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

Abstract

The astrophysical 𝑆 factor for the radiative proton capture process on the N 15 nucleus, i.e., N 15 ( 𝑝, 𝛾) O 16 , at stellar energies are studied within the framework of the cluster effective field theory. The thermonuclear N 15 ( 𝑝, 𝛾) O 16 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 O 16 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 keV < 𝐸 𝑝 < 2500 keV using three different experimental data sets. Considering the recent data sets, we obtain 𝑆(0) = 29.8-34.1 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%.

The $S$ matrices of elastic $α$-$^{12}$C scattering at low energies in effective field theory

“…As mentioned in the introduction, we employed the EFT to the study of the E1 transition of the 12 C(α,γ) 16 O reaction [26] and the β-delayed α-emission from 16 N [7]. Recently, we reported the first application of EFT to the study of the radiative proton capture on 15 N [43,44], which is an important reaction in the CNO cycle. Thus, to construct an EFT would be another theoretical method, as an alternative to the R-matrix analysis, for the studies of nuclear reactions for stellar evolution.…”