A Calculating Particle Lifetimes to Unstable Particle Decay

[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]

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[mfb]

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.

 

[HeavyWater]

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.

 

[mfb]

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.

 

[HeavyWater]

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.