Is the Fermi Coupling Constant Calculation from Oxygen Beta Decay Accurate?

In summary, the conversation discusses the calculation of the fermi coupling constant for oxygen beta decay using the equation Γ = 1/τ = G^2E_0^5/30π^3, with E_0 = 1.81 MeV and τ log 2 = 71 sec. The resulting value for G is approximately 10^-5/m^2_N, where m_N is the nucleon mass. The speaker initially struggles to reproduce this number, but eventually realizes that they need to include factors of c and ħ for the correct dimension. They also mention the use of the conversion constant 1=192.33 MeV-fm, which is more useful than the conversion in Joule-m.
  • #1
rioo
6
0
i'm reading through halzen and martin's chapter 12 on the weak interaction which they calculate the fermi coupling constant form oxygen beta decay using
[itex]\Gamma = 1/\tau = G^2E_0^5/30\pi^3[/itex]
with [itex]E_0 = 1.81[/itex]MeV and [itex]\tau log 2 = 71[/itex] sec. they get [itex]G\approx 10^{-5}/m^2_N[/itex]. where m_N is the nucleon mass.
i can't reproduce this number, just plugging in is way off. are there factors of c or h that i need to include?
 
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  • #2
Actually, to have the right dimension, is [itex]\Gamma=\hbar/\tau[/itex]. If you plug all the numbers considering that the calculation gives the correct answer.
 
  • #3
yes it does thanks. natural units are annoying
 
  • #4
You can use the conversion constant 1=192.33 MeV-fm
 
  • #5
You can use the conversion constant 1=192.33 MeV-fm
Close. ħc = 197.326 MeV-fm.

(Much more useful than whatever it is in Joule-m! :approve:)
 

Related to Is the Fermi Coupling Constant Calculation from Oxygen Beta Decay Accurate?

1. What is the Fermi coupling constant?

The Fermi coupling constant, also known as GF, is a fundamental physical constant that describes the strength of the weak nuclear force. It is used to calculate the rate at which particles decay through the weak interaction.

2. What is the significance of the Fermi coupling constant?

The Fermi coupling constant is an important constant in the Standard Model of particle physics, which describes the fundamental particles and their interactions. It is also used in calculations related to nuclear decay and particle interactions.

3. How is the Fermi coupling constant measured?

The Fermi coupling constant is measured through experiments that involve weak nuclear interactions, such as beta decay. It can also be calculated theoretically using other fundamental constants, such as the fine structure constant and the Planck constant.

4. Has the value of the Fermi coupling constant changed over time?

The value of the Fermi coupling constant is considered to be a constant in the Standard Model, meaning it does not change over time. However, theories beyond the Standard Model may suggest variations in its value, which are currently being studied through experiments.

5. Is the Fermi coupling constant the same for all particles?

Yes, the Fermi coupling constant is considered to be a universal constant, meaning it is the same for all particles that interact through the weak nuclear force. However, the strength of this force may vary depending on the distance between particles and their respective energies.

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