The picture of the atomic nucleus that we are given is that in order for the electrostatic repulsive force of the protons to be “neutralized”, neutrons are required to supply a measure of the “strong” nuclear force to overcome the electrostatic repulsive force. So, why can’t neutrons form their own associations independent of the need for protons? I know “free” neutrons are unstable and decay to protons and electrons, but the half life is about 10 minutes; seems to be plenty of time to form a “neutron nucleus”.

(DAVID KENNEDY posted this)

Answer

There are several issues here. If neutrons are together, They are not much different from free neutrons. The force of attraction between two neutrons will be that of gravitational force, which is so feeble and hence insufficient to hold the neutrons together to form a nucleus. If two neutrons are forced to be together, then one of the neutrons will transform to a proton emitting and electron and become a deuterium atom.

Forcing neutrons together will result in the creation of radioactive atoms.

Further references

https://www.sjsu.edu/faculty/watkins/neutronnucleus.htm

https://en.wikipedia.org/wiki/Neutron

Suresh Sir from S&G Institute responds:
If neutrons only are there in the nucleus, then, because they are neutral, the only force operating b/w them and atom will be gravity. It will be very weak and “neutron nucleus” cannot exist.
http://sandgscience.com/

An independent neutron will split up into proton and electron, because, the splitting is energy feasible. (Mass of neutron is greater than the sum of masses of proton and electron.)
In case of proton – neutron pair, the splitting is not energy feasible. So neutron in pair with proton is more stable.