Proton Rich Nuclear Statistical Equilibrium

Abstract

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 56 Ni 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.10th Symposium on Nuclei in the Cosmos

r-Java: anr-process code and graphical user interface for heavy-element nucleosynthesis

“…3. Comparing the former to the results of Clifford & Tayler 1965, and the latter with Figure 3 of Seitenzahl et al 2008, we find very good agreement with these established results. In Fig.…”

“…However, we should caution that the success of the Newton-Raphson method depends sensitively on a proper choice for the initial value of µ p , µ n and the starting composition. We chose to use the NSE calculations of Seitenzahl et al 2008 as a test of our code. We have plotted our NSE results in Fig.…”

NSE abundance data

“…Therefore we have made some tests to verify results and accuracy estimates. Despite known physical issues (temperature-dependent partition function, Coulomb corrections [13], screening [7]) one of the most important factors is number and selection of species included in equations (1). Even a single one important nuclei missing in NSE ensemble may lead to radically different results.…”

“…(1a, 1b) has been solved numerically using MATHEMATICA code. 3 Integrated MATHEMATICA [6] database has been [16,8,13] with good agreement.…”

Ti44 and Ni56 in core-collapse supernovae

“…For Y e < 0.5 the major flows proceed towards more neutron rich, heavier nuclei and 56 Ni does not dominate the final composition. For Y e > 0.5, instead of being dominated by the Fe-peak nuclei with the largest binding energy per nucleon that have a proton to nucleon ratio close to the prescribed electron fraction, proton-rich material minimizes its Helmholtz free energy by being mainly composed of 56 Ni and free protons [7]. Fig.…”