Separation energy of nucleons and Coulomb barrier

In summary, separation energy refers to the energy required to remove a nucleon (proton or neutron) from an atomic nucleus, reflecting the binding strength of the nucleons within the nucleus. The Coulomb barrier, on the other hand, is the energy barrier due to the electrostatic repulsion between positively charged protons in a nucleus, which must be overcome for nuclear reactions, such as fusion, to occur. Understanding both concepts is crucial in nuclear physics, as they influence nuclear stability and reaction rates.
  • #1
ValeForce46
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Why is a neutron easier to extract than a proton? It should be the other way around because Coulomb force is repulsive and the only attractive force in the nucleus is the strong force.
My professor and the book I'm reading (Particles and Nuclei: An Introduction to the Physical Concepts by Povh et al.) says that "The emitted nucleons are primarily neutrons since they are not hindered by the Coulomb threshold" which means that a neutron has a separation energy lower than a proton. They take this as true, indeed for example when a nucleus decays to another nucleus in an excited state, we compare the energy of this excited level and the separation energy of neutron to check if it's bonded for nucleons' emission (like in the ##\beta##-decay
##^{60}_{27}##Co ##\to## ##^{60}_{28}##Ni).

I still don't get how, although the Coulomb force between protons is repulsive, the existence of this force makes it harder to separate a proton from a nucleus. I'd expect the proton to see something which reduce the confinement inside the well (of the nucleus) but this is not the true, it sees a barrier caused by this force. Instead a neutron doesn't see a barrier because there's no Coulomb force and therefore (I guess?) it's easier to separate.

So, why the Coulomb force, which should facilitate the separation as it's repulsive, makes it harder for a proton to be separated than a neutron?

However, my professor gives an explanation which I really hate (or maybe I don't understand?). She says that to understand this, you have to see the process in time-reverse, which means the proton that "enters" the nucleus and of course it meets a barrier. Then something about conservation of the energy in the reverse process and that's it.
 
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  • #2
If isotopes are stable against beta decays then p -> n + e+ has to be forbidden. In that reaction we would gain energy from the positron leaving the nucleus, that means the highest filled proton energy level has to be lower than the highest filled neutron energy level, otherwise you would get beta+ decays. How much lower is given by the Coulomb potential.
 

FAQ: Separation energy of nucleons and Coulomb barrier

What is the separation energy of a nucleon?

The separation energy of a nucleon is the energy required to remove a single nucleon (either a proton or a neutron) from a nucleus. It is a measure of the binding energy that holds the nucleon within the nucleus. This energy varies depending on the nucleon and the specific nucleus from which it is being removed.

How is the separation energy of a nucleon calculated?

The separation energy of a nucleon is calculated using the difference in the binding energy of the nucleus before and after the nucleon is removed. Mathematically, it can be expressed as the difference between the total binding energy of the original nucleus and the binding energy of the resulting nucleus plus the nucleon. For example, the neutron separation energy (Sn) can be calculated as Sn = BE(Z, A) - BE(Z, A-1), where BE(Z, A) is the binding energy of the nucleus with Z protons and A nucleons.

What is the Coulomb barrier?

The Coulomb barrier is the energy barrier due to electrostatic repulsion that charged particles, such as protons, must overcome to get close enough to each other to engage in nuclear reactions. This barrier arises because like charges repel each other, and protons within a nucleus are all positively charged. The height of the Coulomb barrier depends on the charge and size of the nucleus.

Why is the Coulomb barrier important in nuclear reactions?

The Coulomb barrier is important because it affects the likelihood of nuclear reactions occurring. For fusion reactions, where two nuclei must come close enough to merge, the particles must have enough kinetic energy to overcome this barrier. In astrophysical processes, such as in stars, the Coulomb barrier influences the rate of nuclear fusion and thus the energy production and evolution of stars.

How does the separation energy of nucleons relate to nuclear stability?

The separation energy of nucleons is directly related to nuclear stability. Higher separation energy indicates that more energy is required to remove a nucleon, which implies a more stable nucleus. Conversely, lower separation energy suggests that the nucleus is less stable and more likely to undergo nuclear reactions or decay. The balance of separation energies for protons and neutrons contributes to the overall stability and the likelihood of various nuclear processes.

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