The element following hydrogen in the periodic table is helium, which has two protons in its nucleus. In addition, the helium nucleus also contains two neutrons (which carry no net electric charge). Helium is the second most abundant element, making up about 24 percent of the cosmic ordinary matter. Atoms of the same chemical element have the same number of protons, and this number is called the atomic number of that element. Hydrogen has the atomic number 1, helium is 2, iron is 26, uranium is 92. The total number of protons and neutrons in the nucleus is called the atomic mass. Hydrogen has the atomic mass of 1; helium, 4; carbon (which has six protons and six neutrons), 12. Nuclei of the same chemical element can have different numbers of neutrons, and those are called isotopes of that element. For instance, neon (which has ten protons), can have isotopes with ten, eleven, or twelve neutrons in the nucleus. The common notation for these different isotopes is ²⁰Ne, ²¹Ne, and ²²Ne. Similarly, hydrogen (one proton, or ¹H) also has in nature an isotope usually called deuterium (one proton and one neutron in the nucleus, or ²H), and an isotope called tritium (one proton and two neutrons, or ³H).

Returning now to the central problem of the synthesis of the different elements, the physicists of the first half of the twentieth century were faced with a series of questions related to the periodic table. First and foremost: How were all of these elements formed? But also: Why are some elements, such as gold and uranium, extremely rare (hence, their high price!), while others, such as iron or oxygen, are much more common? (Oxygen is about a hundred million times more common than gold.) Or: Why are stars composed mostly of hydrogen and helium?

Since their inception, ideas about the process of the formation of the elements have been linked intimately to those on the enormous energy sources of stars. Recall that Helmholtz and Kelvin proposed that the Sun’s power comes from slow contraction and the associated release of gravitational energy. However, as Kelvin had clearly demonstrated, this reservoir could provide for the Sun’s radiation for only a limited time: no more than a few tens of millions of years. This limit was disturbingly at odds with geological and astrophysical evidence that was pointing with increasing accuracy to ages of billions of years for both the Earth and the Sun. Eddington was fully aware of this glaring discrepancy. In his address to the British Association for the Advancement of Science meeting in Cardiff, Wales, on August 24, 1920, he made the following prescient statement:

Only the inertia of tradition keeps the contraction hypothesis alive—or rather, not alive, but an unburied corpse. But if we decide to inter the corpse, let us frankly recognize the position in which we are left. A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the subatomic energy which, it is known, exists abundantly in all matter [emphasis added].

Despite his enthusiasm for the idea that stars could derive their power from four hydrogen nuclei fusing together to assemble a helium nucleus, Eddington had no specific mechanism for this process to actually take place. In particular, the problem of the mutual electrostatic repulsion, mentioned above, had to be solved. Here is the obstacle: Two protons (the nuclei of hydrogen atoms) repel each other electrostatically because both have positive electric charges. This Coulomb force (named after the French physicist Charles-Augustin de Coulomb) has a long range, and it is therefore the dominant force between protons at distances larger than the size of the atomic nucleus. Within the nucleus, however, the strong, attractive nuclear force takes over, and it can overcome the electric repulsion. Consequently, in order for protons in the cores of stars to fuse together as envisioned by Eddington, they need to have sufficiently high kinetic energies in their random motions to overcome the “Coulomb barrier” and allow them to interact via the attractive nuclear force. The apparent snag in Eddington’s hypothesis was that the temperature calculated for the center of the Sun was not high enough to impart protons with the necessary energy. In classical physics, this would have been a death sentence for this scenario; particles with insufficient energy to overcome such a barrier just cannot make it. Fortunately, quantum mechanics—the theory that describes the behavior of subatomic particles and light—came to the rescue. In quantum mechanics, particles can behave like waves, and all processes are inherently probabilistic. Waves are not precisely localized like particles but are spread out. In the same way that some parts of an ocean wave crashing against a seawall can splash to the other side, there is a certain (albeit small) probability that even protons with insufficient energy to overcome their Coulomb barrier would still interact. Using this quantum mechanical effect of “tunneling” through barriers, physicist George Gamow and, independently, the two teams of Robert Atkinson and Fritz Houtermans, and Edward Condon and Ronald Gurney, demonstrated in the late 1920s that under the conditions prevailing in stellar interiors, protons could indeed fuse.