Astrophysical $S$ factor for the ${}^{15}\mathrm{N}(p,\gamma ){}^{16}\mathrm{O}$ reaction from $R$-matrix analysis and asymptotic normalization coefficient for ${}^{16}\mathrm{O}\to {}^{15}\mathrm{N}+p$. Is any fit acceptable?

Abstract

The ${}^{15}\mathrm{N}(p,\gamma {)}^{16}\mathrm{O}$ reaction provides a path from the CN cycle to the CNO bi-cycle and CNO tri-cycle. The measured astrophysical factor for this reaction is dominated by resonant capture through two strong $J^{\pi }=1^{-}$ resonances at $E_R=312$ and 962 keV and direct capture to the ground state. Recently, a new measurement of the astrophysical factor for the ${}^{15}\mathrm{N}(p,\gamma {)}^{16}\mathrm{O}$ reaction has been published [P. J. LeBlanc {\it et al.}, Phys. Rev. {\bf C 82}, 055804 (2010)]. The analysis has been done using the $R$-matrix approach with unconstrained variation of all parameters including the asymptotic normalization coefficient (ANC). The best fit has been obtained for the square of the ANC $C^2=539.2$ fm${}^{-1}$, which exceeds the previously measured value by a factor of $\approx 3$. Here we present a new $R$-matrix analysis of the Notre Dame-LUNA data with the fixed within the experimental uncertainties square of the ANC $C^2=200.34$ fm${}^{-1}$. Rather than varying the ANC we add the contribution from a background resonance that effectively takes into account contributions from higher levels. Altogether we present 8 fits, five unconstrained and three constrained. In all the fits the ANC is fixed at the previously determined experimental value $C^2=200.34$ fm${}^{-1}$. For the unconstrained fit with the boundary condition $B_c=S_c(E_2)$, where $E_2$ is the energy of the second level, we get $S(0)=39.0\pm 1.1$ keVb and normalized ${\tilde{\chi }}^2=1.84$, i.e. the result which is similar to [P. J. LeBlanc {\it et al.}, Phys. Rev. {\bf C 82}, 055804 (2010)]. From all our fits we get the range $33.1\le S(0)\le 40.1$ keVb which overlaps with the result of [P. J. LeBlanc {\it et al.}, Phys. Rev. {\bf C 82}, 055804 (2010)]. We address also physical interpretation of the fitting parameters.

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References in corpus (5)

• Direct measurement of the 15N(p,gamma)16O total cross section at novae energies
• Constraining the S factor of 15N(p,g)16O at Astrophysical Energies
• Unitary correlation in nuclear reaction theory
• Astrophysical S factor for the radiative capture 12N(p,gamma)13O determined from the 14N(12N,13O)13C proton transfer reaction
• Computation of spectroscopic factors with the coupled-cluster method

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