How Does The Nucleus Hold Together? (Script) (Patreon)

Two protons next to each other in an atomic nucleus are repelling each other electromagnetically with enough force to lift a medium-sized labradoodle off the ground. Release this energy and you have, well, you have a nuclear explosion.

Just as well there's an even stronger force than the electromagnetism holding our nuclei together. But it's not the strong force, as you might have imagined. At least not directly. Nuclei are held together by a quirk of nature, without which we would have no complex atoms, no chemistry, and certainly no labradoodles.

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Quantum chromodynamics is a complicated sounding name, but the fundamental force of nature it describes - the strong force - is actually even more complicated. In our previous episode we saw how the strong force binds the elementary quarks into protons and neutrons. But that’s where we left it.  Based on what we learned in that episode, the strong force is entirely confined to the nucleons, and yet somehow it’s also the force that binds protons and neutrons together to form most atomic nuclei. That process is strange enough that it deserves its own episode - especially because it was this very question - how are atomic nuclei held together, that led to the discovery of both the strong and weak nuclear forces in the first place. But this is also the story of the meson - the obscure cousin to the proton and neutron that, while less well known, is just as essential to the existence of all complex matter in the universe.

Our story starts with Hideki Yukawa, a young physicist who graduated from the University of Osaka in 1929, before moving back in with his parents and working for no money as a university assistant. Due to the Great Depression, not because he wasn’t a great physicist. All the while, Yukawa was focused on the problem of how nucleons stuck together. He was perplexed about why a force so strong shouldn’t be observable outside atomic nuclei.

Yukawa had one intriguing clue to the inner lives of nuclei, and that was beta decay - the tendency of large nuclei to occasionally spit out an electron, and in the process convert one of their neutrons into a proton. He knew that the electromagnetic force is communicated by the exchange of photons, and it stood to reason that this nuclear force also be mediated by a particle. So what if this particle was the electron, and beta decay is the side effect of the exchange of electrons between nucleons?

Like, if protons and neutrons were playing catch with the electron and sometimes they fumble the ball. It turns out this is totally not what’s happening, but the insight that forces should be mediated by particles was new in its time, and it eventually led Yukawa to the right answer.

Having a massive exchange particle is a great first step to making a short-range force. These exchange particles are what we call virtual particles - which we’ve discussed before. Virtual particles can sort of break the laws of physics, in the sense that they can pluck the energy needed for their existence out of nowhere, as long as they give it back again.

This is a result of the Heisenberg uncertainty principle, which in one form says that we can never know both the energy and the duration of a phenomenon to better than a certain tiny accuracy. That means, for very short periods of time, the amount of energy in a patch of space can vary.

Mass is a form of energy, so a virtual particle can briefly gain mass from nothing - but the more mass it has, the less time it can exist. Hideki Yukawa used the electron mass to calculate the strength and range of a force mediated by this particle, assuming it’s traveling near the speed of light. The resulting force turned out to be around 1-200th of the strength needed to hold the nucleus together, and had a range much larger than the size of the atomic nucleus. So much for that. But Yukawa now had an equation that described the type of force he wanted.

He adjusted it to describe a force with the appropriate strength and range, and found that it required a much more massive exchange particle. He called this hypothetical particle the "meson" from the Greek “mesos” for middle - because it had to have a mass somewhere between that of the proton and the electron.

Yukawa also predicted that these particles had to have electric charge. Just like with Beta Decay, a neutron could emit a negative meson and transform into a proton, a proton could emit a positive meson and transform into a neutron, and the neutral meson could be exchanged between protons or between neutrons. As a result, Yukawa predicted 3 mesons types, one for each possible charge value.

Unfortunately this new theory didn’t explain beta decay at all. In fact, Yukawa reasoned that beta decay required a completely different nuclear force, much weaker than the one holding the nucleus together. He correctly predicted the existence of both the strong and the weak forces at the same time. Although the weak force isn’t mediated by electrons, and we have videos explaining everything you probably want to know about it.

Yukawa published his theory in 1935, and it was almost completely ignored. To be fair, proposing the existence of two new forces of nature was an extraordinary claim, and such claims require extraordinary evidence. No one was going to believe it until we’d detected a meson.

These days we routinely create countless mesons by smashing atoms together in particle accelerators. But back then particle accelerators were just being developed, so we had to rely on cosmic rays - high energy particles that rain down on the Earth from natural space particle accelerators like supernovae and quasars.

Yukawa wrote a letter to Nature magazine explaining why cosmic radiation could contain mesons, hoping to inspire other researchers to look for them, but his letter it was rejected

Nonetheless, others had independently thought of searching for new particles in cosmic radiation. We have Bibha Chowdhuri and Debendra Mohan Bose for example, who developed a method using photographic plates. They set these up at high altitudes in India and Tibet due to the fact that our atmosphere is so good at blocking cosmic rays - which is annoying if you’re a particle physicist, but great if you’re anyone else. And Chowdhuri and Bose did indeed spot the meson at around the mass Yukawa predicted. Sadly their research went mostly unnoticed until British scientists independently found mesons in 1947.

Anyway, not only were these new particles in the right mass range, there were three of them as predicted by Yukawa, one positive, one negative, and one neutral. But then things got awkward. Over the next couple of years, thanks to better particle accelerators and improved  understanding of radiation, more and more mesons were discovered, with a range of properties.

The first mesons, the ones found by Bose and Chowduri, are called pions, and these are the particles actually exchanged by protons and neutrons in the nucleus, while these new mesons were called kaons, eta mesons, D mesons, B mesons…

To make matters worse, scientists also found more particles that could "play catch with mesons" just like protons and neutrons. These particles were named baryons, after the Greek word for "heavy". There was the Lambda, Sigma, Xi, Omega, and more. Again, all with different masses, charges and spins.

This endless collection of baryons and mesons came to be known as the Particle Zoo and it was a huge problem for physics. According to Yukawa's theory, the atomic nucleus only needs two baryons - the proton and neutron - and three mesons—the pions. So what was with all this extra junk that nature doesn’t seem to need outside of particle colliders?

This problem was finally solved by Murray Gell-Mann, who realized that mesons and baryons are not elementary particles, but rather are made of quarks. Hadron is the general name for a particle made of multiple quarks. The particle zoo just results from all the quark combinations that are possible. We covered this in our episode on quantum chromodynamics, but here’s a quick refresher so we can get to the punchline of this video.

With the discovery of quarks, it was clear that we needed the strong force to not only hold the nucleus together, but also hold the nucleons together. In fact, the latter is what the strong force does best. Binding nucleons is sort of an afterthought. Just as electromagnetism works on things with electric charge, the strong force works on things with color charge. There are 3 types of color charge, unlike the single type of electric charge. A quark, for example, could have a colour charge of red, green, or blue, or the opposite colour charge of antired, antigreen, or antiblue. These names are just analogies of course.

Composite particles need to be colour neutral, so the 3-quark baryons have one of each colour charge which cancels out, while 2 quarks of a meson will have a colour and its anti-colour. These quarks are bound by the strong force, which is mediated by a massless particle called the gluon. Gluons each carry one regular and one anti-colour charge, and they cause the colours of quarks to flip when absorbed. Baryons and mesons are held together by a continuous exchange of virtual gluons.

But wait, haven't we been saying the entire video that the reason the Strong Force has a short range is because it is transmitted mesons with mass? That was Yukawa's whole deal, but now it turns out mesons aren't the real exchange particles? And the real ones - the gluons - don't have mass? What's going on?

Actually, the colour-neutral hadrons can’t even feel the strong force directly, just as electrically neutral objects don’t exert an electrostatic force on each other. But there’s a workaround. Atoms seem electrically neutral from afar, but if you were close enough to the nucleus you would feel its positive electric charge. Similarly if protons or neutrons get close enough to each other, their internal quarks will feel each other’s presence. A quark from, say, a proton, will want to tug at a quark from a neighboring neutron. But they can’t simply exchange a gluon to do that - because gluons have colour charge, so exchanging a gluon would cause the hadrons to no longer be colour neutral, which is not allowed. In order to properly feel the strong force the hadrons need to exchange a neutral particle. And nature has found a way to make that happen.

Here’s how it goes. A pair of nucleons get close and a quark from one gets pulled towards the other. Its gluon connection to the other quarks in its nucleus - what we call a flux tube - extends and snaps, and in the process generates two new quarks. One remains in the nucleus, while the other forms a quark-antiquark pair with the original escaped quark. This is our meson - our pion. It’s colour neutral and so it can be absorbed by the second nucleus without breaking any physics. There, one of the meson’s quarks annihilates with an antiquark counterpart in that nucleus. Ultimately we’re left with two nucleons of the same type that we started with, but they have now communicated the strong force. They did it a roundabout way, but the process nonetheless exchanged energy and momentum, binding the particles together. This is how the strong force finds its way around its lack of a neutral gluon. It cobbles together a neutral exchange particle - the meson.

But the meson has mass. A virtual meson has to borrow a lot of energy to create its mass, and so the uncertainty principle says that it can’t exist for very long. Its range defines the possible size for an atomic nucleus. If a nucleus gets too big then its nucleons are too far apart to exchange mesons effectively, and it’ll decay. By the way, when we talk about the force between quarks we call it the strong force, but this residual strong force that exists between nucleons is called the strong nuclear force.

It's funny, this reminds me of our episode about quasi particles. In that episode we talked about how fields can arise as emergent behaviors of other fields, and these quasifields will have their own quasiforces and quasiparticles… That's sort of what's happening here. The strong nuclear force is a quasi-force mediated by a quasi-particle, the meson. Without this little quirk of nature - this emergence of a force that’s not really supposed to be there, the most complex atom in the universe would be hydrogen. Fortunately nature stumbled on a way to bind the nuclei, which gave us chemistry, and biology, and ourselves, including a young physicist named Hideki Yukawa, who was able to figure out some of the most important forces from which emerges this richly complex spacetime.