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

Abstract

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.

7 pages, 1 figure