According to the Fermi gas model of the nucleus, its protons and neutrons
exist in a box of nuclear dimensions and fill the lowest available quantum
states to the extent permitted by the exclusion principle. Since both protons
and neutrons have spins of \(\frac{1}{2}\) they are fermions and obey Fermi-
Dirac statistics. (a) Find an equation for the Fermi energy in'a nucleus under
the assumption that \(A=\) 2Z. Note that the protons and neutrons must be
considered separately. (b) What is the Fermi energy in such a nucleus for
\(R_{0}=\) \(1.2 \mathrm{fm}\) ? \((c)\) In heavier nuclei, \(A>2 Z\). What effect
will this have on the Fermi energies for each type of particle?