by Harry Cliff
Georgii Antonovich Gamow was born in 1904, in the Ukrainian city of Odessa on the coast of the Black Sea. Even as a little boy he had a fierce curiosity and a healthy disrespect for authority. Aged ten, he began to doubt his priest’s claim that communion bread was transubstantiated into the flesh of Christ, and so one Sunday he snuck a crumb home in his cheek and examined it using a small microscope bought for him by his father. He concluded that the body of Christ had more in common with ordinary bread than it did with human flesh, using a piece of skin sliced off the tip of his own finger for comparison. He later wrote, “I think this was the experiment which made me a scientist.”
Despite turmoil caused by the First World War and the subsequent Bolshevik Revolution, Gamow managed to get an excellent education, first at Odessa and then at Petrograd, the top university for theoretical physics in the Soviet Union. However, his big break came in 1928 when he got to spend the summer in Göttingen, Germany, working at the Institute for Theoretical Physics, which was headed by one of the leaders of the quantum revolution, Max Born.
Gamow found the place “buzzing with excitement,” its seminar rooms and cafés crowded with physicists arguing over the consequences of the new theory. However, Gamow liked to work in less crowded fields and so took himself off to the library in search of a problem that he could claim for himself. It was there that he came across a paper by Ernest Rutherford describing experiments where he had fired alpha particles (helium nuclei made of two protons and two neutrons) at uranium. The article left Gamow scratching his head. Rutherford had found it impossible to get alpha particles to penetrate the uranium nucleus, and yet it was well-known that uranium spontaneously spat out alpha particles. How could it be that alpha particles couldn’t get into the nucleus from outside, and yet ones with only half as much energy could escape from within?
Gamow suspected that the explanation could be found by applying the groundbreaking theory of quantum mechanics to the nucleus, something nobody had tried before. At the time, quantum laws had only been used to explain the way electrons orbit around atoms—it wasn’t at all clear if the same rules applied in the mysterious nuclear realm.
At the heart of quantum mechanics is one of the most counterintuitive and yet profound ideas in all of physics: wave-particle duality. At the end of the nineteenth century physicists had believed that light was a wave, a spread-out wibbly-wobbly thing, like a ripple on the surface of a lake. Experiments had conclusively demonstrated light’s wavelike behavior, including its ability to spread out into circular ripples when shined through a small hole, a behavior known as diffraction, and its ability to interfere with itself (not like that) when two light waves combine to make a larger wave or cancel each other out if the crest of one wave meets the trough in another.
However, at the start of the twentieth century things started to get confusing. First off, the German physicist Max Planck showed that it was only possible to explain the colors of light given off by a hot body—say a red-hot piece of iron—if you did your calculations assuming that light came in discrete little packets known as “quanta.” At first Planck regarded this as a mere mathematical trick to get the right answer, but then, in 1905, Einstein published a paper showing that a puzzling phenomenon known as the “photoelectric effect” could be explained if light really did come in quantized little lumps. In other words, light was a flow of particles, known as photons.
These two seemingly contradictory assertions about the nature of light kick-started the quantum revolution. At first it was thought that only photons exhibited this weird wave-particle duality, but in 1924 the French physicist Louis de Broglie argued that it wasn’t just a property of light; it applied to particles of matter as well. Electrons, protons, and even atoms—particles that had previously been thought of as little hard nuggets with well-defined positions—could be made to behave like spread-out waves too. The year before Gamow arrived in Göttingen, de Broglie’s bizarre hypothesis had been dramatically vindicated when George Paget Thomson, son of J.J., fired electrons through thin metal films and discovered that they formed a diffraction pattern,*4 apparently contradicting his own dad’s experiments showing that the electron is a particle.
If all this leaves your head spinning, don’t worry. It confused the hell out of the entire physics community well into the 1920s. The most intuitive, or perhaps I should say least counterintuitive, description of this quantum weirdness was devised by the German theorist Erwin Schrödinger. It’s known as “wave mechanics.”
In general, particles, including photons, electrons, and protons, are detected at specific points in space. For example, if you fire an electron through some experiment at a detection screen, the electron will arrive at a well-defined location on that screen. The fact that the electron appears to arrive in only one location, rather than being spread out all over the place, is what we refer to as the particle bit of its behavior. However, wave mechanics says that in between the electron being emitted and detected, it doesn’t behave like a particle at all—instead, it travels as a wave.
This wave isn’t a wave in water, or air, or indeed any other medium, it’s a wave of probability, known as the “wavefunction.” The size of the wavefunction is related to the probability of finding the electron at a certain point on the screen; the bigger the wavefunction is at a given point, the more likely we’ll find the particle there. Then comes the really mysterious bit. Somehow, the wavefunction collapses from being spread out through space, down to a single point where the electron is detected. It is impossible to know which point the wave will collapse to in advance; we can only calculate the probability of the wavefunction collapsing at different locations on the screen. This nonsensical process is known as “wavefunction collapse,” and to this day, no one really knows how it works.*5 All we do know is that this is really how things appear to behave in the subatomic world.
Okay, back to our boy George. Gamow realized that if he used wave mechanics to describe the behavior of alpha particles shot out by a uranium nucleus, then the paradox that they didn’t have enough energy to escape could be overcome. Let’s return to our castle analogy, which I actually stole from Gamow’s own description in Mr. Tompkins. In the analogy, the nucleus is like the inside of a castle, protected by a high wall that keeps intruders out and the inhabitants in. Gamow imagines the alpha particle before it escapes the nucleus as bouncing about back and forth inside the castle walls. If we think of the alpha particle in the old-fashioned way, as a hard little sphere, then it doesn’t have enough energy to get over the top of the walls and escape.
However, if instead we think of the alpha particle as a wave, then something very strange indeed can happen; it can leak out through the walls, like water seeping through cracks in the brickwork. That leaves a little bit of it outside the castle so that there is now a small but nonnegligible probability of the alpha particle being found outside the castle walls. When the wavefunction collapses, the alpha particle can suddenly appear outside the uranium nucleus, as if it has tunneled through the barrier. It’s a bit like a prisoner furiously hurling themselves at their cell wall over and over again until quite suddenly, as if by magic, they pass straight through and find themselves outside and free. Amazingly, there is a tiny, tiny probability that such a thing could really happen to a real prisoner in an actual prison, but the probability of all the atoms in a prisoner’s body simultaneously tunneling through the walls of their cell are so vanishingly small that it will almost certainly never happen, even though in principle it could.
Gamow’s theory turned out to be a triumph, unraveling the paradox of how an alpha particle escapes from the uranium nucleus.*6 While working on his theory over that summer in Göttingen, Gamow struck up a friendship with another physicist one year his junior, the German-born Fritz Houtermans. Gamow and Houtermans clicked instantly; they were both young, charming, and enjoyed reckless bohemian lifestyles, shared a wicked sense of humor that frequently got them into
trouble, and were both passionate about physics. Houtermans was very taken with Gamow’s alpha decay theory; when he returned to Berlin, he continued to turn it over in his mind.
A few months later, Gamow received a letter from his friend. Back in Berlin, Houtermans had run into a visiting British astrophysicist, Robert Atkinson. While discussing Gamow’s theory they had realized that if particles could tunnel out of a nucleus, they should also be able to tunnel in. Atkinson was familiar with Eddington’s work on the temperature at the center of the Sun and stars and wondered whether nuclear fusion might be possible after all. If protons at the center of the Sun were able to quantum tunnel through the repulsive electrical barrier that kept them apart, then perhaps nuclear fusion could go on at lower temperatures than previously thought. Maybe, just maybe, Eddington had been right.
The three men settled on the picturesque skiing resort of Zürs in the Austrian Alps as the most agreeable place to work through the theory. Gamow found to his satisfaction that Fritz and Robert “were almost ready with their calculations, so the discussion did not impose on our skiing time.”
Houtermans and Atkinson’s theory was the exact reverse of Gamow’s. Instead of a particle inside the nucleus tunneling out, this time they considered protons hurling themselves against the nucleus’s electrical barrier from the outside, like soldiers assaulting the walls of a castle. Eddington’s calculations had shown that protons in the Sun weren’t moving fast enough to get to the very top of the castle’s walls. However, the repulsive barrier around the nucleus gets thinner and thinner the higher up the walls you get. If protons in the center of the Sun were moving fast enough to climb to a point where the barrier became thin enough, then quantum tunneling might allow some small fraction of them to jump through and appear inside the nucleus without having to get right over the top.
The question was whether the tunneling probability was high enough to allow nuclear fusion to go on in the center of the Sun. After a few days of skiing and drinking, and presumably also a bit of physics, the three arrived at an equation describing the rate of fusion as a function of the temperature and density at the center of a star. Unfortunately, due to scant knowledge of the makeup of the nucleus in 1929, Gamow got his calculations wrong by a factor of ten thousand. But in one of the most remarkable pieces of dumb luck in the history of science, Houtermans and Atkinson made a second mistake that shifted the answer by a factor of ten thousand in the opposite direction. Miraculously, the two mistakes canceled each other out and the equation they ended up with was essentially correct.
Plugging in Eddington’s estimate of the conditions in the solar core, they found to their delight that nuclear fusion really did seem to be possible, and what’s more it could easily keep the Sun shining for billions of years.
Houtermans later recounted the climax of their work in typically colorful style. After putting the finishing touches to the article, he went for an evening stroll with Charlotte Riefenstahl, a young physicist whom both he and Robert Oppenheimer*7 were courting at the time.
“As soon as it grew dark the stars came out, one after another, in all their splendor. ‘Don’t they shine beautifully?’ cried my companion. But I simply stuck out my chest and said proudly: ‘I’ve known since yesterday why it is that they shine.’ ”
That has got to be one of the best chat-up lines in history. It seems to have worked; Charlotte and Fritz went on to marry, not once, but twice. Houtermans and Atkinson submitted their article under the playful title of “How to Cook Helium in a Potential Pot.” Unfortunately, a rather unimaginative journal editor renamed it to the decidedly less punchy “On the Question of the Possibility of the Synthesis of Elements in Stars.”
Titles notwithstanding, their article made little impact, at least at first. Nuclear physics was mired in uncertainty and what today seem like bonkers ideas were making the rounds. The great Niels Bohr had proposed that the sacred law of the conservation of energy might be broken inside the nucleus, ultimately accounting for the power output of the Sun. To get any traction, Atkinson and Houtermans would need experimental evidence for their tunneling theory. Fortunately, it would soon be provided by Ernest Rutherford and his team of physicists at the Cavendish Laboratory.
In 1932, Cavendish physicists John Cockcroft and Ernest Walton used one of the first-ever particle accelerators to bombard a lithium target with a beam of protons, splitting the lithium nucleus in two in the process. This incredible feat was only possible thanks to Gamow’s nuclear tunneling theory. Although Cockcroft and Walton’s machine could accelerate protons to an impressive 800,000 volts, that fell well short of the several million volts required to get the protons moving fast enough to get directly over the top of the electrical barrier protecting the lithium nucleus. The only way to explain the fact that they had managed to split the atom was if protons were quantum tunneling through the barrier, just as Gamow’s theory predicted.
With experimental confirmation that quantum mechanics really does apply to the nucleus, the way was finally open to explain how helium gets made inside the Sun and stars. However, there were still some serious obstacles to overcome. We are missing two vital ingredients. One is a rare isotope of hydrogen, the other is beloved of science fiction writers everywhere: antimatter.
HELIUM MADE TWO WAYS
Thanks to the idea of quantum tunneling we now know that the Sun and stars are hot enough to force two protons together. In other words, we have found the thermonuclear ovens needed to cook helium. But there’s a problem. If we’re really starting from scratch, then our recipe for helium must surely start by fusing two protons, and there we immediately run into trouble. There is no stable nucleus made of two protons. If there were, it would technically be known as helium-2, but there ain’t no such thing.
There is, however, a nucleus made of one proton and one neutron, a heavy isotope of hydrogen known as deuterium, which was discovered by the American chemist Harold Urey in 1931. This gives us a glimmer of hope. What if there were a way of combining two protons and at the same instant transforming one of the protons into a neutron? If we could do that, then we’d be able to make deuterium, the first vital step in our recipe for helium.
Until 1932, turning a proton into a neutron seemed to be impossible. For one thing, where would the positive charge of the proton go? It can’t simply vanish out of existence. We’re missing a second ingredient, one that was discovered in 1932: the positron. Also known as the antielectron, this new particle is exactly like an electron, except it has a positive electric charge. The positron was the first-ever particle of antimatter to be detected, an incredibly profound discovery that we’ll discuss later on, but for now it plays only a small if vital supporting role in our thermonuclear cooking story.
In 1934, physics’ Parisian power couple Irène and Frédéric Joliot-Curie discovered a brand-new type of radioactive decay, one in which an unstable nucleus shoots out one of these positrons. They soon realized that deep inside the decaying nucleus a proton had transformed into a neutron. One of the reasons it took so long to discover is that isolated protons can’t decay in this way; a proton actually weighs less than the neutron it turns into. However, in certain unstable nuclei, a proton can absorb some energy from its host nucleus, allowing it to turn into a heavier neutron, releasing a positron and a neutrino.
Armed with deuterium and a way to turn protons into neutrons, we can at last make progress in our attempt to forge helium. In 1936 Robert Atkinson pointed out a potential first step on the route to building the heavy elements out of hydrogen. At the extreme temperatures present at the center of the Sun two protons could be forced together, forming for a fantastically brief instant an unstable two-proton nucleus. Then, before it could fall apart, one of the protons converts into a neutron, creating a nucleus of deuterium.
Atkinson’s suggestion was the beginning of a period of rapid progress that soon came to a dramatic climax. Af
ter several years wandering across Europe, often roaring into quiet university towns on his motorbike, Gamow had defected from the Soviet Union in 1933. Now based at George Washington University in the United States, he had become increasingly interested in what was known as the “stellar energy problem”—in other words, why the stars shine—so in 1938 he organized a conference on the topic, inviting thirty-four of the world’s top astro-, nuclear, and quantum physicists.
Among them was Hans Bethe, one of the brightest theorists of his generation, who, as Gamow put it, “knew nothing about the interior of stars, but everything about the interior of the nucleus.” In fact, shortly before the conference, Bethe had been contacted by a former student of Gamow’s, Charles Critchfield, who had taken Atkinson’s proposed reaction where two protons fuse to make deuterium and run with it, coming up with an entire scheme that started with just protons and through various steps built up a freshly baked helium nucleus. Along the way, Critchfield had run into some mathematical difficulties and so turned to Bethe for help.
Bethe was impressed with the young physicist’s work, and after some tweaks to make the calculations more elegant the two of them produced a complete recipe for cooking helium. Today it’s known as the “proton-proton chain.” The modern version of it goes like this:
A RECIPE FOR HELIUM— THE PROTON-PROTON CHAIN
Step 1: Two protons collide, briefly forming a highly unstable two-proton nucleus.
Step 2: Before the two-proton nucleus can disintegrate, one of the protons decays into a neutron, forming a deuterium nucleus (one proton, one neutron) and releasing a positron and a neutrino.
Step 3: Another proton collides with the newly formed deuterium nucleus to form helium-3 (two protons, one neutron) and releasing a gamma ray.
Step 4: Two helium-3 nuclei smack into each other and form a nucleus of helium-4 (two protons, two neutrons) sending the two leftover protons flying out.
