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Concept
Nuclear structure
Summary
Understanding the structure of the atomic nucleus is one of the central challenges in nuclear physics.
Semi-empirical mass formula
The liquid drop model is one of the first models of nuclear structure, proposed by Carl Friedrich von Weizsäcker in 1935. It describes the nucleus as a semiclassical fluid made up of neutrons and protons, with an internal repulsive electrostatic force proportional to the number of protons. The quantum mechanical nature of these particles appears via the Pauli exclusion principle, which states that no two nucleons of the same kind can be at the same state. Thus the fluid is actually what is known as a Fermi liquid.
In this model, the binding energy of a nucleus with protons and neutrons is given by
where is the total number of nucleons (Mass Number). The terms proportional to and represent the volume and surface energy of the liquid drop, the term proportional to represents the electrostatic energy, the term proportional to represents the Pauli exclusion principle and the last term is the pairing term, which lowers the energy for even numbers of protons or neutrons.
The coefficients and the strength of the pairing term may be estimated theoretically, or fit to data.
This simple model reproduces the main features of the binding energy of nuclei.
The assumption of nucleus as a drop of Fermi liquid is still widely used in the form of Finite Range Droplet Model (FRDM), due to the possible good reproduction of nuclear binding energy on the whole chart, with the necessary accuracy for predictions of unknown nuclei.
Nuclear shell model
The expression "shell model" is ambiguous in that it refers to two different items. It was previously used to describe the existence of nucleon shells according to an approach closer to what is now called mean field theory.
Nowadays, it refers to a formalism analogous to the configuration interaction formalism used in quantum chemistry.
Systematic measurements of the binding energy of atomic nuclei show systematic deviations with respect to those estimated from the liquid drop model.
Official source
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