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Free neutrons, as we know them, are unstable and hence undergo a three-body decay into proton, electron and antineutrino with a mean lifetime of just under 15 minutes.

But there are astrophysical objects called neutron stars which are produced at the end of the lives of moderately massive stars. These objects are made entirely of neutrons in order to support the strong gravitational pulls. These are pretty stable objects in cosmological time scales lasting at least for billions of years.

So, why they are simply not decaying into proton stars due to unstable nature of neutrons? How to explain this apparent contradiction?

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  • $\begingroup$ The beta electrons from decaying neutrons will start to occupy all the energy levels available for decay. So, the Fermi level of the electrons will become just as high as the maximum decay energy and then no more neutrons can decay. $\endgroup$
    – Count Iblis
    Commented Apr 12, 2017 at 2:26
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    $\begingroup$ Possible duplicate of What stabilizes neutrons against beta decay in a neutron star? $\endgroup$
    – Alfred Centauri
    Commented Apr 12, 2017 at 2:31

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Neutron stars aren't made out of free neutrons; they're held together by immense pressure at the bottom of a huge gravitational well. So your first argument does not apply and there is no contradiction.

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    $\begingroup$ Why this answer got -1? Bound neutron frequently doesnt decay and nobody is curious about that.... $\endgroup$
    – jaromrax
    Commented Apr 24, 2017 at 14:17

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