The Mysterious Nature of Neutrons: Stability & Binding

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Neutrons bind Protons in nuclei, and/or the other way around, but why don't

Neutrons bind Neutrons, with clumps of neutrons whizzing about?

And, I'm guessing this is related: Why is a Neutron unstable outside

its nucleus with about a 10.3 minute half-life?
 
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If we consider the neutron alone, it has a mass of 939.565330 MeV/c2, and a lifetime of 885.7 seconds. The proton mass is 938.271998 MeV/c2, so the difference is 1.2933 MeV/c2. But the binding energy of the deuteron is about 2.2 MeV, and the only possible final state of neutron decay in the deuteron is two free protons plus an electron (+ neutrino). because the electron mass is 0.511 MeV/c2, neutron decay in the deuteron is energetically not possible. This true for all neutrons in all stable nuclei.
 
The nucleus is a bag of nucleons (neutrons and protons) held together by pion exchange. The process is analogous to how Van de Waals forces can hold molecules together.

(Every time I try to write something like this I cringe a little at how wrong it is...)
 
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