This might seem like a really strange question, but here's my reasoning.

A proton-proton fusion reaction proceeds in two steps:

\begin{align*} p + p + \text{1.25 MeV} &\rightarrow {}^2_2\mathrm{He} \\ {}^2_2\mathrm{He} &\rightarrow {}^2_1\mathrm{D} + e^+ + \nu_e + \text{1.67 MeV} \end{align*}

The second step produces one electron neutrino. However, what if there were so many neutrinos that the chemical potential was more than 1.67 MeV? Would the reaction still be able to proceed?

Motivation: The chemical potential for neutrinos is pretty low in the universe today, but it's not zero. Neutrino degeneracy becomes significant at very low densities. Shortly after the Big Bang, the chemical potential would have been much higher. So I'm curious about whether this affected Big Bang nucleosynthesis.

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    $\begingroup$ Interesting concept. We also need to include the counteracting effect of the antineutrinos, but I can't find any info on the primordial neutrino : antineutrino ratio, either prior to BBN or after. :( $\endgroup$
    – PM 2Ring
    Commented Aug 18, 2020 at 15:33
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    $\begingroup$ BTW, that reaction is a simplification, and the 1.442 MeV includes the 1.022 MeV released by the positron annihilating with an electron. The reaction actually proceeds in 2 stages: 1st, a diproton is produced endothermically, consuming 1.25 MeV, then the diproton might convert to a deuteron, positron & neutrino, releasing 0.42 MeV. The conversion has a probability $\approx 10^{-26}$. $\endgroup$
    – PM 2Ring
    Commented Aug 18, 2020 at 15:44
  • $\begingroup$ @PM2Ring Thanks, I should be more careful about copying things from Wikipedia :) I've edited the question to include the correct reaction steps. $\endgroup$
    – Thorondor
    Commented Aug 18, 2020 at 16:26
  • $\begingroup$ Much better! I guess my main point is that the conversion step is really rare: on average, you have to produce a mole of diprotons to get a single deuteron. At least, that's the rate in stars doing predominantly p-p fusion, I don't know what effect temperature has on the conversion rate, but I assume that at significantly higher temperatures the diproton is more likely to fall apart into 2 protons. $\endgroup$
    – PM 2Ring
    Commented Aug 18, 2020 at 16:37
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    $\begingroup$ See physics.stackexchange.com/q/308496/123208 which has no answers, but a comment links to arxiv.org/abs/1211.6721 which says "We find a slight preference for negative neutrino chemical potentials, which would imply an excess of anti-neutrinos and thus a negative lepton number of the Universe". $\endgroup$
    – PM 2Ring
    Commented Aug 18, 2020 at 17:11


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