The observation of secondary $\gamma$-rays provides an alternative method of measuring cross sections that populate excited final states in nuclear reactions. The angular distributions of these $\gamma$-rays also provide information on the underlying reaction mechanism. Despite the large number of data of this type in the literature, publicly available $R$-matrix codes do not have the ability to calculate these types of angular distributions. In this paper, the mathematical formalism derived by C. R. Brune and R. J. deBoer [Phys. Rev. C 102, 024628 (2020)] is implemented in the $R$-matrix code azure2 and calculations are compared with previous data from the literature for the ${}^{15}\mathrm{N}(p,{\alpha }_1\gamma ){}^{12}\mathrm{C}^{*}$ reaction. In addition, new measurements, made at the University of Notre Dame Nuclear Science Laboratory using the Hybrid Array of Gamma Ray Detectors (HAGRiD), are reported that span the energy range from $E_p=0.88$ MeV to $E_p=4.0\mathrm{MeV}$. Excellent agreement between the data and the phenomenological fit is obtained up to the limit of the previous fit at $E_p=2.0\mathrm{MeV}$ and the $R$-matrix fit is extended from $E_x\approx 13.5$ MeV up to $E_x\approx 15.3$ MeV, where ${}^{15}\mathrm{N}+p$ and ${}^{12}\mathrm{C}+\alpha$ reactions are fit simultaneously for the first time. An excellent reproduction of the ${}^{15}\mathrm{N}(p,{\alpha }_1\gamma ){}^{12}\mathrm{C}^{*}$ and ${}^{12}\mathrm{C}(\alpha ,\alpha ){}^{12}\mathrm{C}$ data is achieved, but inconsistencies and difficulty in fitting other data are encountered and discussed.

中文翻译：

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使用N15(p,α1γ)C*12反应研究二次γ射线角分布

二次观察 $\gamma$-rays 提供了另一种测量横截面的方法，这些横截面填充了核反应中的激发态终态。这些角分布$\gamma$-射线还提供有关潜在反应机制的信息。尽管文献中有大量此类数据，但公开可用$\mathrm{电阻}$-matrix 代码无法计算这些类型的角分布。在本文中，由 CR Brune 和 RJ deBoer 推导出的数学形式[ Phys. Rev. C 102 , 024628 (2020)] 在$\mathrm{电阻}$-matrix代码azure2和计算与来自文献的先前数据进行比较${}^{15}\mathrm{N}(磷,{\alpha }_1\gamma ){}^{12}\mathrm{C}^{*}$反应。此外，据报道，圣母大学核科学实验室使用混合伽马射线探测器阵列 (HAGRiD) 进行的新测量涵盖的能量范围从${乙}_{磷}=0.88$ 兆欧至 ${乙}_{磷}=4.0\mathrm{电动汽车}$. 获得了数据和现象学拟合之间的极好一致性，直至达到先前拟合的极限${乙}_{磷}=2.0\mathrm{电动汽车}$ 和 $\mathrm{电阻}$-矩阵拟合扩展自 ${乙}_X\approx 13.5$ 高达 ${乙}_X\approx 15.3$ MeV，其中 ${}^{15}\mathrm{N}+磷$ 和 ${}^{12}\mathrm{C}+\alpha$反应第一次同时拟合。完美再现${}^{15}\mathrm{N}(磷,{\alpha }_1\gamma ){}^{12}\mathrm{C}^{*}$ 和 ${}^{12}\mathrm{C}(\alpha ,\alpha ){}^{12}\mathrm{C}$ 获得了数据，但遇到并讨论了拟合其他数据的不一致和困难。