Fermi's Golden Rule (Decay Amplitude)

In summary, the question discusses the decay of a neutral pion into two photons, and the amplitude for this process is determined by the momentum of the secondary photons. It is noted that conservation of momentum dictates that the momentum of the two photons must be equal in magnitude but opposite in direction. However, Griffiths states that the amplitude has no angular dependency, which is due to the fact that the pi zero has spin zero and its decay cannot have any angular dependence.
  • #1
getPhysical()
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0
This question relates to Griffiths: Introduction to Elementary Particles, p. 196

The process in question is a neutral pion decay into two photons. It is stated that because the secondary particles are massless, the amplitude for this process is:

[tex]
M(p_2,p_3)
[/tex]

where [tex]p_2[/tex] and [tex]p_3[/tex] are the momentum three-vectors of the secondary photons. Conservation of momentum further implies that [tex]p_2=-p_3[/tex]. So far, so good.

However, Griffiths then states that
[tex]
|M|^2
[/tex]
is a function of |p_2| only, meaning that |M|^2 has no angular dependency. Why is this?
 
Last edited:
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  • #2
The pi zero has spin zero, so its decay cannot have any angular dependence.
 

Related to Fermi's Golden Rule (Decay Amplitude)

1. What is Fermi's Golden Rule?

Fermi's Golden Rule is a fundamental concept in quantum mechanics that describes the probability of a quantum system transitioning from an initial state to a final state. It is used to calculate the decay rate or lifetime of a quantum system.

2. What is the formula for Fermi's Golden Rule?

The formula for Fermi's Golden Rule is given by Γ = 2π|Hfi|^2ρ(Ef), where Γ is the decay rate, Hfi is the transition matrix element, and ρ(Ef) is the final state density of states.

3. How is Fermi's Golden Rule applied in real-world situations?

Fermi's Golden Rule is commonly used in the study of radioactive decay, particle physics, and spectroscopy. It is also used in the design of electronic devices such as lasers and transistors.

4. What are the limitations of Fermi's Golden Rule?

Fermi's Golden Rule assumes that the system is in a stationary state and does not take into account the effects of external perturbations. It also assumes that the system is in a vacuum and does not account for interactions with the environment.

5. How does Fermi's Golden Rule relate to other concepts in quantum mechanics?

Fermi's Golden Rule is closely related to other concepts such as the Heisenberg uncertainty principle and the time-evolution of quantum systems. It is also based on the principles of quantum mechanics, such as superposition and the probabilistic nature of quantum systems.

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