Nuclear statistical equilibrium (NSE)

At sufficiently high temperature and density, forward and inverse nuclear reactions can balance so that abundances are determined by thermodynamic conditions, nuclear binding and conserved quantities. Silicon burning approaches such an equilibrium among iron-group nuclei. Weak reactions can separately change the electron fraction, so the favored mixture need not be pure iron.

Nickel-56 and iron-54 have the same neutron number and differ by two protons. Dividing their nuclear statistical equilibrium abundance formulas cancels the neutron density and leaves the displayed ratio, with $\Delta B=B_{56}-B_{54}$ and $K$ containing temperature-independent statistical and mass factors in the simplified model. For material with equal total proton and neutron numbers and only these nuclei plus free protons, charge balance gives $n_p=2n_{54}$. Thus $n_{56}/n_{54}^3\propto T^{-3}{e}^{\Delta B/(kT)}$. This has a finite temperature maximum only if the signed energy difference is negative; conventional positive total nuclear binding energies for these two actual isotopes instead give a positive difference.

For electrically neutral fully ionized matter, $Y_e$ is the number of electrons, or total protons, per baryon. With isotope mass fractions $X_i$, charge numbers $Z_i$ and mass numbers $A_i$, the displayed sum neglects small nuclear mass-defect corrections. Strong and electromagnetic reactions preserve it, while electron capture and beta-plus decay reduce it. The proton-to-neutron number ratio is $Y_e/(1-Y_e)$.

The neutron excess is the number of neutrons minus protons per baryon. A mixture of carbon-12 and oxygen-16 has zero neutron excess, while neon-22 contributes $2/22$ per baryon in that isotope. Thus a neon-22 mass fraction $X_{22}$ gives $\eta =X_{22}/11$. A nonzero excess shifts iron-group ashes from symmetric nickel-56 toward neutron-rich isotopes, even before additional weak reactions occur.