Determination of the astrophysical<i>S</i>factor for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>11</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">C</mml:mi><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:math>from the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mover><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover><mml:mrow><mml:mn>11</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">C</mml:mi><mml:mo>+</mml:mo><mml:mi>p</mml:mi></mml:math>asymptotic normalization coefficient

The evolution of very low-metallicity, massive stars depends critically on the amount of CNO nuclei that they produce. Alternative paths from the slow $3\ensuremath{\alpha}$ process to produce CNO seed nuclei could change their fate. The ${}^{11}\mathrm{C}(p,\ensuremath{\gamma}{)}^{12}\mathrm{N}$ 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 $\mathrm{the}{ }^{11}\mathrm{C}(p,\ensuremath{\gamma}{)}^{12}\mathrm{N}$ reaction using the asymptotic normalization coefficient for ${}^{12}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{N}}}^{11}\mathrm{C}+p$ 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, ${(C}_{{p}_{\mathrm{eff}}}^{{}^{12}N}{)}^{2}{=(C}_{{p}_{1/2}}^{{}^{12}N}{)}^{2}{+(C}_{{p}_{3/2}}^{{}^{12}N}{)}^{2}=1.73\ifmmode\pm\else\textpm\fi{}0.25{\mathrm{fm}}^{\ensuremath{-}1},$ 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 ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}.$ We find the S factor for ${}^{11}\mathrm{C}(p,\ensuremath{\gamma}{)}^{12}\mathrm{N}$ 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.

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