Nuclear Fusion

Nuclear fusion exploits the OTHER, rising part of the binding-energy curve (Fig.15.6), on its light-nucleus side: light nuclei (with mass number below about A = 40) have a lower binding energy per nucleon than somewhat heavier nuclei. So if two light nuclei can be brought close enough together to combine into one heavier nucleus, the resulting nucleus is more tightly bound than the two original light nuclei were separately -- its mass is less than their combined original mass, with the difference (typically also of order MeV) released as energy. This combining process is called nuclear fusion.

For two nuclei to actually fuse, they must approach to within about 1 fm of each other -- close enough for the short-range nuclear force to take over from the electrostatic repulsion between their positive charges. This is genuinely difficult to achieve: ordinary neutral atoms are kept apart by the mutual electrostatic repulsion of their surrounding electron clouds long before their nuclei ever get close, so the electrons must first be stripped away entirely (by heating the material enough to exceed the atoms' ionization energies, producing a fully ionized plasma of bare nuclei). Even once bare, the resulting positively charged nuclei still strongly repel one another electrostatically, and overcoming that repulsion requires giving them very large kinetic energies -- equivalently, heating the plasma to an extremely high temperature. Because the electrostatic repulsion between two nuclei grows with their atomic numbers, the temperature required for fusion to occur increases as the atomic number of the fusing nuclei increases -- light-element fusion (like hydrogen fusing to helium) is comparatively 'easy', while fusing heavier elements demands far higher temperatures.

Inside the Sun's core, at a temperature of roughly $10^7$ K, the net nuclear reaction taking place is the fusion of four hydrogen nuclei (protons) into one helium nucleus: $4\,^1H\rightarrow\,^4He+2e^++2\nu+26.7$ MeV. Despite this simple-looking net equation, four protons essentially never collide simultaneously in a single event -- given the density and the strength of electrostatic repulsion even at solar-core conditions, this reaction actually proceeds through several distinct intermediate steps (the proton-proton chain), with the net effect summarised by the equation above. This fusion process has been powering the Sun continuously for roughly 4.5 billion years already, and is expected to continue for a comparably long time into the future; the same basic process, at even higher temperatures, powers other, hotter stars, which can go on to fuse progressively heavier nuclei.

Stellar fusion, however, has a hard upper limit: it can only build elements up to iron (A = 56), because iron sits exactly at the PEAK of the binding-energy curve (Fig.15.6) -- fusing an iron nucleus with anything else would produce a LESS tightly bound product, meaning the reaction would need to ABSORB energy rather than release it, so it simply does not happen spontaneously inside ordinary stars. Almost all elements heavier than boron, up through iron, that exist in the universe today were produced by fusion inside stars over cosmic history; elements heavier than iron are instead produced by entirely different nuclear processes occurring during violent stellar explosions (supernovae). The very lightest elements of all -- deuterium, helium, lithium, beryllium and boron -- were not made inside stars at all, but were instead created within the first roughly 200 seconds after the Big Bang itself, when the temperature of the infant universe was still high enough to sustain nuclear reactions; after about 200 seconds, the universe had cooled enough that further nuclear fusion became impossible, freezing the early cosmic abundances of these lightest elements in place. …