Bound-to-continuum potential model for the $(p,\gamma )$ reactions of the CNO cycle

Abstract

The study of CNO cycle involves the examination of the proton radiative capture, or the $(p,\gamma )$ reactions below 2 MeV. The astrophysical $\mathcal{S}$ factor characterizing the $(p,\gamma )$ reaction is usually reduced to the electric dipole transition $E1$ from the scattering state to the bound state. In this work, the partial scattering and the single-particle bound wave functions in the reduced matrix element of the transition are obtained from the single self-consistent mean-field potential deduced from the Skyrme Hartree-Fock calculation. The astrophysical $\mathcal{S}$ factors of the $(p,\gamma )$ reactions in the CNO cycle were successfully reproduced. The self-consistent Hartree-Fock calculation from the discrete to the continuum is a promising approach for the microscopic analysis of the nucleon-induced reactions in nuclear astrophysics.

arXiv comment16 pages, 7 figures, submitted to Physical Review C, revised version with suggestions of referee taken into account

References in corpus (7)

• NACRE II: an update of the NACRE compilation of charged-particle-induced thermonuclear reaction rates for nuclei with mass number $A<16$
• Radiative capture of nucleons at astrophysical energies with single-particle states
• New reaction rate for 16O(p,gamma)17F and its influence on the oxygen isotopic ratios in massive AGB stars
• Microscopic positive-energy potential based on Gogny interaction
• Effects of nonlocality of nuclear potentials on direct capture reactions
• Low lying excited states of ${}^{24}$O investigated by self-consistent microscopic description of proton inelastic scattering
• Folding model approach to the elastic $p{+}^{12,13}$C scattering at low energies and radiative capture ${}^{12,13}$C$(p,\gamma )$ reactions

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• Potential model with bound-to-continuum approach for low-energy nucleon radiative capture by ${}^{12}$C and ${}^{16}$O
• Proton \textit{s}-resonance states of ${}^{12}$C and ${}^{14,15}$O within the Skyrme Hartree-Fock mean-field framework