Pauli Exclusion Principle-question

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In summary, the Pauli Exclusion Principle states that two identical fermions cannot coexist in the same energy level within a nucleus. However, this principle may not apply if the fermions have opposite isospin. Isospin is not a fundamental quantum number, but rather an approximate symmetry between different types of fundamental fermions, such as up and down quarks. In the case of composite fermions, the Pauli Exclusion Principle may not apply. The Shell model of the nucleus also treats protons and neutrons as nonidentical particles, with each energy level able to hold 4 nucleons with different z-component of intrinsic spin.
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Rade
Pauli Exclusion Principle--question

According to the Pauli Exclusion Principle, two identical FERMIONS cannot coexist in the same energy level within a nucleus.

My question is, could two identical fermions coexist if they had opposite isospin, that is, does isospin make the two otherwise identicle fermions "not-identicle" such that the Pauli EP does not apply? Thanks in advance for any help, I would appreciate mathematical details in any answer.
 
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Electrons in atoms come in pairs (except for possibly one left over) with opposite spin, but otherwise identical properties.
 
  • #3
Rade said:
According to the Pauli Exclusion Principle, two identical FERMIONS cannot coexist in the same energy level within a nucleus.

My question is, could two identical fermions coexist if they had opposite isospin, that is, does isospin make the two otherwise identicle fermions "not-identicle" such that the Pauli EP does not apply? Thanks in advance for any help, I would appreciate mathematical details in any answer.
It is wrong to say "cannot coexist in the same energy level ".
If the energy level is degerate, then a number of fermions equal to the degeneracy coulld fill the same enrgy level.
The deuteron with n of I3=-1/2 and p of I3=+1/2 is an example of
two nucleons with opposite Ispins n the same space-spin state.
 
  • #4
Meir Achuz said:
It is wrong to say "cannot coexist in the same energy level ". If the energy level is degerate, then a number of fermions equal to the degeneracy could fill the same energy level. The deuteron with n of I3=-1/2 and p of I3=+1/2 is an example of two nucleons with opposite Ispins in the same space-spin state.
Yes, thank you, of course the P and N "coexist" with opposite isospin as the deuteron--but they are not a priori "identical". So this example you give will not answer the OP question. My question is ...can two identical fermions coexist (use whatever concept you like for energy level such as "space-spin state") if the ONLY difference between them is ISOSPIN... ?
 
  • #5
mathman said:
Electrons in atoms come in pairs (except for possibly one left over) with opposite spin, but otherwise identical properties.
Thank you, but the "spin" of the electron is not the same as "isospin" ---see below from Wiki-- so I do not see how your response in any way helps with the OP question--but thank you for your time:

Heisenberg's contribution was to note that the mathematical formulation of this symmetry was in certain respects similar to the mathematical formulation of spin, from whence the name "isospin" derives. To be precise, the isospin symmetry is given by the invariance of the Hamiltonian of the strong interactions under the action of the Lie group SU(2). The neutron and the proton are assigned to the doublet (the spin-1/2 or fundamental representation) of SU(2). The pions are assigned to the triplet (the spin-1 or adjoint representation) of SU(2).

Just as is the case for regular spin, isospin is described by two numbers, I, the total isospin, and I3, the component of the spin vector in a given direction. The proton and neutron both have I=1/2, as they belong to the doublet. The proton has I3=+1/2 or 'isospin-up' and the neutron has I3=−1/2 or 'isospin-down'. The pions, belonging to the triplet, have I=1, and π+, π0 and π− have, respectively, I3=+1, 0, −1.
 
  • #6
Rade said:
According to the Pauli Exclusion Principle, two identical FERMIONS cannot coexist in the same energy level within a nucleus.

My question is, could two identical fermions coexist if they had opposite isospin, that is, does isospin make the two otherwise identicle fermions "not-identicle" such that the Pauli EP does not apply? Thanks in advance for any help, I would appreciate mathematical details in any answer.
Depends. Yes, they could, if you're talking about quarks. If you're talking about composite fermions that's another issue.

The key point here is that isospin is not a fundamental quantum number. Rather, it is an approximate symmetry relating two distinct types of fundamental fermions: up and down quarks. Since up and down quarks correspond to different fields, the Pauli exclusion principle does not apply to them together, and they could be in the same state.
 
  • #7
Rade said:
According to the Pauli Exclusion Principle, two identical FERMIONS cannot coexist in the same energy level within a nucleus.

My question is, could two identical fermions coexist if they had opposite isospin, that is, does isospin make the two otherwise identicle fermions "not-identicle" such that the Pauli EP does not apply? Thanks in advance for any help, I would appreciate mathematical details in any answer.

You can also look at the motivation for the Shell model of the nucleus, and you will se that protons and neutrons are treated as nonidentical fermions a priori. You will se that for each energy level, 4 nucleons can be contained: 2 protons and 2 neutrons. Were the protons differs by their z-component of intrinsic spin, and also for the neutrons. I think it is quite trivial to see that protons and neutrons are nonidentical particles=)
 

1. What is the Pauli Exclusion Principle?

The Pauli Exclusion Principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously.

2. Why is the Pauli Exclusion Principle important?

The Pauli Exclusion Principle is important because it explains many fundamental properties of matter, such as the electron configuration of atoms and the stability of matter. It also plays a crucial role in understanding the behavior of electrons in materials and the formation of chemical bonds.

3. Who discovered the Pauli Exclusion Principle?

The Pauli Exclusion Principle was first proposed by Austrian physicist Wolfgang Pauli in 1925.

4. How does the Pauli Exclusion Principle affect electron shells in atoms?

The Pauli Exclusion Principle dictates that each electron in an atom must have a unique set of quantum numbers, which determines its energy level and location in an atom's electron shell. This results in the filling of electron shells in a specific order and explains the stability of atoms.

5. Does the Pauli Exclusion Principle apply to all particles?

No, the Pauli Exclusion Principle only applies to fermions, which include particles such as electrons, protons, and neutrons. Bosons, on the other hand, do not follow this principle and can occupy the same quantum state simultaneously.

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