Evaluation of the N13(α,p)O16 thermonuclear reaction rate and its impact on the isotopic composition of supernova grains

Background: It has been recently suggested that hydrogen ingestion into the helium shell of massive stars could lead to high $^{13}\mathrm{C}$ and $^{15}\mathrm{N}$ excesses when the shock of a core-collapse supernova passes through its helium shell. This prediction questions the origin of extremely high $^{13}\mathrm{C}$ and $^{15}\mathrm{N}$ abundances observed in rare presolar SiC grains which is usually attributed to classical novae. In this context the $^{13}\mathrm{N}(\ensuremath{\alpha},p)^{16}\mathrm{O}$ reaction plays an important role since it is in competition with $^{13}\mathrm{N}\phantom{\rule{4pt}{0ex}}{\ensuremath{\beta}}^{+}$ decay to $^{13}\mathrm{C}$.Purpose: The $^{13}\mathrm{N}(\ensuremath{\alpha},p)^{16}\mathrm{O}$ reaction rate used in stellar evolution calculations comes from the Caughlan and Fowler compilation with very scarce information on the origin of this rate and with no associated uncertainty. The goal of this work is to provide a recommended $^{13}\mathrm{N}(\ensuremath{\alpha},p)^{16}\mathrm{O}$ reaction rate, based on available experimental data, with a meaningful statistical uncertainty.Method: Unbound nuclear states in the $^{17}\mathrm{F}$ compound nucleus were studied using the spectroscopic information of the analog states in $^{17}\mathrm{O}$ nucleus that were measured at the Tandem-Alto facility using the $^{13}\mathrm{C}(^{7}\mathrm{Li},t)^{17}\mathrm{O}$ $\ensuremath{\alpha}$-particle-transfer reaction. The $\ensuremath{\alpha}$-particle spectroscopic factors were derived using a finite-range distorted-wave Born approximation analysis. This spectroscopic information was used to calculate a recommended $^{13}\mathrm{N}(\ensuremath{\alpha},p)^{16}\mathrm{O}$ reaction rate with meaningful uncertainty using a Monte Carlo approach.Results: The $^{13}\mathrm{N}(\ensuremath{\alpha},p)^{16}\mathrm{O}$ reaction rate from the present work is found to be within a factor of two of the previous evaluation in the temperature range of interest, with a typical uncertainty of a factor $\ensuremath{\approx}2--3$. The source of this uncertainty has been identified to come from the three main contributing resonances at ${E}_{r}^{\mathrm{c}.\mathrm{m}.}=221$, 741, and 959 keV. This new error estimation translates to an overall uncertainty in the $^{13}\mathrm{C}$ production of a factor of 50 when using the lower and upper reaction rates in the conditions relevant for the $^{13}\mathrm{N}(\ensuremath{\alpha},p)^{16}\mathrm{O}$ activation.Conclusions: The main source of uncertainty on the re-evaluated $^{13}\mathrm{N}(\ensuremath{\alpha},p)^{16}\mathrm{O}$ reaction rate currently comes from the uncertain $\ensuremath{\alpha}$-particle width of relevant $^{17}\mathrm{F}$ states.