New astrophysical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>factor for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">N</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>15</mml:mn></mml:mrow></mml:mmultiscripts></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">O</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>16</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>reaction via the asymptotic normalization coefficient (ANC) method

The ${}^{15}\mathrm{N}(p,\ensuremath{\gamma}){}^{16}\mathrm{O}$ reaction provides a path from the CN cycle to the CNO bi-cycle and CNO tri-cycle. The measured astrophysical factor for this reaction is dominated by resonant capture through two strong ${J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}$ resonances at ${E}_{R}=312$ and 962 keV and direct capture to the ground state. Asymptotic normalization coefficients (ANCs) for the ground and seven excited states in $^{16}\mathrm{O}$ were extracted from the comparison of experimental differential cross sections for the $^{15}\mathrm{N}$($^{3}\mathrm{He}$,$d)$$^{16}\mathrm{O}$ reaction with distorted-wave Born approximation calculations. Using these ANCs and proton and \ensuremath{\alpha} resonance widths determined from an $R$-matrix fit to the data from the ${}^{15}\mathrm{N}(p,\ensuremath{\alpha}){}^{12}\mathrm{C}$ reaction, we carried out an $R$-matrix calculation to obtain the astrophysical factor for the ${}^{15}\mathrm{N}(p,\ensuremath{\gamma}){}^{16}\mathrm{O}$ reaction. The results indicate that the direct capture contribution was previously overestimated. We find the astrophysical factor to be $S(0)=36.0\ifmmode\pm\else\textpm\fi{}6.0$ keV b, which is about a factor of 2 lower than the presently accepted value. We conclude that for every $2200\ifmmode\pm\else\textpm\fi{}300$ cycles of the main CN cycle one CN catalyst is lost due to this reaction.

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