Calculating Particle Lifetimes to Unstable Particle Decay

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    Lifetime Particle
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Discussion Overview

The discussion centers around calculating the lifetimes of unstable particles, specifically mentioning Tritium, positronium, pions, and muonium. Participants explore theoretical approaches, decay modes, and relevant literature on the topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes the lifetimes of Tritium and positronium and seeks guidance on calculating the lifetime of other unstable particles like pions and muonium.
  • Another participant expresses interest in the topic and shares a link to a related article.
  • A participant suggests identifying possible decay modes and approximating their amplitudes, indicating that more complex systems require extensive work for accurate calculations.
  • Discussion includes the nature of muonium as a bound state of an electron and an antimuon, with its lifetime being similar to that of a free muon.
  • One participant raises questions about the decay of positronium in the singlet spin state, pondering the reasons behind its decay despite the stability of its constituents.
  • Another participant proposes that simple particle/antiparticle annihilation could be a decay mode and mentions the existence of publications on lifetime calculations.
  • A participant references a specific source, JJ Sakurai's book, for calculating the lifetime of positronium and reflects on their previous misconceptions regarding the relationship between decay volume and lifetime.
  • One participant expresses enjoyment in contemplating the topic and suggests a potential link to Chaos Theory.

Areas of Agreement / Disagreement

Participants express various viewpoints and hypotheses regarding particle lifetimes and decay mechanisms, with no consensus reached on specific calculations or interpretations.

Contextual Notes

Some discussions involve assumptions about decay modes and the nature of interactions, which may not be fully resolved. The complexity of calculating lifetimes for different particles is acknowledged, with varying levels of detail provided by participants.

Who May Find This Useful

Readers interested in particle physics, quantum mechanics, and the theoretical aspects of unstable particle decay may find this discussion relevant.

HeavyWater
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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.
 
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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.
 
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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.
 
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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.
 
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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.
 
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