Filling order in the Shell Model of the nucleus

Question

I have read that, in the nuclear shell model, nucleons are distributed filling energy levels following the Pauli exclusion principle. These energy levels can be designed with the $nl_j$ notation: $1s_{1/2},1p_{3/2},1p_{1/2}, 1d_{5/2},...$
I have two questions in relation to this matter:

Do protons and neutrons fill the same levels or do they fill separate levels? For example, would level $1s_{1/2}$ be filled by a neutron and a proton or would there be two different levels $1s_{1/2}$, one for each particle type?
Is there a mnemonic rule or diagram with which to remember the order of filling of the energy levels, in the style of that for the electrons?

ZeroTheHero · Accepted Answer

Protons and neutrons fill different levels.  On the one hand they are distinct fermions and on the other they evolve in a slightly different average potential because of the residual electromagnetic interaction.

There is no obvious mnemonic device.  In fact it depends a bit on how one models the nuclear potential.  Phenomenologically at least, the ordering of shell model levels is given by

which predicts the correct magic numbers, and which are the same for protons and neutrons.  The ordering is based on a harmonic oscillator core potential, with a small $ell^2$ and spin-orbit interactions added, with interaction strengths chosen to produce the correct magic numbers.

Filling order in the Shell Model of the nucleus

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