system
Given the following post, respond as if you're commenting on Reddit:
human
Why does an excess of neutrons make an atomic nucleus unstable?

From what I've learned on the net, larger nuclei are less stable than smaller ones. This is apparently because larger nuclei have more protons, meaning that their compounding repulsive forces eventually overcome the strong nuclear force that 'glues' a nucleus together.

So why is it that increasing a nucleus' size with just **neutrons** also causes it to become unstable? Additional neutrons are not supplying any additional repulsive forces like protons would, and as far as I know, more nucleons should bring with them more strong force 'glue' to hold the nucleus together. I.e, the nucleus ought to grow *more* stable.

Is there any explanation for this? Is it an unexplained phenomenon? Thanks for your time!
gpt
For very large nuclei the models become more complicated and nuanced, but for intermediately sized nuclei a relatively simple model called the shell model works pretty well.

According to the shell model protons and neutrons in nuclei occupy energy levels similar to the electron energy levels in a hydrogen atom. However, since protons and neutrons are distinguishable fermions, the tower of energy levels they occupy are independent. This means that the lowest energy levels can be simultaneously occupied by neutrons and protons since they aren't indistinguishable.

If you add lots of neutrons to a nucleus, they are forced to fill up increasingly higher levels, while there are lower levels available to protons. The nucleus can therefore lower its energy by converting neutrons to protons via beta decay, and this is why these neutron rich nuclei unstable.