SystematicR-matrix analysis of theC13(p,γ)N14capture reaction

Abstract

Background: The proton capture reaction $^{13}\mathrm{C}(p,\ensuremath{\gamma})^{14}\mathrm{N}$ is an important reaction in the CNO cycle during hydrogen burning in stars with mass greater than the mass of the Sun. It also occurs in astrophysical sites such as red giant stars: the asymptotic giant branch (AGB) stars. The low energy astrophysical $S$ factor of this reaction is dominated by a resonance state at an excitation energy of around 8.06 MeV $({J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}},T=1)$ in $^{14}\mathrm{N}$. The other significant contributions come from the low energy tail of the broad resonance with ${J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}},T=1$ at an excitation of 8.78 MeV and the direct capture process.Purpose: Measurements of the low energy astrophysical $S$ factor of the radiative capture reaction $^{13}\mathrm{C}(p,\ensuremath{\gamma})^{14}\mathrm{N}$ reported extrapolated values of $S(0)$ that differ by about $30%$. Subsequent $R$-matrix analysis and potential model calculations also yielded significantly different values for $S(0)$. The present work intends to look into the discrepancy through a detailed $R$-matrix analysis with emphasis on the associated uncertainties.Method: A systematic reanalysis of the available decay data following the capture to the ${J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}},T=1$ resonance state of $^{14}\mathrm{N}$ around 8.06 MeV excitation had been performed within the framework of the $R$-matrix method. A simultaneous analysis of the $^{13}\mathrm{C}(p,{p}_{0})$ data, measured over a similar energy range, was carried out with the capture data. The data for the ground state decay of the broad resonance state $({J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}},T=1)$ around 8.78 MeV excitations was included as well. The external capture model along with the background poles to simulate the internal capture contribution were used to estimate the direct capture contribution. The asymptotic normalization constants (ANCs) for all states were extracted from the capture data. The multichannel, multilevel $R$-matrix code azure2 was used for the calculation.Results: The values of the astrophysical $S$ factor at zero relative energy, resulting from the present analysis, are found to be consistent within the error bars for the two sets of capture data used. However, it is found from the fits to the elastic scattering data that the position of the ${J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}},T=1$ resonance state is uncertain by about 0.6 keV, preferring an excitation energy value of 8.062 MeV. Also the extracted ANC values for the states of $^{14}\mathrm{N}$ corroborate the values from the transfer reaction studies. The reaction rates from the present calculation are about $10--15%$ lower than the values of the NACRE II compilation but compare well with those from NACRE I.Conclusion: The precise energy of the ${J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}},T=1$ resonance level around 8.06 MeV in $^{14}\mathrm{N}$ must be determined. Further measurements around and below 100 keV with precision are necessary to reduce the uncertainty in the $S$-factor value at zero relative energy.