New measurements of the 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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msup><mml:mi mathvariant="normal">C</mml:mi><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:msup><mml:mi/><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msup><mml:mi mathvariant="normal">N</mml:mi></mml:mrow></mml:math>reaction at low energies and the asymptotic normalization coefficient (nuclear vertex constant) for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:msup><mml:mi/><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mrow/><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msup><mml:mi mathvariant="normal">N</mml:mi></mml:mrow></mml:math>reaction
Abstract
New measurements of differential and total cross sections for the ${}^{12}\mathrm{C}(p,\ensuremath{\gamma}){}^{13}\mathrm{N}$ reaction have been made at beam energies of ${E}_{p}=354,390,460,463,565,750$, and 1061 keV. Analysis of the astrophysical $S$ factor $S(E)$ for the ${}^{12}\mathrm{C}(p,\ensuremath{\gamma}){}^{13}\mathrm{N}$ reaction at low energies and of the reaction rates has been carried out within the R-matrix approach by using the previously measured nuclear vertex constant (or the respective asymptotic normalization coefficient) for the virtual decay ${}^{13}\mathrm{N}\ensuremath{\rightarrow}p+{}^{12}\mathrm{C}$ to fix the direct capture part of the amplitude in $S(E)$. It is demonstrated that the R-matrix approach, using the measured asymptotic normalization coefficient, can be employed as an ideal tool, minimizing the uncertainties associated with a calculation of the direct capture cross section of the ${}^{12}\mathrm{C}(p,\ensuremath{\gamma}){}^{13}\mathrm{N}$ reaction at extremely low energies. New information on the proton and $\ensuremath{\gamma}$ width for the first excited state of $^{13}\mathrm{N}$ is obtained.