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.
I do not know why this is the case, and I believe it is not entirely understood by anyone
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.
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,
Sphericality and cubicality are orthogonal issues, and not that big a deal in the grand scheme of things. The main issues that make nucleons harder than electrons are:
1) There isn’t an externally imposed force that dominates the system (for the electrons, that’s the nucleus); it’s all internal, and that’s harder. Every time you add a new particle, the new ground state is little like the old ground state. For electrons, a thorough understanding of Hydrogen tells you nearly everything you need to know about, say, Oxygen; at a nuclear level, a thorough understanding of Hydrogen barely tells you anything about Oxygen.
2) The questions you need to answer are much much harder. You aren’t perturbing the system and finding the new ground state, like in chemistry. You need to find barrier heights and transition rates on upheavals to the whole system.
3) Last and least, there are two species (electrons → protons AND neutrons), with differences in how they feel the forces.
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 harder than electrons are:
1) There isn’t an externally imposed force that dominates the system (for the electrons, that’s the nucleus); it’s all internal, and that’s harder. Every time you add a new particle, the new ground state is little like the old ground state. For electrons, a thorough understanding of Hydrogen tells you nearly everything you need to know about, say, Oxygen; at a nuclear level, a thorough understanding of Hydrogen barely tells you anything about Oxygen.
2) The questions you need to answer are much much harder. You aren’t perturbing the system and finding the new ground state, like in chemistry. You need to find barrier heights and transition rates on upheavals to the whole system.
3) Last and least, there are two species (electrons → protons AND neutrons), with differences in how they feel the forces.