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

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 $10\%$.

12 pages, 6 figures, 3 tables, to be published in Phys. Rev. C

References in corpus (11)

• alpha-alpha Scattering in Halo Effective Field Theory
• LUNA: Status and Prospects
• Radiative Neutron Capture on Lithium-7
• The Future of Solar Neutrinos
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• Constraining the S factor of 15N(p,g)16O at Astrophysical Energies
• Constraining Low-Energy Proton Capture on Beryllium-7 through Charge Radius Measurements
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the bound states of ${}^{16}$O in effective field theory
• Narrow resonances and short-range interactions
• Study of the neutron and proton capture reactions 10,11b(n, g), 11b(p, g), 14c(p, g), and 15n(p, g) at thermal and astrophysical energies
• Combining Halo-EFT descriptions of nuclei and precise models of nuclear reactions

Cited by in corpus (2)

• The $S$ matrices of elastic $\alpha$-${}^{12}$C scattering at low energies in effective field theory
• Fixing effective range parameters in elastic $\alpha$-${}^{12}$C scattering: an impact on resonant $2_4^{+}$ state of ${}^{16}$O and $S_{E2}$ factor of ${}^{12}$C($\alpha$,$\gamma$)${}^{16}$O