Radiative proton capture on $^{15}\mathrm{N}$ within effective field theory

TL;DR

This paper models the astrophysical $S$ factor for the $^{15}\mathrm{N}(p, \gamma)^{16}\mathrm{O}$ reaction at stellar energies using effective field theory, including resonances, and fits experimental data to predict reaction rates relevant to stellar nucleosynthesis.

Contribution

The study develops an effective field theory framework for the reaction, incorporating resonances and fitting to experimental data, providing a new approach to calculate the astrophysical $S$ factor.

Findings

Calculated $S(0)$ between 29.8 and 34.1 keV·b.

Found $S$ at Gamow energy exceeds $S(0)$ by about 10%.

Results agree with $R$-matrix estimates in literature.

Abstract

The astrophysical $S$ factor for the radiative proton capture process on the $^{15}\mathrm{N}$ nucleus, i.e., $^{15}\mathrm{N}(p, \gamma)^{16}\mathrm{O}$, at stellar energies are studied within the framework of the cluster effective field theory. The thermonuclear $^{15}\mathrm{N}(p, \gamma)^{16}\mathrm{O}$ reaction links the type-I to type-II cycles of the carbon-nitrogen-oxygen cycle and affects the abundances of elements in the univere. For investigating this reaction in the effective field theory formalism, we first construct an effective Lagrangian that is appropriate for this reaction at low-energies. Since the intermediate excited states of the $^{16}\mathrm{O}$ nucleus have a crucial role in this reaction, we include these resonances in the formalism. The corresponding radiative capture amplitudes and cross section are calculated, which lead to the astrophysical $S$ factor. The low energy constants introduced in the effective Lagrangian are determined by fitting the theoretical results to the observed $S$ factors in the range of $130~\mathrm{keV} < E_p < 2500~\mathrm{keV}$ using three different experimental data sets. Considering the recent data sets, we obtain $S(0) = 29.8\mbox{-}34.1~\mathrm{keV\ b}$, which is in a good agreement with the estimates from $R$-matrix approaches in the literature. The values of $S$ at the Gamow energy are found to be larger than $S(0)$ values by about $10\%$.