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Here's what I know about the matter:
At low atomic number, isotopes that are more stable tend to be close to a 1:1 ratio of neutrons to protons. At high atomic number, this ratio approaches 3:2. I do not know why this is the case, and I believe it is not entirely understood by anyone. Also, this is not a very good predictor anyway.
The real problem is that unlike electron energy levels in an atom, which are well known and easily approximable by various systems and techniques, the nuclear energy levels are not very well understood, and I think to an extent they are even difficult to measure. I believe it is known that unlike the electrons' spherical potential well, the nucleons are bound in a well that is a mixture of a spherical and cubic well, and the exact form is unknown, thus we can't predict the levels very well. I don't know why this is the case, and I believe it is not entirely understood by anyone else either.
In short, I think that a good theoretical model that predicts these kind of things has yet to come.
We know exactly why the balance tends more towards the neutrons for heavier elements, but the system is messy enough that it's very hard to predict just how much it does.
Sphericality and cubicality are orthogonal issues, and not that big a deal in the grand scheme of things. The main issues that make nucleons... (read more)