Differential number of particles in Fermi gas model

[Ross Greer]

I'm practicing for the Physics GRE, and came across a question that has me stumped.
"In elementary nuclear physics, we learn about the Fermi gas model of the nucleus. The Fermi energy for normal nuclear density (ρ₀) is 38.4 MeV. Suppose that the nucleus is compressed, for example in a heavy ion collision. What is the dependence of Fermi energy on density?"

I took a peek at the solution, but I've forgotten where I would have seen the first step:
"The differential number of particles is dN = 4V/(2π)³ d³K, where g = 4 is the nuclear degeneracy."
Where does this equation come from?
Are there any books or online readings you could recommend to better learn this material?

I would be able to finish the problem if I could recall the first step. (For those curious, the solution was ρ^2/3

Side note: If anyone has any Physics GRE prep materials they would recommend, I'd greatly appreciate it!

Thanks for your help!

 

[nasu]

I'm practicing for the Physics GRE, and came across a question that has me stumped.
"In elementary nuclear physics, we learn about the Fermi gas model of the nucleus. The Fermi energy for normal nuclear density (ρ₀) is 38.4 MeV. Suppose that the nucleus is compressed, for example in a heavy ion collision. What is the dependence of Fermi energy on density?"

I took a peek at the solution, but I've forgotten where I would have seen the first step:
"The differential number of particles is dN = 4V/(2π)³ d³K, where g = 4 is the nuclear degeneracy."
Where does this equation come from?
Are there any books or online readings you could recommend to better learn this material?

I would be able to finish the problem if I could recall the first step. (For those curious, the solution was ρ^2/3

Side note: If anyone has any Physics GRE prep materials they would recommend, I'd greatly appreciate it!

Thanks for your help!

You can find the same method used in I to Solid state books like Kittel.