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Strong Nuclear Force

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There are four fundamental forces in nature. These four forces are called the gravitational force, the electromagnetic force, the weak nuclear force, and the strong nuclear force. The strong nuclear force is also called the strong force, and it is the strongest out each of the four fundamental forces in nature. Though it is the strongest force, it is essential to understand that the strong nuclear force is only effective in very small ranges.


Protons, and neutrons are subatomic particles that are contained in the nucleus. Protons are positively charged, while neutrons are neutral, and carry no charge. The leading purpose of the strong nuclear force is to hold these quarks (the subatomic particles that are found in the nucleus) together to form hadrons. Its carrier particles are called gluons, and they "glue" quarks together. Quarks contain electromagnetic charge and are viewed to be conjoined by something called the color force. The strong nuclear force uniting the nucleons (protons and neutrons) is sometimes considered to be an excess color force.

History Edit

Protons and neutrons were once thought to be fundamental particles prior to the 1970s. The term, "strong force" is also known as the Strong Nuclear Force or the Residual Strong Force. The residual effects of the strong force were being studied. These effects act on hadrons (subatomic particles that are composed of quarks and take part in the strong interaction), baryons (also called the heavy particle, it is any of a family of subatomic particles that participate in strong interactions, are more massive than mesons, and are composed of three quarks), and mesons (any of a family of subatomic particles that participate in strong interactions, they are composed of a quark and an antiquark, and have masses in between leptons and baryons). It was assumed that this force could overcome electric repulsion. This force has such great strength at short distances that it was named the “strong force.” Once quarks were discovered, scientist realized that the strong force was acting upon the quarks and gluons making up the protons, not the actual protons themselves. Now, this is referred to the residual strong force, and the correct theory of strong interaction is called the color force.


Gluons are particles in the color force between quarks. This is similar the swap of photons, which takes place between two charged particles in the electromagnetic force. Gluons are seen as the most important exchange particle in the strong nuclear force, taking place between protons and neutrons in a nucleus. The strong nuclear force is short range, and the interactions between nucleons are the excess color force. This excess color force extends outside of the boundary of the proton or neutron.


The above diagram is called a Feynman diagram. As shown, the gluon produces color change for the quarks. Gluons carry a unit of color and a unit of anti-color; therefore, they are bi-colored. The blue quark is changed into a green quark, and the green quark is changed into the blue quark. The range of the strong force is bounded by the interacting gluons and the quarks (quark confinement). These assets differ from the properties of photons, since photons have no mass and have infinite range. Photons do not carry charge, while gluons carry the color charge.

Gluons interact with each other, and make quark-antiquark pairs, within a specific range. This property is something that only occurs in gluons, and can possibly create gluon collections called “glue balls.” A dynamic cloud of gluons and quark-antiquark pairs in equilibrium are the interior state of a hadron in a fixed number of quarks.

Color ForceEdit

Color is an essential part of the quark model. The color force is the force between quarks. Quarks are made up of baryons, and the strong force takes place betweens baryons; therefore, the color force is the cause of strong interaction and the strong interaction is an excess color force. This excess color force binds protons and neutrons together in a nucleus.

There are some properties between nucleons that are not seen in the strong force, but seen in the color force, taking place inside a baryon. The color force is responsible for the confinement of quarks, and it does not drop off with distance. The exchange of gluons is involved with color force, and the color force is so strong that the quark antiquark pair production energy is reached before quarks can be separated. The color force only gives a small amount of force at short distances, meaning that the quarks act as free particles within the restricted boundary of the color force; quarks only feel the strong restricted force the farther apart they grow.

"Asymptotic freedom" is an expression used to describe the gluon interaction between quarks.

The Confinement of QuarksEdit

The color force does not drop off with distance like the other forces. It is assumed that it increases with distance at a rate of about 1 GeV per Fermi. Free quarks aren’t observed; by the time the separation is on an observable scale, the energy is far above the pair production energy for quark-antiquark pairs. U and D quarks have masses of 10s of MeV, meaning pair production occurs for distances less than a Fermi. Many mesons are expected in high-energy collision experiments.

One cannot see an isolated quark because of the fact that the color force does not allow it. The energy that is required to separate these quarks creates quark-antiquark pair’s way before these quarks are far enough to be observed.
The quarks of a proton are free to move within the proton volume If you try to pull one of the quarks out, the energy required is on the order of 1 GeV per fermi, like stretching an elastic bag. The energy required to produce a separation far exceeds the pair production energy of a quark-antiquark pair, so instead of pulling out an isolated quark, you produce mesons as the produced quark-antiquark pairs combine.


Above is a table showing the bag model. Picture quarks enclosed in an elastic bag, and in this elastic bag, quarks are free to move around. Quarks are free to move around as long as nothing tries and pulls them further apart from each other; if something tries to pull a quark out, the elastic bag will resist and stretch. James William Rolf explains the quark confinement in another way, "when we try to pull a quark out of a proton, for example by striking the quark with another energetic particle, the quark experiences a potential energy barrier from the strong interaction that increases with distance."

Asymptotic FreedomEdit

The force of containment loses strength and gets closer and closer to zero without ever actually meeting zero in close restriction. The only problem is that quarks in close restriction are free to move around as they please (like in the “ bag model” above). The following equation expresses quark systems:


In the equation, the quark strength decreases when r-values are small. This quality is the effect of the diffusion of the gluon cloud that surrounds the quarks. The diffusion of the gluon cloud reduces the color change of the quark since gluons carry “color charge.”

Using strong force with a constant that depends on the quarks wavelength is another way of finding asymptotic freedom. This equation expresses this:


In this equation, the constant will have a value of about 1 with the radius of a proton. The product is the strength of the strong nuclear force inside of the nuclei. When the proton goes though a radius that has energy of 1 TeV, the constant goes down by about 0.1, resulting in asymptotic freedom.

Pion Range of Strong ForceEdit

One can estimate the range of the strong force if one assumes that it is a force that involves pions (any of the group of three mesons that have positive, negative, or zero charge, a mass of about 270 times greater than an electron, and spin zero). The equation ( is used with a pion mass of

p0 mass = 264 me = 135.0 MeV/c2,

and the range produced is

Range = 0.73 x 10-15 m = 0.61 x classical proton radius.

Hideki Yukawa said that the rage of the nuclear force was approximately a Fermi, and computed that the mass of the exchange particle should be about 100 MeV. This lead to the discovery of the pion. When particles in the nucleus are near each other, other particles with greater mass must be included in this model of the strong force.

Though the force between quarks does not decrease inside a proton, neutron, or any hadron (the confinement of quarks), the strong force decreases sharply outside a proton or neutron, within a Fermi of distance. The pion range is this sharp decrease and helps understand the inconsistency of the strong nuclear force. In order for neighboring protons to attract to each other, an exchange must take place, but an isolated quark cannot be exchanged (the confinement of quarks). Though this is true, quark-antiquark pairs (mesons) can be exchanged. A pion is the lightest of the mesons. Since it is lighter, it has a longer range, meaning the range of a pion can quickly exchange force that has to do with quark-antiquark pairs.

Practice ProblemsEdit

Q1) (a)If force is defined as minus the rate of change of potential energy with distance or in symbols

F = - dE / dr,

then sketch a force-separation curve for two nucleons , explaining clearly your reasoning.

(b) If a deuteron is an ordinary hydrogen atom with an extra bound neutron, show that the binding energy of the deuteronis about 2.2 MeV. Hence determine the least frequency of gamma rays that could be used to split a deuteron into a free neutron and a proton.

Q2) (a)Calculate the mass of the field quanta of the strong force(in MeV). Look up the mass of Pions (Pi - Mesons).

(b)Pions have a baryon number of zero and may be neutral(po), negative (p-), or positively charged (p+). If mesons consist of a quark/antiquark pair, deduce the quark structure of pions, using quark data.

Q3) (a) If the nuclear radius R is given by the simple formula

R = RoA^1/3

where A is the mass number and Ro is a constant then show that the density of any nucleus is constant.

(b) If the value of Ro is 1.2 x 10^-15 m then deduce the radius of a 12C atom and calculate its density. (the density of gold is 1.96 x 10^3 kgm^-3.)

Q4) If the uncertainty principle is stated in the form

DE.Dt > h / 2p

and we assume that the speed of pion travel is c, then deduce the Yukawa formula

m = h / 2pRc.

This will only apply for an event in which energy DE is NOT conserved if the duration of the event is less than

h / 2pDE.

References and ResourcesEdit









8. Rohlf, James William, Modern Physics from a to Z0, Wiley, 1994









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