Nuclear statistical equilibrium

The most tightly bound nuclei, i.e. the most stable and robust, in the iron peak are not symmetric arrangements bringing together equal numbers of protons and neutrons (N = Z). Rather, they possess a neutron excess (N − Z) between 2 and 4. Close to iron, the most stable nucleus 56Fe has a number of neutrons which exceeds the number of protons by 4 units (N − Z = 4).

The isotopic and elemental abundance table shows that, in the Solar System, iron is more abundant than its neighbours. Analysis of stellar spectra confirms this result, giving it a universal character.

Theoretically, nuclear strength is enhanced by internal transmutations of protons into neutrons, under the mandate of the weak interaction, either by positron emission (p → n + e+ + ν) or by electron capture (p + e− → n + ν). However, the weak interaction is much slower than the strong interaction. The question remains as to whether it will happen inside the star, or outside, once the matter has been expelled, i.e. after the explosion. This is not just an academic question. The answer we give will determine whether or not we can corroborate explosive nucleosynthesis by observation.

Any attempt to understand the conditions in which iron and its kin were created, and identify the astrophysical site of their birth, must focus on the idea of nuclear statistical equilibrium. The situation is the exact nuclear analogy of the ionisation equilibrium occurring in hot gases.