# Differential number of particles in Fermi gas model

• I
• Ross Greer

#### 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 ρ2/3

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

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 ρ2/3

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