Fermi energy of nucleus

In summary, the calculated Fermi energy of neutrons and protons in a heavy nucleus may differ, but it has been observed that they have the same energy. However, the Coulomb repulsion of the protons plays a factor in this as it favors lowering the number of protons to balance the Coulomb energy and the symmetry energy. The average Coulomb energy per proton may be twice the difference of the average Fermi energies per nucleon, but this is due to differences in units and the fact that not all neutrons will have the same energy.
  • #1
gildomar
99
2
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 

What is Fermi energy of nucleus?

The Fermi energy of a nucleus is the maximum energy that an individual nucleon (proton or neutron) can have within the nucleus at absolute zero temperature. It is a measure of the energy required to remove a nucleon from the nucleus.

How is Fermi energy of nucleus calculated?

The Fermi energy of a nucleus can be calculated using the semi-empirical mass formula, which takes into account the number of protons and neutrons in the nucleus, as well as the binding energy of the nucleus. It can also be calculated using experimental data from scattering experiments.

What is the significance of Fermi energy of nucleus?

The Fermi energy of a nucleus is important in understanding the stability and structure of nuclei. It also plays a role in nuclear reactions and nuclear fusion, as well as in the study of nuclear matter and the properties of nuclear forces.

What factors affect the Fermi energy of nucleus?

The Fermi energy of a nucleus is primarily affected by the number of nucleons in the nucleus, as well as the distribution of protons and neutrons within the nucleus. Other factors that can influence the Fermi energy include the nuclear spin and the shape of the nucleus.

How does the Fermi energy of nucleus compare to the Fermi energy of electrons?

The Fermi energy of nucleus is much higher than the Fermi energy of electrons. This is because the strong nuclear force that binds nucleons together is much stronger than the electromagnetic force that binds electrons to atoms. Additionally, the Fermi energy of electrons is dependent on the number of electrons, while the Fermi energy of nucleus depends on the number of nucleons.

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