The Big Bang light-element network

At high temperature, neutron–proton weak interconversion can be rapid enough to track an equilibrium ratio related to their mass-energy difference. The simplest expression assumes small relevant chemical potentials and thermal particle distributions. As expansion and cooling reduce weak rates, the ratio departs gradually from equilibrium. The often used instantaneous freezeout estimate is a simplifying approximation to this evolving kinetic competition; it does not mean every weak event suddenly ceases at one exact temperature.

After weak interconversion becomes ineffective, free-neutron decay continues while the universe cools toward efficient nuclear assembly. Each neutron that decays becomes a proton while emitting leptons, conserving total baryon number. Thus both the numerator and denominator of the neutron-to-proton ratio change. Multiplying the ratio alone by a survival factor neglects the accompanying growth of the proton population. This can be acceptable in a stated approximation when the neutron fraction is small, but exact finite-inventory bookkeeping is straightforward and safer for the exercise.

A neutron and a proton can form deuterium by radiative capture, but abundant photons can break it apart. The baryon-to-photon ratio is small, so even an exponentially rare energetic photon population can remain numerous compared with the nuclei being assembled. The deuterium bottleneck therefore persists until temperature is well below the deuterium binding-energy scale. A logarithmic tail estimate makes this qualitative point but does not supply the exact reaction-rate crossing or the full abundance history.

Once deuterium survives sufficiently, captures and rearrangements build helium three, tritium, and helium four. Most surviving neutrons can become locked into tightly bound helium four under the standard light-network conditions. Residual deuterium and helium three depend on incomplete burning as expansion dilutes the plasma. The absence of stable mass-five and mass-eight stepping stones, together with the short declining-density interval, suppresses sustained assembly of much heavier nuclei; the dense, long-lived helium-burning route of a star is unavailable here.

If all surviving neutrons enter helium four and other bound products are neglected, each alpha requires two neutrons and two protons. Dividing the baryons in helium by the conserved total gives a simple approximate helium mass fraction. The approximation uses mass numbers rather than exact nuclear masses and assumes enough protons remain. It explains why neutron survival strongly affects helium, while it cannot predict residual deuterium or lithium from one scalar ratio alone.

A precision network must evolve nuclear and weak rates, expansion, thermodynamic distributions, and the baryon density consistently. Observations require additional astrophysical interpretation because later stellar processing can destroy or produce light isotopes. Discrepancies in an isotope such as lithium should therefore be framed as a comparison between specified calculations and inferred primordial abundances, with their uncertainties; the hand-counting model below cannot diagnose a unique explanation. Its purpose is to expose conservation and timing before those more detailed comparisons are attempted.