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

[rioo]

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 $E_0 = 1.81$MeV 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?

 

[Einj]

Actually, to have the right dimension, is $\Gamma=\hbar/\tau$. If you plug all the numbers considering that the calculation gives the correct answer.

 

[rioo]

yes it does thanks. natural units are annoying

 

[Meir Achuz]

You can use the conversion constant 1=192.33 MeV-fm

 

[Bill_K]

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! )