Secondary $\gamma$-ray decays from the partial-wave $T$ matrix with an $R$-matrix application to ${}^{15}\mathrm{N}(p,{\alpha }_1\gamma ){}^{12}\mathrm{C}$

The secondary $\gamma$ rays emitted following a nuclear reaction are often relatively straightforward to detect experimentally. Despite the large volume of such data, a practical formalism for describing these $\gamma$ rays in terms of partial-wave $T$-matrix elements has never been given. The partial-wave formalism is applicable when $R$-matrix methods are used to describe the reaction in question. This paper supplies the needed framework, and it is demonstrated by the application to the ${}^{15}\mathrm{N}(p,{\alpha }_1\gamma ){}^{12}\mathrm{C}$ reaction.

Figure 1

The total cross section and $\gamma$-ray angular distribution coefficients for the ${}^{15}\mathrm{N}(p,{\alpha }_1\gamma ){}^{12}\mathrm{C}^{*}$ reaction. The experimental results of Bray et al. [6] are shown as points. Calculations using the Bray et al. [6] and deBoer et al. [24] $R$-matrix parameters are shown as the solid red and dashed blue curves, respectively.