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I know that Fluorine-18 becomes stable when a neutron takes the place of a proton and becomes Oxygen-18 where a positron and nutrino are emitted. Using Einstein formula, I can find the maximum energy ($E_{max}$) using atomic masses difference between the Fluorine-18 and the Oxygen-18 minus 1.022 MeV to obtain 0.635 MeV.

I easily found on many papers that $E_{mean} = 0.249$ MeV and saw distribution plots that show $E_{max}$ and $E_{mean}$. Some papers say that $E_{mean} \approx \frac{1}{3}E_{max}$ (which gives 0.212 MeV $\neq 0.249$ MeV).

How is $E_{mean}$ really calculated to get 0.249 MeV?

Thanks!

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  • $\begingroup$ That is probably experimental measurement derived. However, have you tried picking considering the 3-body decay and integrating out to get a mean value assuming equal probabilities of decay for each direction and mode? $\endgroup$
    – naturallyInconsistent
    Commented Jun 7 at 1:12
  • $\begingroup$ What you have calculated is the energy released for the $e^+$ emission spectrum. There are other processes occurring e.g., electron capture. The mean energy would therefore be averaged over all processes, proportioned according to their respective transition probabilities. As Nicholas has stated, you need to find that mean value and not just the energy for positron emission. $\endgroup$
    – joseph h
    Commented Jun 7 at 5:04
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    $\begingroup$ You might find the Fermi theory of beta decay of interest? $\endgroup$
    – Farcher
    Commented Jun 7 at 7:59
  • $\begingroup$ @Farcher thank you very much! I started to read it and it'll definitly help me. It's well explained. $\endgroup$
    – Gabriel L.
    Commented Jun 8 at 18:18

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