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3-2: The Nuclear Force

On the preceding page, we learned that the origin of the huge amount of nuclear energy is the binding energy of nuclei.
Then, what is the binding energy of nuclei? It has been explained in detail on the page, 2-3: "Mass of Nuclei, Binding Energy". We can review it as follows:
The atomic nucleus consists of many nucleons (protons and neutrons) which bind to each other through the interaction called nuclear force. The mass of a nucleus is slightly less than the sum of masses of its constituent nucleons. This mass difference called the mass defect. According to Einstein's Mass-Energy Equivalence, the mass defect is converted into an energy. This is the binding energy of the nucleus. The strength of its binding is therefore represented by the magnitude of the binding energy.
Hence, we can say that the final origin of the origin of the nuclear energy is nothing but the nuclear force.
Then, what is the nuclear force?

[The Origin of the Coulomb force]
The Coulomb force works between two electric charges, q and q'. If the two charges are of the same sign, it is repulsive. If they are of opposite sign, then they attract each other.
In the Quantum Mechanics of Electromagnetic Fields (or Quantum Electrodynamics), the exchange of photons between two charges causes the Coulomb force between them. (See the following figure.)
[The Origin of the Coulomb Force]
If two charges, q and q' , exchange photons, the Coulomb force occurs between them. This figure is its schematic drawing. The solid lines represent particles running upward.

[Yukawa's Meson Theory]
In 1935, H. Yukawa (Japan, 1907 - 81) proposed a theory for the origin of the nuclear force on an analogy with the above-mentioned interpretation of the Coulomb force. He thought that the nuclear force might be caused by the exchange of some massive unknown particles between nucleons. Now this particle is known as the pi-meson or pion. (See the following figure.)
The pion was found in cosmic rays by C. F. Powell (UK, 1903 - 69) et al. in 1947 and produced artificially by an accelerator in 1948.
If pions are exchanged between two nucleons, the nuclear force occurs. (See the following figure.)

There exist three types of pions, with charge 0, with charge +e, and with charge -e. Their masses are nowadays known well as

[Properties of the Nuclear Force]
The nuclear force is one of the strong interactions. It is about ten times as strong as the Coulomb force. However it is of very short-range compared with the Coulomb force; namley, the nuclear force is very strong but it does not work unless two nucleons approach to each other in a very short distance. Moreover, it is known that, when they approach very close to each other, ( ), an extremely strong repulsive force works.
The detailed properties of the nuclear force at the distance smaller than are not sufficiently clarified yet.
In the following figure, the potential of the nuclear force between two nucleons is roughly compared with the Coulomb potential between two charges, e and -e.

[Comparison between the Nuclear Force and the Coulomb Force]
A rough comparison between the nuclear force (between two nucleons) and the Coulomb force (between charges e and -e ) is shown. The red solid curve indicates the nuclear force and the blue dashed curve the Coulomb force. The abscisa denotes the distance between particles, r. In the region of r < 3 fm, the nuclear force is overwhelmingly stronger than the Coulomb force. You should notice that, in the very inner region ( r < ), an extremely strong repulsive force works.
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