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.

• Received 12 June 2020
• Revised 11 May 2021
• Accepted 1 June 2021

DOI:https://doi.org/10.1103/PhysRevC.103.065801