me how to calculate the lifetime of an unstable particle? For example, suppose I want to calculate the lifetime of the pion? Or muonium? Etc.

NikolaTesla2
Identify possible decay modes (at least the most common ones). Approximate their amplitudes, then integrate over the available phase space for the decay. For the muon or Z boson you can get a good approximation on one page, for more complicated systems you are looking at much more work.

Muonium is (unlike the name would suggest) a bound state between an electron and an antimuon. It "decays" via the antimuon decaying, so it has nearly the same lifetime as a free muon.
A bound state between a muon and an antimuon would be called "true muonium" and hasn't been observed yet.

vanhees71
Thank you mfb. I did not expect such a quick response. I am intrigued by the decay of positronium in the singlet spin state. Each of the constituents is a stable particle; yet this composite state decays into two gammas. We have an EM interaction between a particle and its anti particle--this would seem like a sure bet for a stable composite system. (Now, it didn't occur to me until today, that the positron should be treated as a Dirac anti particle). What do you think is causing this system to decay: a lack of enough binding energy? A surface tension type effect? No rush needed on your response.

YoungPhysicist
HeavyWater said:
What do you think is causing this system to decay
A possible decay mode. Simple particle/antiparticle annihilation. I'm sure there are publications calculating the lifetime.

YoungPhysicist
Thank you to everyone for your helpful comments. The calculation of the lifetime of positronium is described on p227 of JJ Sakurai's book on Advanced Quantum Mechanics. I didn't think that the volume per unit time of positron decays could be inverted to give the lifetime of a unit volume of positronium. I also didn't think about Fermi's Golden Rules.

I had a lot of fun thinking about positronium--I thought that this might be an application of Chaos Theory. Thanks to everyone for your encouragement.

YoungPhysicist