Proton rich nuclear statistical equilibrium

Proton-rich material in a state of nuclear statistical equilibrium (NSE) is one of the least studied regimes of nucleosynthesis. One reason for this is that after hydrogen burning, stellar evolution proceeds at conditions of equal number of neutrons and protons or at a slight degree of neutron richness. Proton-rich nucleosynthesis in stars tends to occur only when hydrogen-rich material that accretes onto a white dwarf of neutron star explodes, or when neutrino interactions in the winds from a nascent proto-neutron star or collapsar-disk drive the matter proton rich prior to or during the nucleosynthesis. In this paper we solve the NSE equations for a range of proton-rich thermodynamic conditions. We show that cold proton-rich NSE is qualitatively different from neutron-rich NSE. Instead of being dominated by the iron-peak nuclei with the largest binding energy per nucleon that have a proton to nucleon ratio close to the prescribed electron fraction, NSE for proton-rich material near freeze-out temperature is mainly composed of ⁵⁶Ni and free protons. Previous results of nuclear reaction network calculations rely on this non-intuitive fact, which this paper will explain. We show how the differences and especially the large fraction of free protons arises as a direct result from the minimization of the Helmholtz free energy.