Gravitational-wave observations have renewed interest in the black-hole mass gap and in the maximum mass of first-generation black holes below its lower edge. The ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction plays a central role in this problem because it determines the carbon-to-oxygen ratio after core-helium burning and thereby affects the later evolution of massive stars toward pulsational pair instability and pair-instability supernovae. Recent attempts to constrain $S\left(300\mathrm{keV}\right)$ from gravitational-wave population inferences face important limitations, because the lower edge of the black-hole mass gap is not directly measured. It is inferred model dependently from assumptions about stellar evolution, metallicity, mass loss, rotation, binary evolution, hierarchical mergers, selection effects, priors, and the adopted population model. Therefore, values of $S\left(300\mathrm{keV}\right)$ inferred from black-hole populations must remain consistent with independent nuclear-physics constraints. In this work the low-energy ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O} S$ factor is reanalyzed using updated information on the subthreshold $1^{-}$ and $2^{+}$ asymptotic normalization coefficients (ANCs) and on the ground-state ANC of ${}^{16}\mathrm{O}$, together with direct capture data. These constraints favor a lower $S\left(300\mathrm{keV}\right)$ than the older central evaluation and disfavor very large values required by some black-hole-population interpretations. Combining the resulting ANC-constrained $S\left(300\mathrm{keV}\right)$ range with the transformed relation between this quantity and the lower edge of the pair-instability mass gap gives $\frac{M_{\mathrm{BH}}}{M_{\odot }}\simeq 61-75$. Thus, the present nuclear-physics constraints favor a relatively high lower edge of the first-generation black-hole mass gap.

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• Nuclear astrophysics
• Nuclear reactions
• Radiative capture
• S-factor
• 6 ≤ A ≤ 19
• Monte Carlo methods
• Nuclear data analysis & compilation