Revision of the CNO cycle: Rate of 17O destruction in stars

The CNO cycle powers core H burning, in stars with 𝑀>1.2⁢𝑀⊙, and shell H burning, during the advanced evolutionary phases. Therefore, the uncertainties affecting the reaction rates of proton captures on C, N, and O isotopes limit our understanding of stellar evolution and nucleosynthesis. We aim to develop a general and self-consistent tool for the calculation of nuclear reaction rates and their uncertainties, starting from available experimental data. As a longer term plan, we intend to use this tool to revise the proton-capture reactions of the CNO cycle for which new experimental data are or will be available in the next future. The general procedure consists of 𝑅-matrix cross section calculations based on available measurements of the relevant nuclear parameters (energies, widths, strengths of known resonances, interference patterns, etc.), coupled to a Monte Carlo procedure to evaluate the global reaction rate error. A first application of this method to 17 O ⁡(𝑝,𝛾)⁢ 18 F and 17 O ⁡(𝑝,𝛼)⁢ 14 N , the reactions that determine the 17 O destruction in stellar interiors where the CNO cycle is active, is presented. These two reactions also allow us to test the multichannel and multilevel capabilities of the 𝑅-matrix method. In the temperature range of hydrostatic H burning (𝑇<100 MK), we confirm that the median rates are up to a factor of 2 higher than those suggested in reaction rate libraries commonly used in stellar model calculations. In this temperature range, the 17 O destruction mainly proceeds through the 17 O ⁡(𝑝,𝛼)⁢ 14 N channel, whose rate is known within ±20% (95% C.L.). Based on current stellar models of red giant stars, we show that this uncertainty produces a 10% variation on the predicted 16O / 17 O abundance ratio. Other uncertainties, such as those affecting the 17 O production rate, i.e., the 16O ⁡(𝑝,𝛾)⁢ 17 F reaction, have a stronger impact on this theoretical prediction, a fact that motivates further experimental investigations of the 17 O production channel.