I Neutrino-Nucleus Interactions and Half-Life Constraints

[InkTide]

At what half-life duration, if any, does the likelihood of a neutrino collision within a sample of radionuclide atoms exceed the likelihood of a decay event in those atoms over the same time period? Can they be efficiently excluded by their reaction products, or are they meaningfully difficult to distinguish from nuclear decay? Easy differentiation makes the entire question moot, but what I've read so far suggests this is not easy, especially for heavier nuclei and neutrinos with lower energies. Do we have a sufficient understanding of the energy distribution of Earth's neutrino flux - from solar, terrestrial, and cosmic sources - to determine the likelihood of specific transmutations resulting from neutrino captures, or is this unknown? Would there be a significant difference between isotopes?

I assume what you'd need to determine this is data on both the energy distribution of the average neutrino flux and "neutrino cross sections" of various nuclei, establishing upper bounds on collision rate and the distribution of collision products, but I haven't been able to find much research on either (just theoretical/modeling work like this in the case of neutrino cross sections). I have seen suggestions of general trends that larger nuclei and higher energy neutrinos increase collision probability.

 

[Vanadium 50]

Ballpark, 10^30 years.

 

[InkTide]

Ballpark, 10^30 years.

Are the cross sections consistent enough to stay in that ballpark for pretty much any isotope, or is that more like a ballpark of the highest neutrino cross sections (meaning that'd be the highest rate of neutrino collisions you'd get)? One thing I'm very curious about is super-low-energy neutrinos, because I don't think we know what the fluxes are for neutrinos that lack sufficient energy to induce inverse beta decay (roughly a 1.8MeV threshold), especially if neutrino energy distribution follows something like a power law for those energies that might overcome the influence of reduced neutrino cross-sections at lower energies on the probability of collision - though I think we should be able to establish constraints based on stable isotopes, or potentially long-lived isotopes.

This distribution (y-axis is total energy flux; total neutrino flux is what's relevant here I believe, but it should be trivial to calculate the number of neutrinos based on the neutrino energy given in the x-axis) is the best I've found so far, and it's... kind of bizarre to be honest. Doesn't seem like a power law at all, but doesn't seem to fit the other models either. Is that a consequence of only looking at electron/tau neutrinos? Surely muon neutrinos wouldn't change the distribution that much. Unfortunately, the lack of fit to a model makes it very difficult to extrapolate to lower energies, from what I understand.

 

[Vanadium 50]

The ballpark is comparing the rate of solar/atmospheric neutrinos detected in proton decay experiments with the proton decay limits, degraded by 2 or 3 orders of magnitude.

Make the neutrino energy too low and nothing happens when it strikes a nucleus.

 

[mfb]

Lower energy neutrinos have much smaller cross sections. Beating the reaction rate from solar neutrinos with low-energy neutrinos would need absurd densities of them. Our estimates are not that accurate, but they won't be off by 10 orders of magnitude.

PTOLEMY is a proposed detector for the cosmic neutrino background. It would look for tritium decays at the maximal electron energies for a beta decay and slightly above that. They want to use 100 grams of tritium and estimate 10 neutrino capture events per year (and 2*10²⁴ beta decays), although some models lead to larger predictions. If tritium were stable otherwise this would correspond to a half life of ~10²⁴ years. With a sensitivity in the eV range the experiment doesn't care about solar neutrinos, of course, their energy is far too high to matter.

 

[snorkack]

Make the neutrino energy too low and nothing happens when it strikes a nucleus.

If it strikes a stable nucleus.
When you are speaking of an unstable nucleus like
Re-187=Os-187+e^-+ν^~_e
then this happens with no energy input. Therefore the process
Re-187+ν_e=Os-187+e^-
can happen with arbitrarily small incoming ν_e energy.
It can, but what is the cross-section at low incoming ν_e energy compared to the rate of spontaneous ν^~_e emission?