Matt Strassler [March 4, 2013]
Now that we know a nucleus is tiny, we have to ask an obvious question: why is it so small? Atoms are made from tiny particles, but they are much larger than the particles they contain. We learned why in this article. By contrast, nuclei are not much different in size from the protons and neutrons that they are made of. Is there a reason, or is this a coincidence?
Meanwhile, we know already that electrical forces hold atoms together. What force or forces are holding a nucleus together?
Here we begin to enter new territory, far different from what we’ve explored previously… because it is clear that a new force that we have not yet discussed must be at work.
The Residual Strong Nuclear Force
If nature had only gravitational and electrical forces, the ones we encounter in daily life, a nucleus with multiple protons would blow itself apart: the electrical forces pushing the protons away from each other would be millions of millions of millions of times stronger than any gravitational forces pulling them together. So some other force must provide an attraction even stronger than the electrical repulsion. This force is the strong nuclear force — though only a shadow of its true power will be visible in the structure of the nucleus. When we study the structure of protons and neutrons themselves, then we will see the true capabilities of the strong nuclear force. In the nucleus, we encounter only what’s sometimes called a “residual force” — and I will call it the “residual strong nuclear force”. (Sometimes this term is not used — people just call it the strong nuclear force, but there’s merit in this distinction.)
A caution: In the end, although (as we’ll see) the full-fledged strong nuclear force — the force between the particles (quarks, gluons, anti-quarks) inside a proton or a neutron — is fairly simple, at least in some senses, the residual strong nuclear force is a complicated residue of various cancelling effects, and consequently there is no simple picture that describes all of the physics of a nucleus. This isn’t surprising, when we recognize that protons and neutrons are internally complicated. There’s something of an analogy with atoms and molecules.
In an atom, tiny nuclei and even tinier electrons are relatively far apart compared to their sizes, and the electrical forces that hold them in the atom are simple. But in molecules, the distance between atoms is comparable to the sizes of atoms, so the internal complexity of the atoms comes into play. A diverse and complicated set of partially cancelling electrical forces, and processes in which electrons may actually move from one atom to another, make the story of molecules much richer and more complicated than that of atoms. In a similar way, the distance between protons and neutrons in a nucleus is comparable to their size — and so, as with molecules, the forces that hold nuclei together are much more complicated (in some senses!) than the forces that hold protons and neutrons together.
When we learn about the structure of protons and neutrons, this story will start to become somewhat (but only somewhat) clearer. Basic features of nuclear physics are well understood, but the subject remains very technical, and many of the details are still undergoing active research. I won’t be able to do it justice in this article, partly because I’m not expert enough to simplify it wisely for you… though perhaps one of my nuclear physicist colleagues can assist me.
Let’s see what we can learn from simple considerations about how this force works. One clue is that all nuclei except that of the most common isotope of hydrogen (which has only one proton) contain neutrons; that is, there are no nuclei with multiple protons that do not contain neutrons. (See Figure 2.) So clearly the neutrons play an important role in helping the protons stick together.
Conversely, there are no nuclei made from only neutrons and no protons; most lightweight nuclei, like those of oxygen and silicon, have about the same numbers of neutrons and protons (Figure 2). Larger nuclei with larger masses, like those of gold and radium, have somewhat more neutrons than protons (Figure 3). This suggests two things:
- Not only are neutrons needed to make protons stick together, protons are needed to make the neutrons stick together too.
- If the number of protons and neutrons becomes very large, then the electrical repulsion pushing the protons apart has to be compensated by the addition of a few extra neutrons.
This last statement is illustrated in Figure 3 [taken from Wikipedia] which shows the stable (black) and relatively long-lived though unstable (colored) nuclei, as a function of the number of protons Z and the number of neutrons N that they contain. Notice the stable nuclei have Z and N approximately equal for small Z and N, but N becomes gradually larger than Z as the two increase. Note also that the band of stable and long-lived unstable nuclei remains quite narrow for all values of Z. Despite the immense progress in nuclear physics over the past 80 years, there is no widely-accepted simple explanation of this remarkable fact. I believe it is viewed by most experts as an odd accident.
The Size of a Nucleus
One of the main purposes of this article was to explain why nuclei are small compared to atoms. [Later on we’ll learn why protons and neutrons are small.] To do this, let’s start with the simplest nucleus that has both protons and neutrons: this is the second-most common isotope of hydrogen, consisting of one electron (as for all hydrogen isotopes) and a nucleus made from one proton and one neutron. This isotope is often called “deuterium”, and the nucleus of deuterium (see Figure 2) is sometimes called the “deuteron.” How should we understand what holds the deuteron together? Well, we might naively imagine that it is not so different from a hydrogen atom, which also contains two particles (a proton and an electron). See Figure 4.
As we saw in an earlier article, the fact that electrons have a small mass compared to protons and neutrons assures that
- the mass of an atom is essentially the mass of its nucleus,
- the size of an atom (essentially the size of the electron cloud) is inversely proportional to the electron’s mass and inversely proportional to the overall strength of the electromagnetic force; the uncertainty principle of quantum mechanics plays a crucial role.
What about the deuteron? It is similarly made from two objects, but these are of almost equal mass (the neutron and proton’s mass differ by only one part in about 1500, for reasons we’ll learn later) so both are equally important in determining the deuteron’s mass and its size. Now suppose there were a new force pulling a proton toward a neutron that was much like the electromagnetic force (it isn’t quite like that, but imagine it for a moment); well then, by analogy with hydrogen, we’d expect the deuteron’s size to be inversely proportional to the mass of the proton or neutron, and inversely proportional to the strength of the new force. If the force were just as strong (at a particular distance) as electromagnetism, that would mean, since the proton is about 1850 times heavier than the electron, that a deuteron (and indeed any nucleus) should be at least a thousand times smaller than hydrogen.
But we’ve already guessed that the residual strong force is much stronger than electromagnetism (at the same distance) — because if it weren’t, it wouldn’t be able to prevent the electromagnetic repulsion among the protons from blowing larger nuclei apart. So that extra strength is going to pull the proton and neutron even more tightly together. And thus it’s not surprising that the deuteron and other nuclei are not just one thousand but tens of thousands of times smaller than atoms! Again, this is just because
- protons and neutrons are nearly 2000 times heavier than electrons
- at these distances, the strong nuclear force between the protons and neutrons of a nucleus is many times stronger than corresponding electromagnetic forces (including the electromagnetic repulsion between the protons in the nucleus.)
This naive guess gives roughly the right answer! But it doesn’t fully capture the complexity of the interaction between the proton and neutron in deuterium. One obvious problem with it is that a force similar to electromagnetism but with greater pulling or pushing power would have an obvious impact on daily life, and we don’t observe any such thing. So something about this force must be different from electrical forces.
The Short Range of This Force
What’s different is that this residual strong nuclear force is very important and powerful for protons and neutrons that are a very short distance apart, but beyond a certain distance (called the “range” of the force) it falls away very rapidly, much more rapidly than electromagnetic forces do. The range — somewhat by coincidence — turns out also to be about the size of a moderately large nucleus, just a few times larger than a proton. If you bring a proton and a neutron together at a distance comparable to that range, they will attract each other and form a deuteron; if you leave them at greater distances, they will barely feel any attraction at all. (Actually, if you bring them too close together, so that they start to overlap, they will in fact repel each other; heck, I warned you the residual strong nuclear force was complicated!) In short,
- the residual strong nuclear force is much, much weaker than electromagnetism at distances significantly greater than the size of a typical nucleus, so we don’t encounter it in daily life; but
- at shorter distances comparable to a nucleus it becomes much stronger — an attractive force (as long as the distance is not too short) able to overcome the electric repulsion between protons.
Later on we’ll learn something about why this force is only important at distances comparable to the size of a nucleus.
Larger nuclei are held together by more or less the same force that holds a deuteron together, but the details are complicated, technical, and not easy to describe. Nor are they fully understood. Although the basic outlines of the physics of nuclei have been well understood for decades, many important details are still active subjects of research.
At some point, if and when I learn more things that may be intuitively easy to understand, I may add more to this article. But for now it is time to move on — to a description of protons and neutrons, where the strong nuclear force reveals its true colors. [Coming Soon]