Pauli principle and coupling term in Weizsäcker formula

In summary, the pairing term in the Weizsäcker formula refers to the spin-spin interaction between protons and neutrons in a nucleus. The Pauli exclusion principle states that particles with the same quantum numbers cannot occupy the same quantum state simultaneously. This principle causes the pairing effect, where protons and neutrons fill energy levels in pairs with opposite spins, leading to a lower energy state for the nucleus. Without the Pauli exclusion principle, all particles would occupy the lowest energy state and there would be no pairing effect.
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crick
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Consider the pairing term in Weizsäcker formula. Here https://en.wikipedia.org/wiki/Semi-empirical_mass_formula#Pairing_term it is claimed that:

Due to the Pauli exclusion principle the nucleus would have a lower
energy if the number of protons with spin up were equal to the number
of protons with spin down.
I don't understand how Pauli exclusion principle should be the cause of this. This term comes from spin-spin interaction (or "coupling"), but I do not see the link with the fact that protons (or neutrons) with the same quantum numbers cannot occupy the same quantum state within a quantum system simultaneously
 
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Without the Pauli exclusion principle all protons (and all neutrons) would simply occupy the lowest energy state and you wouldn't see any paring effect. Due to this principle every energy level has only two states (spin up and down) which get filled after each other. Every odd proton (neutron) has to start the next energy level.
 
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What is the Pauli principle?

The Pauli principle, also known as the Pauli exclusion principle, states that no two identical fermions can occupy the same quantum state simultaneously. This principle is a fundamental concept in quantum mechanics and explains the behavior of particles such as electrons in an atom.

What is the significance of the Pauli principle in the Weizsäcker formula?

The Pauli principle is incorporated into the Weizsäcker formula, a semi-empirical formula used to calculate the binding energy of atomic nuclei. The inclusion of the Pauli principle in the formula accounts for the repulsive force between identical fermions in the nucleus, which affects the overall binding energy.

What is the coupling term in the Weizsäcker formula?

The coupling term in the Weizsäcker formula is a term that accounts for the attractive force between nucleons (protons and neutrons) in the nucleus. This term takes into consideration the strong nuclear force, which is responsible for holding the nucleus together.

How does the coupling term affect the binding energy in the Weizsäcker formula?

The coupling term in the Weizsäcker formula contributes to the overall binding energy of the nucleus. A larger coupling term results in a stronger attractive force between nucleons, leading to a higher binding energy and a more stable nucleus.

What is the relationship between the coupling term and the Pauli principle in the Weizsäcker formula?

The coupling term and the Pauli principle are both important factors in the Weizsäcker formula and are interconnected. The Pauli principle introduces a repulsive force between identical fermions, while the coupling term accounts for the attractive force between nucleons. Together, these terms help to accurately predict the binding energy of nuclei.

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