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With such a high number of neutrinos passing through everything all the time, and only rarely colliding with another particle, what is the likelihood of one colliding with a particle while passing through a human body in an average lifetime?

Kevin Rodgers
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  • I suppose because the electron neutrino is so small as compared to an electron that it hardly has any effect if our human body gets hit now-and-then by a couple of neutrinos ($<2.2eV/c^2$ as compared to $0.511MeV/c^2$) – Mihai B. Mar 17 '17 at 10:42
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    xkcd what if estimated that roughly one neutrino collides with your body every 10 years, although it does not source this claim. – By Symmetry Mar 17 '17 at 10:44

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This is an interesting question because although it might seem that there is a simple answer that is not the case.

The Sun is a source of neutrinos with about $10^{15}$ arriving per square metre every second on the Earth.
There are many other sources of neutrinos the Wikipedia article describes.

However a lot of the neutrino fluxes have never been never been measured directly as neutrino detectors are only sensitive to the higher energy neutrinos.

This then shows that to answer the question one must know about the energy spectrum of neutrinos and their interaction cross section with different types of matter.

Not that long ago (late 1980s) there was a very large discrepancy when using a chlorine detector between the observed solar neutrino event "flux" on the Earth, $2.1\pm0.9$ solar neutrino unit (SNU), and the predicted value $7.9\pm0.3$ SNU.

The SNU is in the number of events per target atom per second and is chosen to be $10^{-36}\,\rm s^{-1}$

At the turn of this century it was discovered that some electron neutrinos from the Sun are transformed into mu and tau neutrinos on there passage to the Earth.

So not only do you have neutrinos and anti-neutrinos there are also three type of each of these all with different properties and hence absorption coefficients.

To get a proper estimate one needs to consider the $6$ types of neutrino, the flux of neutrinos of all energies from a variety of sources, and the absorption cross section which will depend on the type of neutrino, the energy of the neutrino, the material through which the neutrino is passing through etc.

Suppose that you had a mass of $70$ kg then this would mean that you were composed of approximately $7 \times 10^{27}$ atoms - unchecked source.

Now further assume that all the atoms in your body behaved like the chlorine atoms in the neutrino detector then the number of events (electron neutrino absorptions) per second would be $2.1 \times 10^{-36} \times 7 \times 10^{27} \approx 10^{-8}$.

A year is approximately $3\times 10^7$ seconds and a lifespan is 70 years.

So the number of electron neutrinos from the Sun absorbed by a human being made of chlorine in a lifetime is $10^{-8} \times 3\times 10^7 \times 70 \approx$ $20$

I leave it to the OP and/or the reader to produce a better estimate.

Farcher
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