The evolution of very low-metallicity, massive stars depends critically on the amount of CNO nuclei that they produce. Alternative paths from the slow $3\alpha$ process to produce CNO seed nuclei could change their fate. The ${}^{11}\mathrm{C}(p,\gamma {)}^{12}\mathrm{N}$ reaction is an important branch point in one such alternative path. At energies appropriate to stellar evolution of very low-metallicity, massive stars, nonresonant capture dominates the reaction rate. We have determined the astrophysical S factor for $\mathrm{the}{\hspace{0.5em}}^{11}\mathrm{C}(p,\gamma {)}^{12}\mathrm{N}$ reaction using the asymptotic normalization coefficient for ${}^{12}{\overrightarrow{\mathrm{N}}}^{11}\mathrm{C}+p$ to fix the nonresonant capture rate. In our experiment, a 110 MeV ${}^{11}\mathrm{C}$ radioactive beam was used to study ${\mathrm{the}}^{14}\mathrm{N}{(}^{11}\mathrm{C}{,}^{12}\mathrm{N}{)}^{13}\mathrm{C}$ peripheral transfer reaction and the asymptotic normalization coefficient, ${(C}_{p_{\mathrm{eff}}}^{{}^{12}N}{)}^2{=(C}_{p_{1/2}}^{{}^{12}N}{)}^2{+(C}_{p_{3/2}}^{{}^{12}N}{)}^2=1.73\mathrm{}\pm 0.25{\mathrm{fm}}^{-1},$ was extracted from the measured cross section. The contributions from the second resonance and interference effects were estimated using an R-matrix approach with the measured asymptotic normalization coefficient and the latest value for ${\Gamma }_{\gamma }.$ We find the S factor for ${}^{11}\mathrm{C}(p,\gamma {)}^{12}\mathrm{N}$ is significantly larger than previous estimates. As a result, the required density for it to contribute is reduced, and more CNO material may be produced.

• Received 20 September 2002

DOI:https://doi.org/10.1103/PhysRevC.67.015804