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

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Discussion Overview

The discussion centers on the accuracy of the Fermi coupling constant calculation derived from oxygen beta decay, as presented in Halzen and Martin's text on weak interactions. Participants explore the mathematical framework and unit conversions involved in the calculation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant references Halzen and Martin's formula for the decay rate, \(\Gamma = G^2E_0^5/30\pi^3\), and expresses difficulty in reproducing the calculated Fermi coupling constant, suggesting potential missing factors of \(c\) or \(\hbar\).
  • Another participant corrects the decay rate formula to \(\Gamma = \hbar/\tau\), implying that this adjustment could lead to the correct dimensional analysis.
  • A third participant acknowledges the correction and expresses frustration with natural units.
  • Participants discuss the conversion constant of \(1 = 192.33 \text{ MeV-fm}\) and clarify that \(\hbar c = 197.326 \text{ MeV-fm}\) may be more useful for their calculations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the accuracy of the original calculation or the necessary factors for dimensional consistency, indicating ongoing debate and exploration of the topic.

Contextual Notes

There are unresolved questions regarding the application of natural units and the specific conversion factors required for accurate calculations, which may depend on the definitions used by participants.

rioo
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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
\Gamma = 1/\tau = G^2E_0^5/30\pi^3
with E_0 = 1.81MeV and \tau log 2 = 71 sec. they get G\approx 10^{-5}/m^2_N. 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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Actually, to have the right dimension, is \Gamma=\hbar/\tau. If you plug all the numbers considering that the calculation gives the correct answer.
 
yes it does thanks. natural units are annoying
 
You can use the conversion constant 1=192.33 MeV-fm
 
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:)
 

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