Within the framework of the modified potential cluster model with forbidden states, the $^{13}$N($p,γ$)$^{14}$O reaction rate and the astrophysical $S$-factor are considered. It is shown that the first $p^{13}$% N resonance determines the $S$-factor and contributions of the $M1$ and $E2$ transitions are negligible at energies $E<1$ MeV, but are significant at high energies. The $S$-factor strongly depends on the $^{3}S_{1}$ resonance parameters. The influence of the width of \ the $^{3}S_{1}$ resonance on $S$% -factor is demonstrated. The reaction rate is calculated and an analytical approximation for the reaction rate is proposed. A comparison of our calculation with existing data is addressed. Results of our calculations for the $^{13}$N($p,γ)^{14}$O reaction rate provide the contribution to the steadily improving reaction rate database libraries. Our calculations of the $% ^{13}$N($p,γ)^{14}$O reaction rate along with results for the rates of $^{14}$N($% p,γ)^{15}$O and $^{12}$C$(p,γ)^{13}$N processes provide the temperature range $0.13<T_{9}<0.97$ for the conversion of CNO cycle to the HCNO cycle. Our results demonstrate that at early stages of a nova explosion at temperatures about $0.1$ $T_{9}$ and at late stages of evolution of supermassive stars at temperatures about $1.0$ $T_{9}$ the ignition of the HCNO cycle could occur at much lower densities of a stellar medium.
$^{14}$N(p,$γ)^{15}$O $S$ factor and the puzzling solar composition problem
School of Science, Huzhou University（湖州学院理学院）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；Grand Accélérateur National d’Ions Lourds (GANIL), CEA/DSM - CNRS/IN2P3（法国国家重离子加速器（GANIL））
Examination and experimental constraints of the stellar reaction rate factor $N_A < σv >$ of the $^{18}$Ne($α$,$p$)$^{21}$Na reaction at temperatures of X-Ray Bursts
Astrophysical $S$ factor for the ${}^{15}{\rm N}(p,γ){}^{16}{\rm O}$ reaction from $R$-matrix analysis and asymptotic normalization coefficient for ${}^{16}{\rm O} \to {}^{15}{\rm N} + p$. Is any fit acceptable?
$^{15}{\rm N}(p,γ)^{16}{\rm O}$反应提供了从CN循环到CNO双环和CNO三环的路径。测量的天体物理因素，这个反应是占主导地位的共振捕获通过两个强$J^π=1^{-}$共振在$E_{R}= 312$和962千电子伏和直接捕获到基态。最近，已经公布了$^{15}{\rm N}(p,γ)^{16}{\rm O}$反应的天体物理因子的新测量[P. J. LeBlanc { \it et al.}，{ \bf C 82}，055804（2010）]。分析已完成使用$R$ -矩阵的方法与无约束的变化的所有参数，包括渐近归一化系数（ANC）。已获得ANC $C^{2}= 539.2$ fm ${}^{-1}$的平方的最佳拟合，其超过先前测量值的因子$\approx 3$。在这里，我们提出了一个新的$R$ -矩阵分析的圣母院-月球数据与固定的实验不确定性平方内的ANC $C^{2}=200.34$ FM ${}^{-1}$。我们不是改变ANC，而是添加来自背景共振的贡献，该背景共振有效地考虑了来自更高水平的贡献。我们总共提出了8个配合，五个无约束和三个约束。在所有拟合中，ANC固定在先前确定的实验值$C^{2}=200.34$ fm ${}^{-1}$。对于具有边界条件$B_{c}=S_{c}(E_{2})$的无约束拟合，其中$E_{2}$是第二能级的能量，我们得到$…
