Atoms of different elements have different binding energies. For us, the most important is the binding energy of helium. According to today’s astrophysicists, the first generation of stars converts hydrogen into helium by fusion. The nucleus of a hydrogen atom contains one proton. The nucleus of deuterium, an isotope of hydrogen, contains one proton and one neutron. When two deuterium atoms fuse, they form an atom of helium, with two protons and two neutrons. The nucleus of the helium atom has a mass equivalent to .993 (99.3 percent) of the mass of the two protons and two neutrons it contains. In the process of fusion, .007 (0.7 percent) of the mass is converted into energy, mostly heat. This number .007 is ε, the binding energy of atomic nuclei. It is related to the strong nuclear force, which keeps the protons in the atom together. Rees (2000, p. 48) says, “The amount of energy released when simple atoms undergo nuclear fusion depends on the strength of the force that ‘glues’ together the ingredients in an atomic nucleus.” The greater the binding energy, the greater the strength of the strong nuclear force. The protons in the nucleus have positive charge, and normally positive charges will repel each other, thus blowing the atom apart. But the strong nuclear force is just strong enough to overcome this repulsion, and holds the protons together in the nucleus. We do not feel this force, because it operates only within the nucleus of the atom.
If the value of ε were even slightly different, there would be major effects on atomic structure. If, for example, the value of ε were .006 instead of .007, this would mean that the strong nuclear force was slightly weaker than it is now. But this would be enough to interrupt the formation of elements heavier than hydrogen. Heavier elements are formed by adding protons to the nuclei of atoms. Hydrogen, with one proton, is the lightest element. Iron has 26 protons. But to get to iron and the heavier elements, we first have to go from hydrogen to helium.The helium nucleus usually contains two protons and two neutrons, while the simple hydrogen nucleus consists of just one proton. So to go from hydrogen to helium requires a middle step, the conversion of hydrogen to its isotope deuterium, which consists of one proton and one neutron. Then two deuterium nuclei can fuse to form a helium nucleus, with two protons and two neutrons. The strength of the nuclear binding force between the protons and neutrons in the helium nucleus causes the release of part of their mass as energy, the binding energy. Now if this binding energy were .006 of the total mass of the protons and neutrons, instead of .007, the strong nuclear force would be weaker. It would be just weak enough so that a neutron could not bind to a proton. Deuterium nuclei could not form, and therefore helium nuclei could not form. The hydrogen atoms would still condense into heavy masses, and these masses would heat up. But there would be no fusion reactions to keep the star going. No other elements would be formed. There would be no planets and no life as we know it.
What if ε was .008 instead of .007, indicating that the strong nuclear force was slightly stronger than it is today? That would lead to a problem of another kind in the process of element formation. As we have seen, the strong nuclear force is needed to bind protons together. Today, the strong force is not strong enough to bind just two protons together. A combination of two protons is called a diproton. There are no stable diprotons in the universe today. This is because the repulsion between the two positively charged protons is stronger than the binding energy of the strong nuclear force. But the binding energy, at its current value of .007, is strong enough to cause a proton to bind to a neutron, thus forming deuterium. And then two deuterium atoms can combine to form helium. This happens because the neutrons supply the extra binding energy needed to bring the two protons together. Because the neutrons are neutral in electric charge, they do not add any additional force of repulsion. Now if ε were .008, then two protons could join together, forming a diproton, an isotope of helium with two protons and no neutrons. This means that all of the hydrogen atoms (each with one proton) in the early universe would quickly combine into diprotons. Today, only some of the hydrogen atoms form deuterium and normal helium, over long periods of time. This leaves hydrogen in the universe for the formation of hydrogen compounds necessary for life. Barrow and Tipler (1996, p. 322) put it like this: “If the strong interaction were a little stronger, the diproton would be a stable bound state with catastrophic consequences—all the hydrogen in the Universe would have been burnt to He2 during the early stages of the Big Bang and no hydrogen compounds or long-lived stable stars would exist today. If the diproton existed we would not!” The most important hydrogen compound is water, and in a universe in which ε was .008, there would be no water. The stable stars would not exist because they require hydrogen for fuel and there would be no hydrogen.
Going from helium to carbon also requires some fine tuning (Barrow and Tipler 1996, pp. 250–253). According to cosmologists, the first generations of stars burn hydrogen nuclei by a fusion process that yields helium nuclei. Eventually, the star runs out of hydrogen, and the helium core of the star begins to become denser. The condensation raises the temperature of the star to the point where helium begins to fuse into carbon. A helium nucleus has two protons. A carbon nucleus has six protons. Theoretically, three helium nuclei could fuse to form a carbon nucleus. But in practice this does not happen, because it is not very likely that three helium nuclei could collide at the same instant in just the way necessary to produce a carbon nucleus. Instead, there is a two step process. First two helium nuclei combine to form a beryllium nucleus, with four protons. Then a beryllium nucleus combines with another helium nucleus to form carbon. The problem is that the beryllium nuclei are unstable and rather quickly break back down into helium nuclei. Therefore, physicists would expect that very little carbon would be produced, certainly not the amounts of carbon present in the universe. But then the English astronomer Fred Hoyle showed that the carbon nucleus just happens to have a particular resonant energy level that lies just above the combined energy levels of beryllium and helium. The additional energy supplied to beryllium and helium by the heat of the solar core brings the beryllium and helium nuclei up to this level, enabling them to combine into carbon nuclei much more rapidly than might otherwise be expected. It is possible that all of the carbon produced in this way could have been immediately converted into oxygen, if the carbon nuclei combined with helium nuclei. But the oxygen nucleus has a resonant energy level that is below the combined energies of carbon and helium. This lucky circumstance means that the fusion reaction between carbon and helium becomes less likely. And therefore we have enough carbon for carbon-based life forms. Rees (2000, p. 50) noted: “This seeming ‘accident’ of nuclear physics allows carbon to be built up, but no similar effect enhances the next stage in the process, whereby carbon captures another helium nucleus and turns into oxygen. The crucial ‘resonance’ is very sensitive to the nuclear force. Even a shift by four per cent would severely deplete the amount of carbon that could be made. Hoyle therefore argued that our existence would have been jeopardized by even a few percentage points’ change in ε.” Commenting on the finely tuned resonances that enabled the production of heavy elements in the stellar interior, Hoyle said, “I do not believe that any scientist who examines the evidence would fail to draw the inference that the laws of physics have been deliberately designed with regard to the consequences they produce inside the stars” (Barrow and Tipler 1996, p. 22).
Ω (omega) and the Cosmic Balance of Forces