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Would dense molecular structures on heavier planets (crystalline or other compounds which are generally unknown to us) allow neutrinos to pass through as easily as on Earth?

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Neutrinos wouldn't pass through white dwarfs or neutron stars as easily as through Earth, measured by the scattering rate per distance, since these types of stars are very dense: white dwarfs about one million times denser than water, neutron stars about as dense as atomic nuclei.

To scatter a neutrino with a chance of > 50%, you "just" need the inner of a neutron star along 10 times the diameter of Earth's orbit around the sun:

The neutrino-nucleon scattering cross section is about $10^{-38}cm^2=10^{-42}m^2$ for neutrinos with energies above about 1 GeV, according to this paper. A proton has a diameter of about $1.75\cdot 10^{-15}m$. With $$1.75\cdot 10^{-15}m/10^{-42}m^2=1.75 \cdot 10^{27}$$ we need about $1.75\cdot 10^{27}$ nucleons in a row to scatter a neutrino. That's about $$1.75\cdot 10^{27}\cdot 1.75\cdot 10^{-15}m=3\cdot 10^{12}m=20\mbox{ a.u.}$$ as a rough estimate. (For simplicity I've neglected the exponentially decreasing intensity of the neutrino beam in the scattering medium.) Neutrinos will probably scatter a little more easily in a neutron star than in the same number of single traversed neutrons, but that's a guess based on the scattering cross section for heavier nuclei.

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One impressive thing about neutrinos is that you would need about one light year of lead to stop a neutrino about 50% of the time. Which is due to neutrinos interacting only weakly with matter.

So, to answer your question, it would make $X$ time difference in neutrino opacity if you take you planet $X$ times larger in radius or $X$ times denser. However, the net effect will be still vanishingly small.

Also, molecular-level structures do not affect the interaction with neutrinos, but rather the nuclear structure.

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  • $\begingroup$ Ok, so is the nuclear density of atoms in red or brown dwarf stars high enough to interact with neutrinos? $\endgroup$
    – Cymatical
    Jan 17, 2014 at 14:49
  • $\begingroup$ It depends on what do you mean by interact. The Earth also interacts with neitrinos. However, for both the Earth and brown dwarfs neutrino opacity is small and close to zero. $\endgroup$ Jan 17, 2014 at 15:24
  • $\begingroup$ @AlexeyBobrick It might help to talk about interaction cross-section. You could be a bit more precise with your answer when you say "still vanishingly small". $\endgroup$
    – astromax
    Jan 19, 2014 at 5:44
  • $\begingroup$ @astromax, given that the question is "interacts or not", the answer is simply "not", on the argument that $10^{4}-10^{6} \textrm{km}$ of ordinary matter is by about ten orders of magnitude smaller than a light year. $\endgroup$ Jan 19, 2014 at 12:15
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    $\begingroup$ Well, hold up a second. You're "impressive thing" in retrospect is incorrect. It's a light year of lead for it to interact 50% of the time. I'm editing your answer to reflect that. Secondly, I would still find it appropriate and informative to include a general discussion about interaction cross-section. Take it or leave it - no need to debate with me regarding this. $\endgroup$
    – astromax
    Jan 19, 2014 at 16:02

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