# Nuclear models

Nuclear models were created to represent the atomic nucleus, which makes it possible to study its properties and characteristics.

The structure of the atomic nucleus is more complex than the structure of the atom itself. This is because the interaction between the components of the atom can be expressed by Coulomb’s law, which has a simple mathematical representation. Also, the center of an atom is well defined as it is its own nucleus. The nuclei are formed by neutrons and protons, not having a well-defined center, which makes the expression to calculate the force between its components much more complex.

To represent the atomic nucleus and facilitate the study of its properties, nuclear models were created . The greater the ability of a model to make predictions to be tested experimentally, the better its efficiency.

The main nuclear models are: liquid drop model, Fermi gas model and layer model. Now let’s see what each of these models is about.

## The liquid drop model

The liquid drop model considers the nucleus as a sphere that has a constant density inside it, which decreases to zero when it reaches the nuclear surface. This model is based on two properties:

1. The density of the nuclei is practically constant;
2. The binding energies are proportional to the nuclear masses.

Among the advantages of the liquid drop model is the fact that it allows predictions of the mass and binding energy of atomic nuclei. However, it is not efficient to explain important concepts, such as the spin and magnetic moments of the atomic nucleus.

The layer model seeks to describe some properties of the atomic nucleus that the liquid drop cannot, such as the energies of the nuclear excited states and the nuclear magnetic moments. For this, this theory makes a description that considers the individual properties of the nucleons, which are not considered in collective models, as is the case of the liquid drop.

This model considers that the atomic nucleus particles do not interact with each other, so they assume separate orbits, and the state of motion is described by specific quantum numbers . From this theory, it is possible to calculate the energy of each of the energy levels of the atomic nucleus.

## Fermi gas model

The Fermi gas model was proposed in 1935 by H Bethe. He considers that the atomic nucleus is constituted by a mass of quantum gas with properties different from classical theories. This gas would be in thermodynamic equilibrium and there would be no transfer of energy or linear momentum between the particles that constitute it, based on the Pauli exclusion principle.

Mathematical calculations obtained with these theories were not considered, since they require higher-level mathematical knowledge.

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