[syhprum (OP)]

It has been suggested that the variations in the Neutrino flux from the Sun due to the eccentricity of the Earths orbit causes a periodic variation in the rate of C14 decay.
Is there any evidence to back this up or has it been discounted.

[evan_au]

The Earth's orbit has an eccentricity of about 1.7%.

Due to the inverse square law, the neutrino flux should vary by about 3.3% over a 12-month cycle (with peak activity in January). This should be measurable with a reasonable sample of carbon.

I am assuming that neutrino oscillation will average out when a source the diameter of the Sun's core irradiates a detector whose distance varies by the diameter of the Earth every 24 hours...

Some people are still looking at it, but it is still controversial.
Especially if you suggest that there are other monthly cycles at play, as suggested by some of the neutrino detectors.
See: https://physicsworld.com/a/do-solar-neutrinos-affect-nuclear-decay-on-earth/

The much greater sensitivity of the ice-cube neutrino detector at the south pole should quickly resolve whether there is a monthly variation in solar neutrinos.

[chiralSPO]

Funny--I was just talking about this with somebody earlier this week!

No, ¹⁴C half life is independent of neutrino flux, so it wouldn't matter how close we are to the sun, or what the solar weather is like, or if there are nearby supernovae.

There are other isotopes whose decay pathways are influenced by neutrino flux. Notably ³⁷Cl (thanks for catching my typo) (https://iopscience.iop.org/article/10.1086/305343/pdf).

Apparently, there is some controversy over whether ⁵⁴Mn does or not:
https://physicsworld.com/a/radioactive-decay-of-manganese-54-is-not-affected-by-the-seasons-says-physicist/
https://www.economist.com/babbage/2012/08/23/and-now-the-space-weather-forecast
http://blogs.discovermagazine.com/80beats/2010/08/26/scientist-smackdown-are-solar-neutrinos-messing-with-matter/#.XKlEletKh0s

[Bored chemist]

There are other isotopes whose decay pathways are influenced by neutrino flux. Notably 39Cl

I think you mean 37Cl
But anyway, I'm not sure that counts as a "decay"- the rate of that reaction without the neutrino flux is zero.
It's a reaction. 37Cl is as stable as anything.

[chiralSPO]

There are other isotopes whose decay pathways are influenced by neutrino flux. Notably 39Cl

I think you mean 37Cl
But anyway, I'm not sure that counts as a "decay"- the rate of that reaction without the neutrino flux is zero.
It's a reaction. 37Cl is as stable as anything.

Indeed--that was a typo! Thank you for catching it. (I have corrected it in the original post). And yes, I suppose that would count as a nuclear reaction.