# Fermi nuclear model

1. Jun 30, 2011

### Sebastian

1. The problem statement, all variables and given/known data

This question is about the Fermi nuclear model (see Das & Ferbel page 56 or http://www.e12.physik.tu-muenchen.de/stud/vorlesungen/fabbietti/WS2007/Lecture3.pdf" [Broken]). Let the nucleon mass be $m$, the number of nucleons be $A$ and the number of protons be $Z$. Assume a hypothetical situation where the only difference between the proton and the neutron is that the proton has magnetic moment $\mu_p$ and the neutron has magnetic moment $\mu_n$. The nucleus is placed in a magnetic field $B$. Assume also that the protons and neutrons may align the directions of their magnetic moments such that energy is minimized.

A. Find a formula connecting the Fermi energy of the protons with that of the neutrons.
B. Find a formula connecting the Fermi momentum of the protons with that of the neutrons.

2. Relevant equations

I think the binding energy of a nucleon should be $-\mu B$. However, I don't see how to continue from here.