Theoretical uncertainty of $(\alpha ,n)$ reactions relevant for the nucleosynthesis of light $r\text{-process}$ nuclei in neutrino-driven winds

Background: Neutrino-driven winds following core-collapse supernova explosions have been proposed as a possible site where light $r\text{-process}$ nuclei (between Fe and Ag) might be synthesized. In these events, $(\alpha ,n)$ reactions are key to moving matter towards the region of higher proton number. Abundance network calculations are very sensitive to the rates for this type of reactions.

Purpose: The present work aims at evaluating the theoretical uncertainty of these $(\alpha ,n)$ reactions calculated with reaction codes based on the Hauser-Feshbach model.

Method: We compared several $\left(\alpha ,n\right)$ rates taken from talys and the non-smoker database to determine the uncertainties owing to the existing technical differences between both codes. In addition, we evaluated the sensitivity of talys rates to variations in the $\alpha$ optical potentials, masses, level densities, optical potentials, preequilibrium intranuclear transition rates, level structure, radiative transmission coefficients, and width-fluctuation correction factors.

Results: The main source of uncertainty at low temperature is mostly attributable to the use of different $\alpha$ optical potentials. Differences between talys and non-smoker at high temperatures arise from the energy-binning algorithm used by each code. We have also noticed that the $\left(\alpha ,n\right)$ rates from the non-smoker database correspond to the inclusive reaction, instead of the exclusive $\left(\alpha ,1n\right)$ channel calculated in the present work and used in network calculations.

Conclusions: Theoretical uncertainties in calculated reaction rates can be as high as one to two orders of magnitude and strongly dependent on the temperature of the environment. Besides direct measurements of the inclusive and exclusive $(\alpha ,1n)$ reaction rates, experimental studies of $\alpha$ optical potentials are crucial to improve the performance of reaction codes.

Figure 1

Nuclear reaction rates (a) and ratio of theoretical-to-experimental rates (b) for the reaction ${}^{21}\text{Ne}(\alpha ,n){}^{24}\text{Mg}$ as a function of temperature. The black dashed lines delimit the experimental uncertainty. The calculated rates correspond to non-smoker (green dotted line), and talys using the default packet of nuclear inputs talys 1 (red solid line), and the packet talys 2 explained in Sec. 3b (blue solid-dotted line). Panels (c) and (d), same as (a) and (b) for the reaction ${}^{25}\text{Mg}(\alpha ,n){}^{28}\text{Si}$; panels (e) and (f), same as (a) and (b) for the reaction ${}^{41}\text{K}(\alpha ,n){}^{44}\text{Sb}$. The experimental rates for ${}^{21}\text{Ne}(\alpha ,n){}^{24}\text{Mg}$ and ${}^{25}\text{Mg}(\alpha ,n){}^{28}\text{Si}$ were taken from the NACRE database [54]. The rates for ${}^{41}\text{K}(\alpha ,n){}^{44}\text{Sb}$ were measured by Scott et al. [55] (note that these authors reported only the uncertainty of the cross sections, not the rates).

Figure 2

(a) talys and non-smoker nuclear rates for the reaction ${}^{86}\text{Se}(\alpha ,n){}^{89}\text{Kr}$. The talys rates were obtained using the packets talys 1 and talys 2 summarized in Table 2. (b) non-smoker and talys 2 rates normalized to the results from talys 1.

Figure 3

(a) Decompositions of the ${}^{86}\text{Se}(\alpha ,n)$ inclusive reaction rate from talys 1 (black solid line) into the main contributing channels ${}^{86}\text{Se}(\alpha ,\times n)$, where $\times =1$ (red solid line), $\times =2$ (red dashed line), $\times =3$ (red solid-dotted line), $\times =4$ (red thick dotted line), and $\times =5$ (red thin dotted line); the non-smoker rates are shown by the green dotted line. (b) Calculated ${}^{86}\text{Se}(\alpha ,n)$ inclusive rates normalized to talys 1 inclusive rates. Red thick solid line, inclusive $(\alpha ,n)$ from talys 1; blue thick solid-dotted line, inclusive $(\alpha ,n)$ from talys 2; green dotted line, $(\alpha ,n)$ from non-smoker.

Figure 4

(a) Decompositions of the ${}^{74}\text{Ga}(\alpha ,n)$ inclusive reaction rate from talys 1 (black solid line) into the main contributing channels ${}^{74}\text{Ga}(\alpha ,\times n)$, where $\times =1$ (red solid line), $\times =2$ (red dashed line), $\times =3$ (red solid-dotted line), $\times =4$ (red thick dotted line), and $\times =5$ (red thin dotted line); the non-smoker rates are shown by the green dotted line. (b) Calculated ${}^{74}\text{Ga}(\alpha ,n)$ inclusive rates normalized to talys 1 inclusive rates. Red thick solid line, inclusive $(\alpha ,n)$ from talys 1; blue thick solid-dotted line, inclusive $(\alpha ,n)$ from talys 2; green dotted line, $(\alpha ,n)$ from non-smoker.

Figure 5

(a) Calculated ${}^{86}\text{Se}(\alpha ,n)$ inclusive rates normalized to talys 1 inclusive rates. Red thick solid line, inclusive $(\alpha ,n)$ from talys 1; blue thick solid-dotted line, inclusive $(\alpha ,n)$ from talys 2; green dotted line, $(\alpha ,n)$ from non-smoker; light-blue thin solid line, inclusive $(\alpha ,n)$ from talys 1 using the equidistant energy binning; purple solid-dotted line, inclusive $(\alpha ,n)$ from talys 2 using the equidistant energy binning. (b) Same as (a) for the reaction ${}^{74}\text{Ga}(\alpha ,n)$. (See text for details.)

Figure 6

talys rates for ${}^{86}\text{Se}(\alpha ,n){}^{89}\text{Kr}$. The calculations were done using the nuclear models of packet talys 1 (Table 2) except for the nuclear input investigated [(a) $\alpha$ optical potentials, (b) masses, (c) level densities, (d) proton-neutron optical potentials, (e) preequilibrium, (f) level structure], which were determined from the models/options listed in Table 1 and the Appendix. All the rates are normalized to the values obtained using the packet talys 1 for all the nuclear inputs. The labels included in the legend are described in Table 1. (See text for details.)

Figure 7

talys rates for the reactions (a) ${}^{82}\text{Se}(\alpha ,n){}^{85}\text{Kr}$; (b) ${}^{83}\text{Se}(\alpha ,n){}^{86}\text{Kr}$; (c) ${}^{84}\text{Se}(\alpha ,n){}^{87}\text{Kr}$; and (d) ${}^{85}\text{Se}(\alpha ,n){}^{88}\text{Kr}$. The different lines shown in each figure were obtained using the list of AOP models listed in Table 1 and the packet talys 1 for the rest of the nuclear inputs. All the rates are normalized to the values obtained using the packet talys 1 for all the nuclear inputs. (See text for details.)