Fermi Gas Model of Nucleus

Fermi Gas Model assumes the Nucleus to behave as a fermi gas. What is a Fermi Gas?
Fermi Gas is collection of non interacting fermions inside a potential well. Fermions are quantum particles like electrons, protons, neutrons etc that follow the Pauli's Exclusion Principle. No two fermions can have the same quantum state in a given system.
Why Gas? Gaseous system usual refers to free moving particles that rarely interact with its nearest neighbors, as opposed to solid particles that experience heavy interaction with its neighbors. In this model the nucleus is assumed to consist of particles that rarely interact with its neighbors, and mostly interact with a general Potential Field. The general potential field is replicated by a finite 3D Square well potential.

Following are the Assumptions of the Fermi Gas Model of the Nucleus:
1) The Nuclear Potential is approximated by a 3D Finite Square Well Potential.
2) Since Neutrons and Protons are distinct particles, the potential for both will be distinct.
3) Since both Neutrons and Protons are fermions, each distinct Energy level will be occupied by two of each type of particles of opposite spin.
4) When two nucleons moving inside the nucleus collide, they will exchange each other's quantum states. This will effectively change nothing as both particles are identical. That's why the particles can in effect be assumed to move freely without any interaction with each other.
Success of Fermi Gas Model of Nucleus:
1) It explains why nucleons inside the nucleus exist in quantised energy levels.
2) It explains pairing of nucleon particles. It also explain why Even-Even nuclei are more stable compared to Even/Odd nuclei, which again is more stable compared to Odd-Odd nuclei.
3) It can calculate the potential depth of both neutrons and protons in a nucleus.
3) It explains by Beta Decay happen. Unstable nuclei have uneven Highest Energy levels. This opens up the possibility of beta decay in which a neutron can get converted to a proton or vice versa.

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NUCLEAR AND PARTICLE PHYSICS - Series :
••••••••••••••••••••••••••••••••••••••••••
1) What is Nuclear Physics? ►    • What is Nuclear Physics? (LECTURE SER...  
2) Nuclear Size / Radius ►    • Nuclear Size / Radius  
3) Quantization of Angular Momentum ►    • What is Quantization of Angular Momen...  
4) Nuclear Spin and Angular Momentum ►    • Nuclear Spin and Angular Momentum  
5) Nuclear Magnetic Moment ►    • Nuclear Magnetic Moment  
6) Binding Energy of Nucleus & BE Curve ►    • What is Nuclear Binding Energy? (and ...  
7) Parity of Wave function ►    • What is Parity of a Wave function? (O...  
8) Symmetric & Anti symmetric Wave func ►    • Symmetric and Anti-symmetric Wave fun...  
9) Liquid Drop Model of Nucleus ►    • Liquid Drop Model of Nucleus ( Bindin...  
10) Corrections to Liquid Drop Model ►    • Corrections to Liquid Drop Model / Se...  
11) NZ Graph (& Maximizing BE) ►    • What is NZ Graph? | Maximizing Bindin...  
12) Fermi Energy of Nucleus ►    • Fermi Energy of Nucleus (Derivation)  
13) Fermi Gas Model of Nucleus ►    • Fermi Gas Model of Nucleus  
14) Shell Model of Nucleus ►    • Shell Model of Nucleus  
15) Nature of (Strong) Nuclear Force) ►    • Nature of (Strong) Nuclear Force  
16) Alpha, Beta & Gamma Decay ►    • Alpha, Beta & Gamma Decay [Complete D...  
17) Gamow's Theory of Alpha Decay ►    • Gamow's Theory of Alpha Decay AND Gei...  
18) Gamow's Theory (DERIVATION) ►    • [DERIVATION ] Gamow's Theory of Alpha...  
19) Q Value and KE of Alpha Decay ►    • Q-Value | KE of Alpha Decay (Kinematics)  
20) Beta Decay & Neutrino Hypothesis ►    • Beta Decay & Neutrino Hypothesis !! (...  
21) Radioactive Decay Law ►    • What is Radioactive Decay? Half Life ...  
22) Nuclear Cross Section ►    • Nuclear Cross Section !!  
23) Interaction of Nuclear Radiation with Matter ►    • Interaction of Nuclear Radiation with...  
24) What is Cherenkov Radiaton? ►    • The Physics of Cherenkov Radiation  
25) Nuclear Detectors ►    • Nuclear Detectors - Ionization Chambe...  
26) Geiger Muller Counter ►    • What is a GM Counter? - Geiger Muller...  
27) Scintillation Detector ►    • What is a Scintillation Detector?  
28) Semiconductor Detectors ►    • What are Semiconductor Detectors?  
29) What are Accelerators? ►    • What are Accelerators? + Electrostati...  
30) Van de Graaff Generator ►    • Van de Graaff | Tandem & Pelletron Pa...  
31) Linear Accelerator ►    • Linear Particle Accelerator (Principl...  
32) Cyclotron ►    • Cyclotron (Principle, Construction, W...  
33) Synchrotron ►    • Cyclotron & Synchrotron (Particle Acc...  
34) Betatron ►    • Cyclotron & Synchrotron (Particle Acc...  
35) Fission & Fusion ►    • Nuclear Fission and Fusion | What rol...  
36) Proton-Proton & CNO Cycle ►    • Proton Proton Cycle & CNO Cycle  
37) Meson Theory of Nuclear Forces ►    • Meson Theory of Nuclear Forces & Esti...  
#NuclearPhysics

Image Attribution :
1) Gas, Solid -
Yelod - Wikimedia Commons * Yelod - Wikipedia (En) *[CC BY-SA 3.0 (https://creativecommons.org/licenses/...)], from Wikimedia Commons
2) Nucleus -
Marekich [CC BY-SA 3.0 (https://creativecommons.org/licenses/...)], from Wikimedia Commons
3) Liquid Drop Model
Daniel FR [CC BY-SA 3.0 (https://creativecommons.org/licenses/...)], via Wikimedia Commons