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This thought was inspired by a comment from the current leading answer, by @Sentry, to the question Where are all the slow neutrinos?

This [slow-neutrino induced nuclear decay] will still be an extremely rare process and the big problem is to distinguish it from normal spontaneous nuclear decay.

Questions which would need to be addressed as corollaries to the main question, I believe, include:

  • Is such a possibility self-consistent as a theory?

  • How does the required energy density of slow neutrinos compare to the postulated energy density of dark matter?

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    $\begingroup$ Remark: dark matter density significantly differs in the outer regions of the galaxies (there is a lot) and in the centre (there is practically none), but as I know, the rate of the radioactive decay doesn't. $\endgroup$ – peterh Jul 9 '16 at 21:07
  • $\begingroup$ @perterh It is quite the reverse. The dark matter density is highest near the centre. $\endgroup$ – Rob Jeffries Jul 9 '16 at 21:44
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    $\begingroup$ The density of cosmological relic neutrinos (of the usual kind) is many orders of magnitude lower than required for dark matter. $\endgroup$ – Rob Jeffries Jul 9 '16 at 21:46
  • $\begingroup$ @RobJeffries True, uhm, sorry. $\endgroup$ – peterh Jul 9 '16 at 22:35
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    $\begingroup$ @PieterGeerkens: my wording in the answer you cited was misleading. I have edited it afterwards to make clearer what I meant. Spontaneous and neutrino induced $\beta$-decay are fundamentally different processes (as described in the answers below), but it will be extremely difficult to distinguish the signature of the latter in terms of detector resolution and background discrimination. $\endgroup$ – Sentry Jul 14 '16 at 18:53
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Consider the average beta decay, which at nucleon level looks like $$ n \longrightarrow p + e^- + \bar{\nu} \,. \tag{1}$$ The distribution of electron energies (as measured in neutron's frame) is controlled by the phase space of the products. We observe an electron energy spectrum consistent with these physics.

What you propose is essentially that this reaction is properly described by $$ n + \nu \longrightarrow p + e^- \,. \tag{2}$$ with a very low energy neutrino. (As an aside, that reaction with high energy neutrinos is seen in accelerator and atmospheric neutrino experiments.)

However, the energy distribution of the electron in the final state of EQN (2) (again, measured in the neuton's rest frame) would be controlled by the incident neutrino's momentum. It could only look like the observed spectrum if the energy-spectrum of the incident neutrinos were like those predicted for the outgoing neutrino in EQN (1). But as those neutrinos have energies of many MeV (depending on the particular decay) they are in no way slow.

Worse, weak universality works using the same effective coupling constant (the Fermi constant) for reactions involving a neutrino in the initial state as for those involving an anti-neutrino in the initial state. (And likewise for (anti-)neutrinos in the final state). So now you need not only a conspiracy to get the right energy spectrum for the neutrinos, but the conspiracy must insure the same number and spectrum for anti-neutrinos as well, despite the nearly factor of two difference in the abundance of quarks for these two kinds to interact with at low energy.

Short answer: No, it's not possible. Not even for weak decays.

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  • $\begingroup$ Okay; so much for idle speculation. $\endgroup$ – Pieter Geerkens Jul 9 '16 at 22:15
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This argument might conceivably work for weak decays, though I believe there is evidence to the contrary. This comes to mind, but I won't 100% swear it's quite what you're after. Peterh mentions in a comment that weak decay rates (e.g. in supernova afterglows) appear to be independent of the local density of dark matter.

There is no reason to believe the neutrinos play any role in triggering alpha decays, where the weak interaction is not involved.

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    $\begingroup$ Dark matter and neutrinos from the cosmic background (from the time when the universe had cooled enough for neutrinos to decouple) are two different things. I would think neutrinos from cosmic nu background were much more homogenously distributed in space (compared to dark matter). $\endgroup$ – Jeppe Stig Nielsen Jul 9 '16 at 21:45
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    $\begingroup$ I'll add an answer explaining why it would take a gobstopping conspiracy to let this explain weak interactions. $\endgroup$ – dmckee Jul 9 '16 at 22:00
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    $\begingroup$ @Jeppe: Slow enough neutrinos should behave a lot like dark matter. They're both composed of stuff that doesn't interact with anything and is not moving at high velocities. $\endgroup$ – Peter Shor Jul 10 '16 at 21:49
  • $\begingroup$ @PeterShor So based on that, when we know neutrinos have mass, what would we expect the cosmic neutrino background to look like today? If all the primordial neutrinos behave like "ordinary" slow and cold (hadronic) matter, at the current stage, maybe they orbit galaxy centers. There is not much "background" characteristics about them anymore, then. Maybe this is material for a new thread (I could ask it)? $\endgroup$ – Jeppe Stig Nielsen Jul 11 '16 at 8:35

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