The Strong Force – By Lukas Karoly

            In an introductory physics course, you learn about a diverse range of forces—friction, normal force, tension, spring force, etc. The majority of these forces are non-fundamental forces, and all boil down to four fundamental forces: gravity, the electromagnetic force, the strong nuclear force, and the weak nuclear force. The first two are probably the most familiar, and for good reason. The majority of forces that we experience every day, such as simple pushing or pulling, are due to the electromagnetic force, which governs interactions between charged particles. When you pick up a glass to drink, the electromagnetic force governs what happens the whole way—seeing the glass, your neurons firing, your muscles contracting, the friction of your hand gripping the glass—it is all due to electromagnetic interactions at the atomic and molecular levels. Gravity, while actually very weak compared the other three fundamental forces (the other three forces are 1025–1038 times stronger), governs most large-scale interactions, such as those of stars and planets. While the electromagnetic force behaves the same as gravity over long distances, both having an infinite range, most matter is electrical neutral on the macroscopic scale, and can therefore only interact through gravity. The last two forces operate on the subatomic scale and are not directly responsible for the forces that we experience every day. The weak nuclear force is fairly limited on scope, being mainly responsible for nuclear decays. The strong nuclear force, however, is still integral to our everyday existence as well as nuclear fusion, being responsible for holding together atomic nuclei.

The feasibility of the atomic nucleus has been in question since its discovery in the early 20th century up to the 1970s. In 1911, experiments done by Ernest Rutherford pointed toward a model of the atom in which the positive components, protons, were all concentrated in center. Given the known physics of the time, this didn’t make much sense, since like-charged particles feel a repulsive electrostatic force. This means that the nucleus, made up of multiple positively charged protons, should fly apart; however, this was never observed. So how do atomic nuclei stay bounded together? The answer lies in the strong nuclear force, also known as the strong interaction. This force was initially theorized as a force that, at least on the scale of the nucleus, was stronger than the electromagnetic force, overcoming it to bind protons and neutrons together in atomic nuclei. It is also responsible for confining quarks into protons and neutrons themselves.

Figure 1. Table of the Standard Model showing the various elementary particles.

This is just about all that is needed to know in order to understand the strong force’s role in fusion—it is the strongest of the fundamental forces, but has a very short range, and binds subatomic particles together. Some of the deeper theory surrounding the strong force, while not strictly necessary, is still interesting, so we will explore it a little bit more. Firstly, it is important to make a distinction—the force that binds the nucleus together is not strictly the strong interaction and is often called the residual strong force or nuclear force to avoid confusion. It is also more complicated, so we will begin by looking at the strong interaction, and then move into the more nuanced nuclear force. In order to get a deeper understanding of the strong interaction, we need to first talk about the Standard Model. In particle physics, the Standard Model is the most successful theory that describes elementary particles and forces (see Fig. 1). In this model, particles are divided into two main groups, fermions and bosons. Fermions are the particles that make up matter—electrons, neutrinos, their more massive counterparts, and quarks. In relation to the strong force, quarks are the most important. You may notice that some particles aren’t listed here, mainly protons and neutrons. That is because these are not actually fundamentals particles; they are hadrons, which are subatomic particles made up of two or more quarks—a proton isn’t actually one of the most fundamental building blocks, quarks are. The strong force is what binds these quarks together to make hadrons. For example, a proton is made up of three quarks, two up quarks and one down quark, which are held together by the strong force. But how does the strong force actually work? This is where things get more abstract. I don’t fully understand it either, but bear with me as we try and get through at least a basic understanding. To begin, we need to talk about the second main group of the standard model, bosons. Bosons are particles that mediate forces and interactions. The most familiar of these is probably the photon, the force carrier for the electromagnetic force. The boson associated with the strong nuclear force is the gluon (since it glues particles together). For electromagnetic interactions, electric charge is a physical property that causes matter to experience an electromagnetic force. Similarly, color charge is a physical property that causes matter to experience a strong force. Quarks and gluons are the only fundamental particles with color charge and are therefore the only ones to interact with the strong force. This interaction is what binds quarks together, creating hadrons, like protons and neutrons. One surprising things about the strong interaction, is that it doesn’t decrease with distance; however, if you tried to pull two quarks apart to test this, new quarks would be created in between. So functionally, the strong interaction only operates on the subatomic scale.

Figure 2. Animation of the nuclear force. A pion is exchanged between a proton and neutron, mediating the nuclear force.

As I mentioned above, the nuclear force that binds hadrons together, like in atom nuclei and fusion, is different from, and a bit more complicated than the strong interaction that binds quarks. While there are only two types of electric charge (positive and negative), there are six types of color charge—three colors and three corresponding anti-colors. For electric charge, a positive and negative charge cancel out to give a neutral charge. This is also true for color and anti-color. Color charge, however, has the additional property wherein the three colors (or anti-colors) will also cancel out. In hadrons, which are made up three quarks, the color charge of the quarks cancels out. This means that protons and neutrons don’t have color charge and therefore can’t interact directly through the strong force. This is where it gets a bit sticky and prickly. There is another type of hadron that I haven’t yet mentioned which becomes relevant in the nuclear force. Protons and neutrons are baryons, hadrons which are made up of an odd number of quarks. The second type of hadrons, called mesons, are composed of an equal number of quarks and anti-quarks. These mesons mediate the nuclear force. Figure 2 shows an animation of the nuclear force. The larger circles are quarks—u for up, d for down. They are also colored to represent their color charge. The top particle is a proton, which is bound to the neutron below (each composed of three quarks). The smaller pairs of colored circles are gluons, which mediate the strong interaction between the quarks. The nuclear force is the transmission of gluons between nucleons (particles that make up the nucleus) via mesons, such as the pion shown in the animation. In this way, there is some residual strong interaction that can bind nucleons, despite them being colorless. I know this is pretty confusing, don’t worry, I don’t understand it fully either. One last thing I would like to mention, is that this nuclear force is weaker than the strong interaction between quarks, and decreases rapidly with distance, giving it a very short range.

Figure 3. Potential energy diagram between two protons (or two nuclei in general). A negative potential corresponds to an attractive force, while a positive potential is a repulsive force. The repulsive electrostatic force dominates for large r. Closer to the nucleus, the attractive nuclear force dominates. An incoming proton needs enough energy to overcome the Coulomb barrier, otherwise it will scatter.

Fusion occurs when two nuclei get close enough to fuse, or bind together, and is therefore mediated by the strong interaction (more specifically, the nuclear force). As mentioned above, like-charged particles feel a repulsive electrostatic force. So, when two nuclei, which are positively charged, are close, they will feel a repulsive force. The strong force is stronger than the electromagnetic force, but again, it has a very short range. In order for fusion to occur, the nuclei need enough energy to get close enough (~10-15 m) for the attractive strong force to overcome the repulsive electromagnetic force. Figure 3 shows a potential energy diagram for fusion. An incoming nucleus approaches from the right at some large distance r. As it gets closer, the electrostatic force creates a Coulomb barrier. If the incoming nucleus does not have enough energy—for deuterium this is about 0.4 MeV—it will scatter away, and no fusion will occur (fusion of low energy nuclei can still occur through quantum tunneling, although it has a fairly low probability of happening). If the incoming nuclei does have enough energy to overcome the Coulomb barrier and enter into the domain of the strong force, the nuclei can fuse. The strong force is also responsible for the energy produced by fusion. Einstein’s special relativity gives us the energy-mass equivalence (the famous E = mc2). One consequence of this is that nuclei masses are significantly different than the sum of the masses of their individual components, known as mass defect. This difference is from the potential energy due to the nuclear force—the negative potential reduces the mass. In fusion reactions (and also fission reactions) energy is produced because of changes in these nuclear potentials. The mass defect in the product nuclei is larger than in the reactant nuclei. This difference is the energy produced in the fusion reaction. So, for a multitude of reasons, fusion would not be possible without the strong force.

Works Cited:

Harms et al. Principles of Fusion Energy, 2000.