In my nuclear physics lecture we learned about the "fermi gas modell" of a nucleus with which I have some problems. First the potential for the nucleons is shown in the picture below and it makes somewhat sense to me.
But now the lecture goes on and says, we use the model of the free nucleon gas. Why does that make sense? There is a potential so the nucleons aren't free at all. To me it looks much more similar to a particle in a box for example. So first question: What das the free nucleon gas have to do with this potential?
Putting that aside, the lecture goes on saying:
To calculate the fermi energy and the depth of the potential, we look at the number of possible states in a volume V with a momentum between $p$ and d$p$:
My second question is: Why is that true? Wher does this formular come from?