The $^{15}{rm N}(p,gamma)^{16}{rm O}$ 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 $^{15}{rm N}(p,gamma)^{16}{rm O}$ 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 $33.1 leq S(0) leq 40.1$ 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.
The 18O(p,alpha)15N reaction rate has been extracted by means of the Trojan-Horse method. For the first time the contribution of the 20-keV peak has been directly evaluated, giving a value about 35% larger than previously estimated. The present appro
ach has allowed to improve the accuracy of a factor 8.5, as it is based on the measured strength instead of educated guesses or spectroscopic measurements. The contribution of the 90-keV resonance has been determined as well, which turned out to be of negligible importance to astrophysics.
The $^{18}{rm O}(p,alpha)^{15}{rm N}$ reaction is of primary importance in several astrophysical scenarios, including fluorine nucleosynthesis inside AGB stars as well as oxygen and nitrogen isotopic ratios in meteorite grains. Thus the indirect meas
urement of the low energy region of the $^{18}{rm O}(p,alpha)^{15}{rm N}$ reaction has been performed to reduce the nuclear uncertainty on theoretical predictions. In particular the strength of the 20 and 90 keV resonances have been deduced and the change in the reaction rate evaluated.
