Fermi energy of nucleus

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Discussion Overview

The discussion revolves around the Fermi energy of neutrons and protons in heavy nuclei, exploring why calculated values differ from observed values and the role of Coulomb repulsion in this context. The scope includes theoretical considerations and conceptual clarifications regarding nuclear physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that the calculated Fermi energies of neutrons and protons differ, yet they are observed to be the same, raising questions about the underlying models.
  • One participant mentions a textbook reference indicating a 5 MeV difference in Fermi energies, while observational data suggests they are equal, with proton repulsion energy estimated at 10 MeV.
  • Another participant explains that Fermi energy is dependent on particle density and the number of protons and neutrons, suggesting that equal numbers lead to equal Fermi energies, while imbalances increase total energy due to symmetry energy considerations.
  • There is a suggestion that Coulomb repulsion energy might equal the difference in Fermi energies, but a participant expresses confusion over a calculation that suggests it is twice that difference.
  • Concerns are raised about comparing total Coulomb energy with Fermi energy per nucleon, emphasizing that Fermi energy represents maximum energy and not all nucleons have the same energy.
  • A later reply clarifies that the comparison was actually made with average Coulomb energy per proton, which was found to be twice the difference of average Fermi energies per nucleon.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between calculated and observed Fermi energies, as well as the implications of Coulomb repulsion. There is no consensus on the correctness of the models or calculations discussed.

Contextual Notes

Participants highlight the importance of definitions and the context of energy comparisons, noting that discrepancies may arise from different interpretations of energy per nucleon versus total energy.

gildomar
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How is it that the calculated Fermi energy of neutrons and protons in a heavy nucleus are different, but it's observed that they have the same energy? And how much is the Coulumb repulsion of the protons play a factor in that?
 
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gildomar said:
How is it that the calculated Fermi energy of neutrons and protons in a heavy nucleus are different, but it's observed that they have the same energy? And how much is the Coulumb repulsion of the protons play a factor in that?
Not sure I understand you - do you have a reference?

If calculated values differ from observed values than the model used for the calculation is wrong in some important way.
 
It was part of a question in a textbook: the back of the book gave their Fermi energies, with about 5 MeV difference between them, but the question said that their observational energies were the same. And later the energy of the proton repulsion was found to be 10 MeV.
 
The Fermi energy depends only on the particle density. Since the nucleons are distributed uniformly throughout the nuclear volume, an equivalent statement is that the Fermi energy for protons depends only on the number of protons Z present in the nucleus, and the Fermi energy for neutrons depends only on the neutron number N. If Z = N the two Fermi energies are equal. If we depart from Z = N the Fermi energies are unequal and the total energy increases. The difference is known as the symmetry energy.

The Coulomb repulsion favors lowering Z, to a point where the Coulomb energy and the symmetry energy balance one another.
 
That's kind of what I was thinking, with the Coulomb repulsion energy equaling the difference of the two Fermi energies. However, the very simple calculation for the Coulomb energy gave an energy of twice the difference of the two Fermi energies. Given that it was off by almost exactly 2, I was thinking that I was missing some physics somewhere.
 
We have to be careful what to compare. The Coulomb energy is usually given as a total energy, whereas the Fermi energy is energy per nucleon. Also it's the maximum energy - not the case that all the neutrons in the nucleus will have the same energy eF, there will be an average < eF.
 
It was actually the average Coulomb energy per proton that I was comparing. That was twice the difference of the average Fermi energies per nucleon.
 

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