# Differential number of particles in Fermi gas model

• I
• Ross Greer
In summary, the conversation discusses the Fermi gas model of the nucleus and its Fermi energy for normal nuclear density. The question at hand is the dependence of Fermi energy on density when the nucleus is compressed. The first step in the solution is the equation dN = 4V/(2π)3 d3K, which comes from solid state books like Kittel. The individual also asks for recommendations on Physics GRE prep materials.
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!

Ross Greer said:
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!

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

## 1. What is the Fermi gas model?

The Fermi gas model is a theoretical model used to describe the behavior of particles in a system, particularly in a solid state. It assumes that the particles are non-interacting and are subject to the Pauli exclusion principle, which states that no two particles can occupy the same quantum state simultaneously.

## 2. What is the significance of the differential number of particles in the Fermi gas model?

The differential number of particles in the Fermi gas model is a measure of the number of particles in a given energy range. It is important because it helps to determine the energy distribution of particles in a system and provides insights into the behavior of the system at different energy levels.

## 3. How does the differential number of particles change with temperature in the Fermi gas model?

In the Fermi gas model, the differential number of particles decreases with increasing temperature. This is because at higher temperatures, more energy is available for particles to occupy higher energy states, resulting in a decrease in the number of particles in lower energy states.

## 4. What is the relationship between the differential number of particles and the Fermi energy?

The differential number of particles is directly related to the Fermi energy, which is the maximum energy that a particle can have at absolute zero temperature. The Fermi energy can be calculated using the differential number of particles and provides important information about the energy distribution of particles in a system.

## 5. How is the differential number of particles in the Fermi gas model related to the density of states?

The differential number of particles is proportional to the density of states, which is a measure of the number of energy levels available for particles in a system. This relationship is described by the Fermi-Dirac distribution, which relates the differential number of particles to the density of states and the temperature of the system.

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