In nuclear physics, the nucleus is sometimes compared to a liquid drop of incompressible nuclear fluid. This was first proposed by George Gamow and developed by Niels Bohr and John Archibald Wheeler. The fluid is made of nucleons (protons and neutrons), which are held together by the strong nuclear force. This is a crude model that does not explain all the properties of the nucleus, but does explain the spherical shape of most nuclei. It also helps to predict the binding energy of the nucleus.
Mathematical analysis of the theory delivers an equation which attempts to predict the binding energy of a nucleus in terms of the numbers of protons and neutrons it contains. This equation has five terms on its right hand side. These correspond to the cohesive binding of all the nucleons by the strong nuclear force, the electrostatic mutual repulsion of the protons, a surface energy term, an asymmetry term and a pairing term.
The volume energy. When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. So, this nuclear energy is proportional to the volume.
The surface energy. A nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area.
The Coulomb energy. The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy.
The asymmetry energy (Pauli energy). If it wasn't for the Coulomb energy, the most stable form of nuclear matter would have N=Z, since unequal values of N and Z imply filling higher energy levels for one type of particle, while leaving lower energy levels vacant for the other type.
The pairing energy. An energy which is a correction term that arises from the tendency of proton pairs and neutron pairs to occur. An even number of particles is more stable than an odd number.
If we define A as the number of nucleons, Z the number of protons and N the number of neutrons, the mass of an atomic nucleus is given by:
where mp and mn are the rest mass of a proton and a neutron, respectively, and EB is the binding energy of the nucleus, and c is the speed of light.
This formula states that the binding energy will take the following form:
Every energy term can be calculated and introduced into the formula along with the numbers A and Z in order to calculate the binding energy.
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