Nucleosynthesis of Pop III and Fe-enriched Pop II Pair-Instability Supernovae

Recently discovered very metal-poor (VMP) star LAMOST J1010+2358 shows a peculiar abundance pattern that is remarkably well fit by a Pop III pair-instability supernova (PISN) of $\simeq 260$ M$_\odot$. Motivated by this, we investigate the nucleosynthetic characteristics of Pop III and Pop II PISNe to provide theoretical constraints for future observations. This paper is divided into two parts. First, we explore the evolution and nucleosynthesis of Pop III PISNe with initial masses of 130 - 300 M$_\odot$. Our main aim is to investigate how the uncertainty in $^{12}$C$(\alpha,\gamma)^{16}$O and $^{16}$O+$^{16}$O reaction rates affect their explosion properties and nucleosynthesis. We find that the yields of odd-$Z$ elements are particularly sensitive to the $^{12}$C$(\alpha,\gamma)^{16}$O rate, while the production of Fe-peak elements shows significant sensitivity to both rates. Second, we investigate the nucleosynthetic features of Pop II PISNe formed in gas enriched exclusively by Pop III PISN ejecta. By employing a time-dependent convection model during the explosion, we demonstrate that metal enrichment increases opacity and triggers vigorous convective mixing. This hydrodynamic effect significantly enhances the explosion energy and $^{56}\text{Ni}$ production. Consequently, Pop II PISNe exhibit distinct chemical signatures, including a weaker odd-even effect and enhanced Zn-Ge production, providing unique diagnostics for identifying PISN remnants in the early Universe.