Investigation of secondary γ -ray angular distributions using the N 15 ( p , α 1 γ ) C * 12 reaction

The observation of secondary $\ensuremath{\gamma}$-rays provides an alternative method of measuring cross sections that populate excited final states in nuclear reactions. The angular distributions of these $\ensuremath{\gamma}$-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 $^{15}\mathrm{N}(p,{\ensuremath{\alpha}}_{1}\ensuremath{\gamma})^{12}\mathrm{C}^{*}$ 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 ${E}_{p}=4.0\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. Excellent agreement between the data and the phenomenological fit is obtained up to the limit of the previous fit at ${E}_{p}=2.0\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and the $R$-matrix fit is extended from ${E}_{x}\ensuremath{\approx}13.5$ MeV up to ${E}_{x}\ensuremath{\approx}15.3$ MeV, where $^{15}\mathrm{N}+p$ and $^{12}\mathrm{C}+\ensuremath{\alpha}$ reactions are fit simultaneously for the first time. An excellent reproduction of the $^{15}\mathrm{N}(p,{\ensuremath{\alpha}}_{1}\ensuremath{\gamma})^{12}\mathrm{C}^{*}$ and $^{12}\mathrm{C}(\ensuremath{\alpha},\ensuremath{\alpha})^{12}\mathrm{C}$ data is achieved, but inconsistencies and difficulty in fitting other data are encountered and discussed.