Nuclear structure

Understanding the structure of the atomic nucleus is one of the central challenges in nuclear physics.

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 ${\displaystyle Z}$ protons and ${\displaystyle N}$ neutrons is given by

where ${\displaystyle A=Z+N}$ is the total number of nucleons (Mass Number). The terms proportional to ${\displaystyle A}$ and ${\displaystyle A^{2/3}}$ represent the volume and surface energy of the liquid drop, the term proportional to ${\displaystyle Z^{2}}$ represents the electrostatic energy, the term proportional to ${\displaystyle (N-Z)^{2}}$ represents the Pauli exclusion principle and the last term ${\displaystyle \delta (A,Z)}$ is the pairing term, which lowers the energy for even numbers of protons or neutrons. The coefficients ${\displaystyle a_{V},a_{S},a_{C},a_{A}}$ 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.

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