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Impact of Nuclear Reaction Rates on Calcium Production in Population III Stars: A Global Analysis

We investigate the sensitivity of calcium production to nuclear reaction rates of a 40 solar-mass Population III star using 1D multi-zone stellar models. A comprehensive nuclear reaction network was constructed, and all $(p,γ)$ and $(p,α)$ reaction rates were individually varied by a factor of 10 up and down, identifying 13 preliminary key reactions for calcium production. To propagate the reaction rate uncertainties on calcium production, two sets of Monte Carlo simulations were performed for these key reactions: one adopting STARLIB reaction rates and the other incorporating updated rates from recent experimental data and evaluations. Our results show that Monte Carlo simulations using the updated rates show good agreement with the observed calcium abundance of the extremely iron-poor star SMSS J031300.36-670839.3 within the 68% confidence interval predicted by the models. In contrast, the observed calcium abundance lies marginally outside the 68% C.I. when using the STARLIB rates. Spearman rank-order correlation analysis and SHAP values show that the $(p,γ)$ and $(p,α)$ reactions of F18 and F19 exhibit strong coupled effects on calcium production. These reaction-rate uncertainties need to be reduced to constrain the stellar model predictions. Our study provides insights for future nuclear physics experiments aimed at reducing reaction rate uncertainties in the nucleosynthesis of Population III Stars. Additionally, comparisons between 20 solar-mass and 40 solar-mass Population III stellar models confirm that the latter, with updated reaction rates, is more capable of reproducing the observed Ca abundance and [Ca/Mg] ratio.